Department of Economics Faculty of Economics and Management doc. Ing. Iveta Zentková, PhD. 07 / 2006

Microeconomics Essays by Alexander Frech Felix Hötzinger Olaf Löbl Eckart Margenfeld Michael Mirz Serge Schäfers

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Content

I. Classical and intertemporal models of consumer behaviour 3 II. Choice under uncertainty 11 III. Asset markets and risk assets 18 IV. The neoclassical theory of production in short-run and long-run 26 V. The neoclassical theory of cost in short-run and long-run 33 VI. The theory of the firm in perfect competition and monopolistic competition 46 VII. The theory of oligopoly and monopoly 57 VIII. Input markets 64 IX. General equilibrium 70 References

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I. Classical and intertemporal models of consumer behaviour 1. Consumer Preferences 1.1 Consumption Bundles The economic model of consumer behaviour is very simple: people choose the best things they can afford. The objects of consumer’s choice are called consumption bundles, i.e. (x1, x2) =X or (y1, y2) =Y The consumer will rank these bundles according to their desirability. In other words, the consumer will decide, whether he strictly prefers one over the other (i.e. X > Y), or, that he is indifferent between X and Y (X ≈ Y). If the consumer prefers or is indifferent between X and Y we would call this weakly prefers one or the other (X ≥ Y). X ≈ Y bundles can be shown graphically below in a so-called indifference curve, where goods x1 and x2 are shown on the two axes. The shaded area to the right of the indifference curve represents any weakly preferred set:

1.2 Assumption about Preferences It is unrealistic to find a situation i.e., where X > Y and, at the same time, Y > X. Therefore, assumptions about the consistency of consumers’ preferences are made. Some of these assumptions are so fundamental, that they are referred to as “axioms” of consumer theory:

x2

x1

Indifference curve curve

Weakly preferred

set

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Complete Any two bundles can be compared, that is X ≥ Y or Y ≥ X, or both, in which case the consumer is indifferent between the two bundles not realistic, unimportant in Microeconomics. Reflexive Any bundle is at least as good as an identical bundle (X ≥ Y). Transitive If X ≥ Y and Y ≥ Z, than the assumption is made that X is at least as good as Z. Monotonicity More is superior; bundle X (x1, y1 + one unit) is preferred over bundle Y (y1, y2). Satiation Satiation point or bliss point is the overall best bundle for the consumer in terms of his own preferences. Both possibilities, too much of something or too little of something, equally do not satisfy the consumer. 2. Utility Utility today is seen as a way to describe consumer preferences. A utility function is a way of assigning a number to every possible consumption bundle such that more preferred bundles get assigned larger numbers than less preferred bundles. I.e. a bundle (x1, x2) is preferred over a bundle (y1, y2) if and only if the utility of X is larger than the utility of Y. u (x1, x2) > u (y1, y2) 2.1 Ordinal Utility The only importance of a utility assignment is how it orders / ranks the bundles of goods. The size of utility difference of any different consumption bundle does not matter. Because of the emphasis on ordering bundles of goods, this kind of utility is referred to as ordinal utility. Bundle u1 u2 A 3 17 B 2 10 C 1 .002 2.2 Cardinal Utility Cardinal utilities are theories which deal with the significance of the magnitude of a utility. The size of the utility difference between two bundles is supposed to have some sort of significance, i.e.: “I am willing to pay twice as much for bundle A as opposed to bundle B”. This can be also shown in a so called utility function where 4(A) > 2(B). More advanced theories of cardinal utility functions include “Perfect Substitutes”, “Quasilinear Preferences”, “Cobb-Douglas Preferences”…

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2.3 Marginal Utility The rate of change measured when the consumer gets a little more of good 1 in a bundle of (x1, x2) is called the marginal utility MU1 with respect to good 1, mathematically: MU1 = change U / change x1. 3. Choice 3.1 Optimal Choice Consumers choose the most preferred bundle from their budget set. Below, a budget set and several indifference curves of the consumer are drawn in the diagram.

In the diagram, the bundle of goods that is associated with the highest indifference curve that just touches the budget line (x1*, x2*) is the optimal choice for the consumer. This is the best bundle, the consumer can afford. In this case, the bundles above the budget line, which do not intersect it, are of higher preference to the consumer, hence are not affordable for the consumer. As shown in the graph, the optimal point (choice) does not cross the budget line. It is also called “Interior Optimum”. 3.2 Substitutes and Compliments The optimal choice of goods 1 and 2 at a certain price and certain income is called the consumers “demanded bundle”. Hence, when prices and income change, the consumer’s optimal choice will change. Different preferences will lead to different demand functions. A demand function is a function that relates the optimal choice – the quantities demanded – to the different values of prices and income. In other words, the demand function shows the optimal amounts of each of the goods as a function of the prices and income faced by the consumer.

x2*

x1*

Budget line

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x1 = x1(p1, p2, m) x2 = x2(p1, p2, m) The left hand side of the equation stands for the quantity demanded. The right hand side of the equation is the function that relates the prices and income to that quantity. If two goods are perfect substitutes, then a consumer will purchase the cheaper one. Perfect compliments are goods, of which the consumer will always buy an equal amount of each. The most obvious example is a pair of shoes. Again, here the optimal choice will be on the budget line. We therefore can solve the equation mathematically as: p1x + p2x = m or x1 = x2 = x = m / p1+p2 The demand function for the optimal choice here is quite obvious. Since the two goods are always consumed together, it is just as if the consumer is spending all his money on a single good that has the price p1 + p2. There are cases where the consumer spends all of his money on the goods he likes and none of “neutral” or even “bad goods” . Thus, if commodity 1 is “good” and commodity 2 is “neutral” or “bad”, the demand function expresses itself as: x1 = m / p1; x2 = 0 Concave preferences always represent a boundary choice; it represents a situation where the consumer spends always his total budget only on one of the two goods of his preference, never on both. 4. Demand Research on how a choice responds to changes in the economic environment is known as comparative statistics. Two situations are compared; before and after the change in the economic environment. Only two things will affect the optimal choice in our model: prices and income. Therefore, the investigation in the model will focus on how the demand changes when prices and income change. “Normal goods” are goods for which the demand increases, when income increases. For a normal good the quantity demanded always changes in the same way as income changes. ∆ x1 / ∆ m > 0 “Inferior goods” are goods for which the demand decreases, when income increases (i.e. low quality goods, fast food, etc.). Whether a good is inferior or not depends on the level of income under examination. It might very well be the case, that an inferior good is consumed more after income increases. After a certain point of income increase, however, demand for that good will usually decline. An income offer curve or income expansion path (shown below) illustrates the bundles of goods that are demanded

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at different levels of income. If both goods are normal goods, the income expansion path will show a positive slope.

5. Slutsky equation It is possible to construct examples where the optimal demand for goods decreases, when prices fall. A good with that property is called “Giffen good”. There are really two effects that appear when the price of a good changes: the rate where you can exchange one good for another changes and your total purchasing power is altered. The first part – the change in demand due to the change in the rate of exchange between the two goods – is called the substitution effect. The second effect – the change in demand due to having more (or less) purchasing power – is called the income effect. In order to illustrate this, it makes sense to break the price movement into two steps: first, to change the relative price and adjust money income so as to hold the purchasing power constant; second, adjust purchasing power while holding relative prices constant. This can be seen graphically in two phases. Pivot and Shift, when the price of good 1 changes and income stays fixed. Therefore, first, the budget line pivots around the vertical axis (X to Y). A parallel shift of the budget line is the movement that occurs when income changes while relative prices remain constant (Y to Z). The figure below will illustrate the two movements of the budget line.

Budget line

Indifference curves

Income offer curve

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5.1 The substitution effect The economic meaning of the pivoted budget line illustrates itself in a constant purchasing power for the consumer in the sense that the original bundle of goods is just affordable at the new pivoted line. The formula for this reads as follows: ∆ m = ∆ p1 * x1 Note that if the price of good 1 goes down, the adjustment of income will be negative. When a price goes down, the consumer’s purchasing power goes up. Therefore one has to decrease the consumer’s income in order to keep purchasing power at its original degree. The optimal purchase in the figure above is denoted at the pivoted budget line at point Y. This bundle of goods is the optimal bundle of goods when prices change and income is adjusted. Once again, the movement from X to Y is called the substitution effect. 5.2 The income effect A parallel shift of the budget line occurs when income changes while relative prices remain constant. This is also called income effect, changing income while keeping prices fixed at the new price. The above figure illustrates this by moving from point Y to Z. More precisely, the income effect is the change in the demand for good 1 when we change income from m’ to m, holding the price of good 1 fixed at p’1: ∆ x1n = x1(p’1,m) – x1(p’1,m’)

Original budget

line

Indifference curve

Shift

Original choice

Final choice

Pivot

x

Y

Z . .

.

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The income effect will either tend to increase or decrease the demand for good 1, depending on whether we have a normal good or an inferior good. 5.3 Slutsky Identity Putting all the above into perspective, the mathematical formula implies further, that the total changes in demand equal the substitution effect plus the income effect. This is also called “Slutsky Identity”. While the substitution effect must always be negative – opposite the change in price – the income effect can go either way. Thus, the total effect may either be positive or negative. However, if we are talking about a normal good, income and substitution effect do go in the same direction. 5.4 Hicks Substitution Effect The Hicks Substitution Effect states that the budget line pivots around the indifference curve rather than around the original choice. In this way, the consumer faces a new budget line that has the same relative price as the final budget line, but has a different income. The consumer’s purchasing power with the new budget line will no longer be sufficient to purchase his original bundle of goods. However, it will be sufficient to purchase a bundle that is just indifferent to his original bundle. This can be illustrated in the chart below.

The Slutsky substitution effect gives the consumer just enough money to get back to his old level of consumption while the Hicks substitution effect gives the consumer just enough money to get back to his old indifference curve.

Original Choice

Final Budget

Final Choice

Substitution e. Income effect.

Original Budget

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6. Intertemporal Choice Choices of consumption over time are known as intertemporal choices. The shape of an indifference curve will indicate the consumers’ tastes for consumption at different times. An indifference curve with the slope of -1 would represent tastes of consumers who did not care whether they consumed today or tomorrow. An indifference curve for perfect complements would indicate that consumers want to consume equal amounts today and tomorrow. Such consumers would be unwilling so substitute consumption from one period to the other. However, in reality, it is most common that consumers are willing to substitute some amount of consumption today for consumption tomorrow ( savings). The optimal choice for consumption can be examined in each of the two periods: • if the consumer chooses a pattern where c1 < m1, he is a lender • if the consumer chooses a pattern where c1 > m1, he is a borrower Graphically shown as:

To be a borrower or lender changes as interest rates changes. Let’s assume the consumer is a lender and now interest rate increase. He will remain a lender. If the consumer is a borrower and the interest rate declines, he will remain a borrower. The above might not be true the other way around. I.e. if a consumer is a lender and increase rates decrease, he might at one point very well switch to become a borrower.

c1 c1

C2

c2

m1 m1

m2

m2 choice

choice

Borrower Lender

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II. Choice under uncertainty Randomness in economic theory is often referred to in two distinct categories: first, situations in which the decision-maker can assign mathematical probabilities to the randomness he faces,1 and second situations when it is impossible to express the randomness in mathematical probabilities.2 According to this distinction, theories can be divided between those which use the assignment of probabilities and those which do not. Corresponding to this standard distinction the first chapter will focus on Subjective Expected Utility Theory in the case of “uncertainty” and on the Von Neumann-Morgenstern Theory in the case of “risk”. 3

1 Expected utility theory

1.1. Bernoulli utility function

We define “Expected Utility Theory” (EUT) as the theory of decision-making under risk based on a set of preferences. The basics of this theory go back to Daniel Bernoulli (1732)4. He showed in the so-called St. Petersburg Paradox, that the principle of maximizing the expected outcome is not a useful concept for decision-making.

In the St. Petersburg game people were asked how much they would pay for the following prospect: if tails comes out of the first toss of a fair coin, to receive nothing and stop the game, and in the complementary case to receive two guilders and stay in the game; if tails come out of the second toss of the coin, to receive nothing and stop the game, and in the complementary case to receive four guilders and stay in the game; and so on ad infinitum. The expected monetary value of this prospect is infinite. Since the people always set a definite, possibly quite small upper value on the St. Petersburg prospect, it follows that they do not price it in terms of its expected monetary value.5

Bernoulli developed the idea of using expected utility of money outcomes as a measure for decision making. He states that each expected outcome has different utilities for the decision maker and thus the outcome with the highest utility will be chosen. This is not necessarily the highest absolute outcome. Or in other words: Decision making of players is not based on statistic outcomes but on expected utilities. And since expected utilities are subject to individual preferences each expected utility function can be considered unique.

1 Referred to as „risk“. See also Knight, F.H., chapter I.I.26 2 Referred to as “uncertainty” 3 Knight, F.H., chapter I.I.26 4 Daniel Bernoulli, (*8.2.1700 - 17.3.1782) 5 Mongin, P. (1997), p. 342-350

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In general, by Bernoulli’s logic, the valuation of any risky venture takes the expected utility form: E (u p, X) = ∑ XE X p (x)u(x) 1.2. Von Neumann-Morgenstern expected utility function

The very foundation of classical utility theory where laid by John von Neumann und Oskar Morgenstern (1947) who used the concept of Bernoulli to develop the expected utility function, combining mathematical probabilities with expected utility. They attempted to axiomatize6 Bernoulli’s hypothesis in terms of agents’ preferences over different ventures with random prospects (lotteries). In other words: The decision-makers problem is to choose among lotteries (set of probabilities) and to find the best lottery. And Von Neumann and Morgenstern showed that if an agent has preferences defined over lotteries, then there is a utility function U: ∆(X)→R that assigns a utility to every lottery p Є ∆ (X) that represents these preferences. They proclaim that this theory describes rational decision making. The expected utility theorem formulates several assumptions which together with a set of axioms form the cornerstone of decision making. Using this framework rational decision making opts for the alternative which maximizes expected utility.7 1.3. Comparative statistics using revealed preferences8

The terminology of comparative statistics refers to the method of comparing two different states or outcomes of a choice. To rationalize observed consumer behavior several distinctions are made defining revealed preferences:

(1) When out of two possible options (x, y), x was chosen instead of y we can deduct that the utility of x is at least as large as the utility of y. In this case x is directly revealed preferred to y.

(2) In case of a sequence of revealed preference comparisons, x would be referred to as revealed preferred.

(3) In case of locally nonsatiated utility functions x’ lies closer to y. This contradicts utility maximization and x’ is strictly directly revealed preferred to x.

Using these observations the generalized axiom of revealed preference as a consequence of utility maximization can be derived. Based on this axiom several statistic demand compensation9 can be shown.

6 Axioms of Preference are: Independence, Transitivity, Completeness, the Archimedean axiom

(continuity) 7 Fishburn, P.C. (1989), p. 127-158 8 Varian, H. (1984), p.141-145

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Comparative statistics typically involve calculations designed to show the direction in which changes in the environment move peoples’ optimal decision. Convincing comparative statistic results are the ones that hold even if you impose only weak restrictions on preferences. That is why the method for comparative statistics sometimes tends to be sophisticated.10 2 Money lotteries and risk aversion

2.1 Arrow-Pratt measure of risk aversion

Risk aversion is a concept in different branches such as economics, finance, and psychology used to explain the behaviour of consumers and investors under uncertainty. Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with more certain but possibly lower expected payoff. The inverse of a person's risk aversion is sometimes called their risk tolerance.11

For example: A person is given the choice between a bet of either receiving $100 or nothing, both with a probability of 50%, or instead, a certain payment. Now he is risk averse if he would rather accept a payoff of less than $50 (for example, $40) with probability 100% than the bet, risk neutral if he was indifferent between the bet and a certain $50 payment, risk-loving (risk-proclive) if it required that the payment be more than $50 (for example, $60) to induce him to take the certain option over the bet. The average payoff of the bet, the expected value would be $50. The certain amount accepted instead of the bet is called the certainty equivalent, the difference between it and the expected value is called the risk premium.

In the theory of Arrow (1965) and Pratt (1964), risk-aversion is characterized by the concavity of the utility function over money income. The diminishing marginal utility of wealth helps to explain aversions to large scale risk. In other words: One Euro that helps us avoid poverty is more valuable than a Euro that helps us become very rich.12 2.2 Relative risk aversion and absolute risk aversion

2.2.1 Absolute risk aversion

The higher the curvature of the utility function u(c), the higher risk aversion. Since utility functions are not uniquely defined a measure that stays constant is needed. This measure is the Arrow-Pratt measure of absolute risk-aversion, or coefficient of absolute risk aversion, defined as

9 e.g. the Hicksian compensation or the Slutsky compensation. Varian, H. (1984), p. 144 10 Peters, M. (2005), page 1-13 11 Peters, M. (2005), page 8 12 Rabin, M. (2000), p.4

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.

The following expressions relate to this term:

• Constant absolute risk aversion if ru(c) is constant with respect to c • Decreasing/increasing absolute risk aversion (DARA/IARA) if ru(c) is

decreasing/increasing.

2.2.2 Relative risk aversion

The Arrow-Pratt measure of relative risk-aversion or coefficient of relative risk aversion is defined as

.

As for absolute risk aversion, the corresponding terms constant relative risk aversion and decreasing/increasing relative risk aversion are used. This measure has the advantage that it is still a valid measure of risk aversion, even if it changes from risk-averse to risk-loving, i.e. is not strictly convex/concave over all c.13

2.3 Jensen’s inequality

Jensen’s inequality is named after the Danish mathematician Johan Jensen, and it relates the value of a convey function of an integral to the integral of the convex function. This inequality can be stated generally using measure theory14, and it can be stated generally using probability theory15. The two statements say the same thing. If preferences admit an expected utility representation with the Bernoulli utility function u(x), it follows from the definition of risk aversion that the decision maker is risk avers if:

13 Mas-Colell, A. (1995), p. 167 f.

14 Let (Ω,A,µ) be a measure space, such that µ(Ω) = 1. If g is a real-valued function that is µ-integrable, and if φ is convex function on the range of g, then

15 In the terminology of probability theory, µ is a probability measure. The function g is replaced by a real-valued random variable X (just another name for the same thing, as long as the context remains one of "pure" mathematics). The integral of any function over the space Ω with respect to the probability measure µ becomes an expected value. The inequality then says that if φ is any convex function, then

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∫u (x)dF(x) ≤ u (∫ x dF(x)) In the context of expected utility theory risk aversion is equivalent to the concavity of the utility function u(*).16 One application of Jensen’s inequality can be found in investment management. The basic idea is that for analyzing the performance of an investment it is necessary not only to look at the overall return, but also of the risk. For example out of two mutual funds with the same returns, a rational investor would choose the less risky fund. Jensen’s measure is a way to determine if a portfolio earns proper returns for its level of risk. 3 Subjective probability function

In the von Neumann-Morgenstern theory, probabilities are assumed to be “objective”. In this respect, they followed the classical view that randomness and probabilities exist inherently in Nature and cannot be influenced by the agent. This point of view can be discussed controversial and some statisticians and philosophers have long objected to this view of probability, arguing that randomness is not an objectively measurable phenomenon but rather “knowledge” phenomenon.

In this view, a coin toss is not necessarily characterized by randomness: if we knew the shape and weight of the coin, the strength of the tosser, the atmospheric conditions of the room in which the coin is tossed, the distance of the coin-tosser’s hand from the ground, etc., we could predict with certainty whether it would be heads or tails. However, as this information is commonly missing, it is convenient to assume it is a random event and ascribe probabilities to heads or tails.

In short, probabilities are really a measure of the lack of knowledge about the conditions which might affect the coin toss and thus merely represent our beliefs about experiment.17 Other economists, such as Irving Fisher (1906) or Frank P. Ramsey (1926) asserted instead that probability is related to the knowledge possessed by an individual alone rather than to general knowledge. In Ramsey’s opinion, it is personal belief that governs probabilities and not disembodied knowledge. As a consequence “probability” is subjective.18 The problem with the subjectivist point of view is that it seemed impossible to derive mathematical expressions for probabilities from personal beliefs. However Frank Ramsey’s great contribution in his 1926 paper was to suggest a way of deriving a consistent theory of choice under uncertainty that could isolate beliefs from preferences while still maintaining subjective probabilities. In so

16 Mas-Colell, A. (1995), p. 185-186 17 As Knight expressed it, “if the real probability reasoning is followed out to its conclusion, it

seems that there is ‘really’ no probability at all, but certainty, if knowledge is complete.” (Knight, 1921:219)

18 Economists following these opinions are often referred to as „subjectivists“.

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doing, Ramsey provided the first attempt for an axiomatization of choice under uncertainty.19 The subjective nature of probability assignments can be made clearer by thinking of situations like horse race. In this case the most spectators face more or less the same lack of knowledge about the horses, the track, the jockeys, etc. Yet, while sharing the same “knowledge” different people place different bets on the winning horse. The basic idea behind the Ramsey’s-de Finetti derivation is that by observing the bets people make, one can presume this reflects their personal beliefs on the outcome of the race. Thus, Ramsey and de Finetti argued, subjective probabilities can be inferred from observation of people’s actions. Leonard Savage (1954) succeeded in giving a simple axiomatic basic to expected utility with subjective uncertainty based on the ideas of Ramsey and de Finetti and the assumptions of transitivity20, order21, invariance22, dominance23, cancellation24 and continuity25. According to this theory the decision is made in dependence to the subjective expected utility (SEU). The subjective expected utility is the sum of all expected utilities of the single consequences multiplied with the probability of realization. SEU = subjective utility x subjective probability of realization Concluding it can be said, that the main difference is the treatment of “uncertainty” and “utility” as subjective variables rather than objective probabilities. 4 State preference approach

The “state preference” approach to uncertainty was introduced by Kenneth J. Arrow (1953) and further detailed by Gerard Debreu (1959:Ch.7). The basic principle is that it can reduce choices under uncertainty to a conventional choice problem by changing the commodity structure appropriately. The state-preference approach is thus distinct from the conventional “microeconomic” treatment of choice under uncertainty, such as that of von Neumann and Morgenstern (1944), in that preferences are not formed over “lotteries” directly but, instead, preferences are formed over state-contingent commodity bundles. In this reliance on states and choices of actions which are effectively functions from states to outcomes, it is much closer in spirit to Leonard Savage (1954). It differs from Savage in not relying on the assignment of subjective probabilities, although such a derivation can be made. The basic proposition of the state preference approach to uncertainty is that commodities can be differentiated not only by their physical properties and

19 Independently of Ramseys, Bruno de Finetti (1931, 1937) had also suggested a similar

derivation of subjective probability. 20 Meaning a consistent rank order preference (prefer A<B<C and not C<A). 21 Meaning a clear preference for one out of two possibilities. 22 Meaning that the decision maker is not affected by the way of how alternatives are presented. 23 Meaning that the choice with greater utility dominates preferences. 24 Meaning that identical probabilities with the same utility leave decision to chance. 25 Meaning that gamble is prefered to „sure outcomes“ if the odds are high enough.

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location in space and time but also by their location in “state”. By this we mean that “ice cream when it is rainy” ia a different commodity than “ice cream when it is sunny” and thus are treated differently by agents and can command different prices. Thus, letting S be the set of mutually-exclusive ”states of nature” (e.g. S =rainy, sunny), then we can index every commodity by the state of nature in which it is received and thus construct a set of “state-contingent” markets.26 Insurance is a natural application of the statepreference approach precisely because it is a explicit “ state-contingent” contract. 5 Concluding considerations

The expected utility model was first proposed by Daniel Bernoulli as a solution to the St. Petersburg paradox. Bernoulli argued that the paradox could be resolved if decision makers displayed risk aversion. Based on these ideas the first important use of the expected theory was that of John von Neumann and Oskar Morgenstern who used the assumption of expected utility maximization in their formulation of game theory. The expected utility theorem says that a von Neumann-Morgenstern utility function exists if the agent's preference relation on the space of simple lotteries satisfies four axioms: completeness, transitivity, convexity/continuity, and independence. Independence is probably the most controversial of the axioms. A variety of generalized expected utility theories have arisen, most of which drop or relax the independence axiom. The in chapter 2 discussed Arrow-Pratt measures of risk aversion for von Neumann-Morgenstern utility functions have become a standard in analyzing problems in microeconomics of uncertainty. They have been used to characterize the qualitative properties of demand in insurance and asset markets, to examine the properties of risk taking in taxation models, etc. to name just a few applications. The limitations of classical expected utility considerations are outlined in chapter 3. The findings of Savage led to a normative theory of decision-making based on subjective utility expectations. Whereas the state-preference approach distinguishes states of nature of commodities (which substitute “lotteries”) and can be related to Savage and the theories of risk aversion.

26 Yaari, M. (1969), p. 315-329

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III. Asset Markets and Risk Assets

Return

The term “return on investment” or simply “return”, is used to refer to any of a number of metrics of the change in an asset's or portfolio's accumulated value over some period of time. Accumulated value can be measured in different ways. In investment management, a distinction is drawn between total returns and net returns. The former are calculated from accumulate values reflecting only price appreciation and income from dividends or interest. The latter are calculated from accumulated values that also reflect items such as management fees, custody fees, transaction costs, taxes, and perhaps even inflation.

Risk is the potential impact (positive or negative) to an asset or some characteristic of value that may arise from some present process or from some future event. In everyday usage, "risk" is often used synonymously with "probability" and restricted to negative risk or threat. In professional risk assessments, risk combines the probability of an event occurring with the impact that event would be. Financial risk is often defined as the unexpected variability or volatility of returns, and thus includes both potential worse than expected as well as better than expected returns. References to negative risk below should be read as applying to positive impacts or opportunity (e.g. for loss read "loss or gain") unless the context precludes.

Risk is often mapped to the probability of some event which is seen as undesirable. Usually the probability of that event and some assessment of its expected harm must be combined into a believable scenario (an outcome) which combines the set of risk, regret and reward probabilities into an expected value for that outcome. In statistical decision theory, the risk function of an estimator δ(x) for a parameter θ, calculated from some observables x; is defined as the expectation value of the loss function L,

where: δ(x) = estimator ; θ = the parameter of the estimator

There are many informal methods used to assess or to measure risk. Although it is not usually possible to directly measure risk. Formal methods measure the value at risk.

Risk Definition:

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In scenario analysis risk is distinct from threat. A threat is a very low-probability but serious event - which some analysts may be unable to assign a probability in a risk assessment because it has never occurred, and for which no effective preventive measure (a step taken to reduce the probability or impact of a possible future event) is available. The difference is most clearly illustrated by the precautionary principle which seeks to reduce threat by requiring it to be reduced to a set of well-defined risks before an action, project, innovation or experiment is allowed to proceed.

RAROC

RAROC is a risk based profitability measurement framework for analysing risk-adjusted financial performance and providing a consistent view of profitability across businesses. RAROC is defined as the ratio of risk adjusted return to economic capital. Economic capital is a function of market risk, credit risk, and operational risk. This use of capital based on risk improves the capital allocation across different functional areas of a bank. RAROC system allocates capital for 2 basic reasons: 1) Risk management and 2) Performance evaluation.

For risk management purposes, the main goal of allocating capital to individual business units is to determine the banks optimal capital structure (i.e. economic capital allocation is closely correlated with individual business risk).

As a performance evaluation tool, it allows Banks to assign capital to business units based on the economic value added of each unit.

Risk Premium

A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to.

Risk premium in finance

In finance, the risk premium can be the expected rate of return above the risk-free interest rate.

Debt: In terms of bonds it usually refers to the credit spread (the difference between the bond interest rate and the risk-free rate).

Equity: In the equity market it is the returns of a company stock, a group of company stock, or all stock market company stock, minus the risk-free rate. The return from equity is the dividend yield and capital gains. The risk premium for equities is also called the equity premium.

Standard deviation

In probability and statistics, the standard deviation is the most common measure of statistical dispersion. Simply put, standard deviation measures how spread out the values in a data set are. More precisely, it is a measure of the average distance of the data values from their mean. If the data points are all close to the mean,

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then the standard deviation is low (closer to zero). If many data points are very different from the mean, then the standard deviation is high (further from zero). If all the data values are equal, then the standard deviation will be zero. The standard deviation has no maximum value although it is limited for most data sets

The standard deviation is defined as the square root of the variance. This means it is the root mean square (RMS) deviation from the arithmetic mean. The standard deviation is always a positive number (or zero) and is always measured in the same units as the original data. For example, if the data are distance measurements in meters, the standard deviation will also be measured in meters.

A distinction is made between the standard deviation σ (sigma) of a whole population or of a random variable, and the standard deviation s of a subset-population sample. The formulae are given below.

Definition and calculation

The standard deviation of a random variable X is defined as:

where E(X) is the expected value of X.

Not all random variables have a standard deviation, since these expected values need not exist. If the random variable X takes on the values x1,...,xN (which are real numbers) with equal probability, then its standard deviation can be computed as follows. First, the mean of X, , is defined as:

Next, the standard deviation simplifies to:

In other words, the standard deviation of a discrete uniform random variable X can be calculated as follows:

For each value xi calculate the difference between xi and the average value .

Calculate the squares of these differences. Find the average of the squared differences. This quantity is the variance σ2.

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Capital market theory

The capital asset pricing model (CAPM) is used in finance to determine a theoretically appropriate required rate of return (and thus the price if expected cash flows can be estimated) of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The CAPM formula takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), in a number often referred to as beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor, William Sharpe, John Lintner and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe received the Nobel Memorial Prize in Economics (jointly with Harry Markowitz and Merton Miller) for this contribution to the field of financial economics.According to the CAPM, the relation between the expected return on a given asset i, and the expected return on a proxy portfolio m (here, the market portfolio) is described as:

Where:

E(ri) is the expected return on the capital asset rf is the risk-free rate of interest βim (the beta) the sensitivity of the asset returns to market returns, or

also , E(rm) is the expected return of the market

E(rm) − rf is sometimes known as the market premium or risk premium (the difference between the expected market rate of return and the risk-free rate of return).

For the full derivation see Modern portfolio theory.

Asset pricing

Once the expected return, E(ri), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate to establish the correct price for the asset. In theory, therefore, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued (and undervalued when the observed price is below the CAPM valuation). Alternatively, one can "solve for the discount rate" for the observed price given a particular valuation model and compare that discount rate with the CAPM rate. If the discount rate in the model is lower than the CAPM rate then the asset is overvalued (and undervalued for a too high discount rate).

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Asset-specific required return

The CAPM returns the asset-appropriate required return or discount rate - i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. The CAPM is consistent with intuition - investors (should) require a higher return for holding a more risky asset.

Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk, the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for the market - and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund) therefore expects performance in line with the market.

Risk and diversification

The risk of a portfolio is comprised of systematic risk and specific risk. Systematic risk refers to the risk common to all securities - i.e. market risk. Specific risk is the risk associated with individual assets. Specific risk can be diversified away (specific risks "average out"); systematic risk (within one market) cannot. Depending on the market, a portfolio of approximately 15 (or more) well selected shares might be sufficiently diversified to leave the portfolio exposed to systematic risk only.

A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context - i.e. its contribution to overall portfolio riskiness - as opposed to its "stand alone riskiness." In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability.

The efficient (Markowitz) frontier

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Efficient Frontier

The CAPM assumes that the risk-return profile of a portfolio can be optimized - an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient (Markowitz) frontier.

Because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta.

The market portfolio

An investor might choose to invest a proportion of his wealth in a portfolio of risky assets with the remainder in cash - earning interest at the risk free rate (or indeed may borrow money to fund his purchase of risky assets in which case there is a negative cash weighting). Here, the ratio of risky assets to risk free asset determines overall return - this relationship is clearly linear. It is thus possible to achieve a particular return in one of two ways:

By investing all of one’s wealth in a risky portfolio or by investing a proportion in a risky portfolio and the remainder in cash (either borrowed or invested).

For a given level of return, however, only one of these portfolios will be optimal (in the sense of lowest risk). Since the risk free asset is, by definition, uncorrelated with any other asset, option 2) will generally have the lower variance and hence be the more efficient of the two.

This relationship also holds for portfolios along the efficient frontier: a higher return portfolio plus cash is more efficient than a lower return portfolio alone for that lower level of return. For a given risk free rate, there is only one optimal portfolio which can be combined with cash to achieve the lowest level of risk for any possible return. This is the market portfolio.

Assumptions of CAPM:

All investors have rational expectations. All investors are risk averse. There are no arbitrage opportunities. Returns are distributed normally. Fixed quantity of assets. Perfect capital markets. Separation of financial and production sectors. Thus, production plans are fixed. Risk-free rates exist with limitless borrowing capacity and universal

access.

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Shortcomings of CAPM

The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict. Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the efficient markets hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes EMH wrong – indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market).

Capital Market Line

James Tobin (1958) added the notion of leverage to portfolio theory by incorporating into the analysis an asset which pays a risk-free rate. By combining a risk-free asset with a portfolio on the efficient frontier, it is possible to construct portfolios whose risk-return profiles are superior to those of portfolios on the efficient frontier. The capital market line is the tangent line to the efficient frontier that passes through the risk-free rate on the expected return axis.

Capital Market Line

In this graphic, the risk-free rate is assumed to be 5%, and a tangent line, called the capital market line, has been drawn to the efficient frontier passing through the risk-free rate. The point of tangency corresponds to a portfolio on the efficient frontier. That portfolio is called the super-efficient portfolio.

Arbitrage Pricing Theory

Arbitrage pricing theory (APT) holds that the expected return of a financial asset can be modelled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor specific beta coefficient. The model derived rate of return will then be used to price the asset correctly - the asset price should equal the expected end of period price discounted at the rate implied by model. If the price

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diverges, arbitrage should bring it back into line. The theory was initiated by the economist Stephen Ross in 1976.

If APT holds, then a risky asset can be described as satisfying the following relation:

where

E(rj) is the risky asset's expected return, RPk is the risk premium of the factor, rf is the risk free rate, Fk is the macroeconomic factor, bjk is the sensitivity of the asset to factor k, also called factor loading, and εj is the risky asset's idiosyncratic random shock with mean zero.

That is, the uncertain return of an asset j is a linear relationship among n factors. Additionally, every factor is also considered to be a random variable with mean zero.

Note that there are some assumptions and requirements that have to be fulfilled for the latter to be correct: There must be perfect competition in the market and the total number of factors.

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IV. The neoclassical theory of production in short-run and long-run 1. Introduction In microeconomic view the production is nothing else as the conversion of inputs into outputs. In other words it is an economic process that uses factor resources to create a commodity that is suitable for exchange. The process can include manufacturing, storing, transportation, and packaging. As a process production occurs through time and space and is measured as a “rate of output per period of time”. Therefore we have three aspects to production processes:

• the quantity of commodity produced • the form of the good produced • the temporal and spatial distribution of the commodity produced.

In this way the production process can be defined as any activity that increases the similarity between the pattern of demand for goods, and the quantity, form, and distribution of these goods available to the market place. The inputs or resources used in any production process are called factors of production. Classical economics distinguish between three factors:

• Land or natural resources – naturally occurring goods such as soil and minerals that are used in the creation of products.

• Labour - human effort used in production which includes technical and marketing expertise.

• Capital goods – human-made goods or means of production which are used for the production of other goods. These include machinery, tools and buildings.

Capital goods are those that have previously undergone a production process. They are previously produced means of production and are sometimes called as “technology” as a factor of production. Investment is important for the future increase of the economy. These factors were codified originally in the analysis of Adam Smith, 1776, David Ricardo, 1817, and the later contributions of Karl Marx, who calls these factors as the “holy trinity” of political economy. But this classical view was further developed and we have until these present days some more means that deals with factors of production:

• Entrepreneurs and managerial skills (people who organize and manage other productive resources to make goods and services).

• Human Capital (the quality of labour resources which can be improved through investments, education, and training).

The translation of demands for commodities into demand for factor services necessitates some clearly defined technologies which tell us how commodities are produced and how factors are distributed and, in addition, how much the process of conversion from services to commodities costs. In this view production is a

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matter of indirect exchange and so we extend the tools of analysis derived in the context of pure exchange to analysing production. In this seminar paper it will be analysed the neoclassical approach of the production theory concerning the importance of the technology in connection with the production functions. 2. The Neoclassical Theories of Production The upper mentioned idea that production is an indirect exchange was the heart of the theory of the Lausanne School of Léon Walras (1874) and Vilfredo Pareto (1896, 1906). These Lausanne theories of production were embedded in the general equilibrium system. As a result, the basic production unit – the “firm” – was relegated into a subsidiary role. Indeed, Walras ignored the decision-making role of producers entirely. Regarding profit-maximization, choice of factor inputs and the marginal productivity theory of distribution we find to a good part in other scholars, notably the “Paretian” school during its height where it was consolidated by Jacob Viner (1931), John Hicks (1939) and Paul Samuelson (1947). To these approaches belongs the integration of the theory of production into the Paretian general equilibrium theory as well. After World War II, the theory of production veered off in another direction, exploiting the activity analysis and linear programming methods developed by the Cowles Commission. The “Neo-Walrasian” theory of production (Koopmans, 1951; Debreu, 1959) covers much of the same ground as the Paretian theory, albeit using somewhat different methods but the Neo-Walrasians have asserted the greater “generality” of their methods. But in all capital is assumed to be an endowed factor of production rather than a produced factor of production. 3. The Properties of Production Function The production function is a mathematical function of input factors that summarizes the process of conversion into a particular commodity. The relationship of output to inputs is non-monetary, i.e. a production function relates physical inputs to physical outputs. Prices and costs are not considered. The analysis of output technologically possible from a given set of inputs abstracts away from engineering and managerial problems inherently associated within a particular production process. The engineering and managerial problems of technical efficiency are assumed to be solved, so that analysis can focus on the problems of allocative efficiency. The general form of a production function was first proposed by P. Wicksteed (1894) and can be expressed as Y = f(X1, X2, X3, ….. Xm) which relates a single output Y to a series of input factors X of production. In the neoclassical way we have a production technology for the one-output/two-inputs case. The two inputs we call L (labour) and K (capital). The production set is

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essentially the set of technically feasible combinations of output Y and inputs, K and L Y = f (K,L) This form excludes joint production, i.e. that a particular process of production yields no more than one output (no multiple co-products). The technologies production function states the maximum amount of output possible from an input bundle and has the form Y = f(X1, Λ, Xn) 3.1 Characteristics The function f(x) is continuous throughout, single valued and has continuous 1st, 2nd, and 3rd order partial derivatives. The functions presuppose technical efficiency and state the maximum attainable output from each (X1, ….. Xn). Inputs and outputs are rates of flow per unit of time t0, where t0 is sufficiently long to allow for completion of technical process. The production functions (one input, one output): Output Level Y

Y = f(x)

Y’ = f(x’) is the maximal output level Y’ obtainable from X’ input units

X’ X

3.2 Total, average, and marginal physical product The total physical product of a variable input-factor identifies what outputs are possible using various levels of variable input. The diagram shows a typical total product curve. Output increases as more inputs are employed up until point A. The maximum output possible is Ym. Ym A

Xn

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The average physical product is the total product divided by the number of units of variable input employed. It is the output of each unit of input. For example 10 employees produce 50 units per day, the average product of variable labour input is 5 units per day. The marginal physical product of a variable input is the rate-of-change of the output level as the level of input changes, holding all other input levels fixed due to a change in the variable input. Typically the marginal product of one input depends upon the amount used of other inputs and is diminishing if it becomes smaller as the level of input increases. This states that you add more and more of a variable input you will reach a point beyond which the resulting increase in output starts to diminish. This concept is also known as the law of diminishing marginal returns. 3.3 Homogeneous and homothetic production functions There are two special types of production functions which are seldom in reality. The production function Y = f(X1, X2) is said to be homogeneous of degree n, if given any positive constant k, f(kX1,kX2) = knf(X1,X2). when n > 1, the function exhibits increasing returns n < 1, the function exhibits decreasing returns n = 1, the function exhibits constant returns Homothetic functions are a special type of homogeneous functions in which the marginal rate of technical substitution is constant along the function. 3.4 Returns-to-Scale Marginal products describe the change in output level as a single input level changes. Returns-to-scale describes how the output level changes as all input levels change in direct proportion (e.g. all input levels doubled, or halved). When all input levels are increasing proportionately, there need be no diminution of marginal products since each input will always have the same amount of other inputs with which to work. Input productivities need not fall and so returns-to-scale can be constant or increasing. The elasticity of production measures the sensitivity of total product to a change in an input in percentage terms (E = %∆Y / %∆L). 3.5 The long-run and the short-runs The long-run is the circumstance in which a firm is unrestricted in its choice of all input levels. If all inputs are allowed to be varied, then the diagram would express outputs relative to total inputs, and the production function would be a long run production function. The short-run is a circumstance in which a firm is restricted in some way in its choice of at least one input level. There are some reasons for that like

temporarily being unable to install or remove machinery being required by law to meet affirmative action quotas having to meet domestic content regulations temporarily being unable to cancel contracts

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A useful way to think of the long-run is that the firm can choose as it pleases in which short-run circumstance to be. It is a managerial task to use economic analysis to make business decisions involving the best allocation of firms’ scare resources in order to achieve the firms’ goals – in particular, to maximize profit. The decision agent acts rationally in pursuit of his goal which is to maximize profits. He has perfect knowledge of technical production relationships and input and product price relationships. 4. Technology Rather than comparing inputs to outputs or the choice between two outputs as it is shown in the elasticity of substitution it is also possible to assess the mix of inputs employed in production. You can use a lot of labour with a minimal amount of capital or vice versa or any combination between. For most goods, there are more than just two inputs. But for better understanding and illustrating we use the two input case. A technology is a process by which inputs are converted to an output. Usually several technologies will produce the same product. The question is which is the best technology and how do we compare technologies. X i denotes the amount used of input i. An input bundle is a vector of the input levels (X1, X2, … Xn). A production plan is an input bundle and an output level Y. A production plan is feasible if Y ≤ f(X1, Λ, Xn). The collection of all feasible production plans is the technology set. 4.1 Technical rate of substitution X2 8 A perfect substitution shows the situation 6 of linear and parallel slopes: 3 9 18 24 X1 The Rate of Substitution answers the question: At what rate will a firm substitute one input for another without changing its output level? 4.2 Fixed proportions technologies (Leontief Technology) If there is no flexibility in technique we have fixed input requirements in order to produce a single unit of output. Consequently we need vY units of capital and uY units of labour. In other words, K=vY are the capital requirements and L=vY are the labour requirements. As a result the only technique is L/K=u/v. In other words there is a particular fixed proportion of capital and labour required to produce output. There are constant returns to scale but no substitution is possible.

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L

L’ Y’ L* Y* u/v K* K’ K Leontief (no Substitution isoquants) Technical Rate of Substitution is the rate X2 at which input 2 must be given up as input 1 increases so as to keep the output level constant. It is the slope of the isoquant l. Y=100

X1 4.3 The Cobb-Douglas technology In contrast to Leontief, Cobb-Douglas production function allows for substitution. The production function has the form Y=aLbKc. The original version Y=aLbK1-b with constant returns to scale (b+1-b=1) was introduced by Cobb in 1928. He estimated the production function of U.S. manufacturing output for the years 1899-1922. If b + c = 1, there are constant returns b + c > 1, increasing returns b + c < 1, decreasing returns to scale. The Cobb-Douglas function is homothetic, i.e. if all inputs are multiplied by λ, the output is multiplied by a function of λ. Specifically it is homogenous if relative price changes and producers will like to change combination of inputs if technology permits this (unlike Leontief). The elasticity of substitution measures how easily inputs can be substituted if relative prices change: percentage change of ratio of inputs for given percentage change of price ratio. For a Cobb-Douglas production function, the elasticity of substitution is 1, i.e. if the relative prices change by 1%, the ratio of inputs will change by 1%. This is so because for a Cobb-Douglas production function, in the optimal combination of inputs, the ratio of total expenditures for the inputs is constant. At the Cobb-Douglas Technical Rate of Substitution (TRS) all isoquants are hyperbolic, asymptoting to, but never touching any axis.

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X2 A Cobb-Douglas example 8 4 X1 4.4 Well-behaved technologies A well behaved technology is monotonic, and convex. Monotonicity means: More of any input generates more output. Convexity means: If the input bundles X´and X´´ both provide Y units of output then the mixture tX´+ (1-t)X´´ provides at least Y units of output, for any 0<t<1. Convexity implies that the TRS increases (becomes less negative) as X1 increases (slope is convex to the origin). Convexity Monotonic and not monotonic X2 Y Y=120 Y=100 X1 X 5. Summary The production theory as shown simplifies the production reality of a firm, yet it is useful for understanding of the characteristics of production processes. But there are some critical annotations to be done. Especially in the decision making process the Neoclassical theory restricts its producer to only one person making a decision. We have today many modern multi-onwner corporations in which hundreds of shareholders with conflicting desires have decision-making-power. The Paretian firm is owned by a single entrepreneur who has an unchallenged power of decisions over all aspects like: product, technique of production, hiring of factors, etc. but not in the decision of any prices, he considers prices as “given”. Today producers take prices as variables and not as parameters for their decisions and are confronted with a perfect competition. Therefore we have to analyse and consider the cost functions within a production process as well.

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V. The neoclassical theory of cost in short-run and long-run Introduction Neoclassical economics refers to a general approach (a “metatheory") to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. Mainstream economics is largely neoclassical in its assumptions, at least at the microeconomic level. There have been many critiques of neoclassical economics, often incorporated into newer versions of neoclassical theory as circumstances change.

Overview Neoclassical economics is the singular element of several schools of thought in economics. There is not complete agreement on what is meant by neoclassical economics, and the result is a wide range of neoclassical approaches to various problem areas and domains -- ranging from neoclassical theories of labor to neoclassical theories of demographic changes. As expressed by E. Roy Weintraub, neoclassical economics rests on three assumptions, although certain branches of neoclassical theory may have different approaches: People have rational preferences among outcomes that can be identified and associated with a value. Individuals maximize utility and firms maximize profits. People act independently on the basis of full and relevant information. From these three assumptions, neoclassical economists have built a structure to understand the allocation of scarce resources among alternative ends -- in fact understanding such allocation is often considered the definition of economics to neoclassical theorists. Here's how William Stanley Jevons presented the basic problem of economics: Given, a certain population, with certain needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce. From the basic assumptions of neoclassical economics comes a wide range of theories about various areas of economic activity. For example, profit maximization lies behind the neoclassical theory of the firm, while the derivation of demand curves leads to an understanding of consumer goods, and the supply curve allows an analysis of the factors of production. Utility maximization is the source for the neoclassical theory of consumption, the derivation of demand curves for consumer goods, and the derivation of factor supply curves and reservation demand. Neoclassical economics emphasizes equilibria, where equilibria are the solutions of individual maximization problems. Regularities in economies are explained by methodological individualism, the doctrine that all economic phenomena can be ultimately explained by aggregating over the behavior of individuals. The emphasis is on microeconomics. Institutions, which might be considered as prior to and conditioning individual behavior, are de-emphasized. Economic subjectivism accompanies these emphases. See also general equilibrium.

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Production and cost

• Production Relationship: Q = f (L, K) • Inputs (L and K) and output (Q) are all expressed as flows (per unit time)

not stocks • Capital usually refers to flows of “services” provided by durable producer

goods (whichare themselves the outputs of production) Example: Beer production

• five ingredients: water, yeast, hops, grain,and malted barley • labor: brewmaster, Laverne and Shirley capital: brewing vats,

bottling/canning facilities, delivery trucks • IP: recipe, business model, trademark, brand image • NB: the recipe is 5,000 years old!

Production function:

• You can think of this production function as the case when with all inputs

besides Labor are held constant. • Production function is “efficient” frontier of production possibilities.

Average and marginal products:

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Relation among TP, AP, MP:

Looking ahead - Cost function with single input: a cost function C(Q) gives the minimum cost of producing each possible quantity of output. Case of Single Input: C(Q) = w*L(Q), where L(Q) is minimum needed to produce (Q)= w*f -1(Q), Example: Q = f(L) = L1/2 Inverting the production function: L(Q) = f-1(Q) = Q2

Cobb-Douglas Production: Q = aLαKβ, where a > 0, α > 0, and β > 0. Isoquants: all possible combinations of inputs that exactly produce a given output level: all (L, K) such that: f(L, K) = Q0 (constant).

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Example Cobb-Douglas:

Q = K1/2 L1/2 Q2 = KL K(L; Q) = Q2/L

Marginal rate of technical substitution Definition: MRTS measures the amount of an input L the firm would require in place of a unit less of another input, K, to be able to produce the same output as before: MRTSL,K = -dK/dL (for constant output). Note: Marginal products and the MRTS are related: MPL * dL + MPK * dK = 0 MPL / MPK = - dK/dL = MRTSL,K

• NB: similarity with indifference curves and MRS! • If both marginal products are positive, the slope of the isoquant is negative

and so MRTS > 0 • If we have diminishing marginal returns, we also have a diminishing

marginal rate of technical • substitution: dMRTSL,K / dL < 0 • Cobb-Douglas: MRTSL,K = αK /βL

Elasticity of substitution Definition: The elasticity of substitution, σ, measures how the capital-labor ratio, K/L, response to a change in the ability to tradeoff inputs (i.e., MRTSL, K): σ = %∆(K/L) / %∆MRTSL,K = [d(K/L) / dMRTSL,K] [MRTSL,K/(K/L)]. Note: “σ” is a pure number that measures the ease with which a firm can substitute one input for another. Example: Cobb Douglas σ = [d(K/L) /dMRTSL,K] [MRTSL,K/(K/L)] = (-3/-3) (4/4) = 1.

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Returns to scale Definition: will output increase more or less proportionately when ALL inputs increase by the same percentage amount? RTS = [%∆Q]/[%∆(all inputs)] If a 1% increase in all inputs results in a …

Then we have returns to scale of this kind:

less than 1% increase in output Decreasing (DRTS) exactly a 1% increase in output Constant (CRTS) greater than 1% increase in Increasing (IRTS) Visualizing returns to scale

Check: Q1 >/=/< 2Q0 then IRTS/CRTS/DRTS Example: Cobb Douglas production: Q = LαKβ

- if α + β > 1 then IRTS - if α + β = 1 then CRTS - if α + β < 1 then DRTS

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Extreme production functions

1. Linear: Q = f(L, K) = aL + bK - • MRTS constant - • Constant returns to scale - • σ = ∞.

2. Fixed proportions: Q = f(L, K) = min aL, bK • L-shaped isoquants • MRTS varies (0, infinity, undefined) • σ = 0

Summary I.

1. Production function relates output to the efficient use of all possible input levels.

2. The effect of an input on production can be measured by its average and marginal products.

3. An isoquant gives all input combinations that generate same level of output.

4. The ability to substitution one input for another is measured by the Marginal Rate of Technical Substitution (MRTS), which normally satisfies diminishing MRTS.

5. The production function, isoquant and MRTS have a direct counterpart in consumer theory to the utility function, the indifference curve and MRS.

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6. We can summarize ability to tradeoff one input for another by the elasticity of substitution.

7. Returns to scale measure how output increases with the proportionate increase in all inputs.

Cost minimization

Significance and meaning of economic cost Why care about costs?

• Should drive business decisions regarding price, production, investment, etc.

• Affects which companies and technologies succeed, and which ones fail. • Determines the size of firms. • Determines the level, structure and trends in prices paid for goods and

services. Meaning of economic cost:

• Measure the use of resources in the production of goods and services. • Accountants measure only explicit expenses (and sometimes not even

those). • “Opportunity cost” includes the value of employed resources in their best

alternative use what matters is expenditure affected by adecision there may also be “external costs” born by those not involved in production (e.g.pollution).

Taxonomy of costs Total v. Average v. Marginal

• AC = TC / Q also referred to as “unit costs” • MC = ÄTC / ÄQ sometimes called “incremental”

Fixed versus variable • how costs vary with level of output • [total cost] = [variable cost] + [fixed cost]

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Short run versus long run

• as before, depends on the time period considered, and hence whether inputs are “fixed” or “variable”

• make distinction between “fixed cost” and “fixed factor” Sunk versus avoidable (non-sunk)

• difference depends on whether cost can be avoided by some decision • e.g., fixed cost can be avoided by shutting down. • usually treat variable costs as avoidable, fixed costs as sunk • because they are unavoidable, “sunk” costs should be ignored when

making decisions Other cost distinctions

• production versus transaction costs • one-time versus recurring costs

Cost minimization The firm’s problem: A profit maximizing firm won’t spend more to produce its output than it has to: MinimizeL,K TC = rK + wL, Subject to: f(L,K) = Q0 The solution: In words: find the cheapest input combination that produces the desired level of output. Iso-quant curve: input combinations that produce the same quantity of output, Slope of iso-quant = - MRTSL,K= - MPL/MPK.

Iso-cost lines: input combinations that cost same amount wL + rK = C (a constant), K = (C - wL ) / r, slope of iso-cost = ∆K / ∆L (along an iso-cost-line) = - w / r, compare: budget lines Putting two together: MRTS L,K = MPL / MPK = w / r Solution: another view - MPL / w = MPK / r

• 1/w = the amount of labor that can be purchased for $1. • MPL = the amount of output that can be produced with last unit of labor. • MPL/w = output derived from last $ spent on labor. • Similar interpretation for capital. • Therefore, equate incremental output of last $ spent on each input across

inputs.

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Comparative statics

• Output Expansion Path: L(Q) and K(Q) are labor and capital levels that minimize cost.

• Plot optimal cost-minimizing input combinations as output increases (i.e., moves in the northeast direction).

• If the cost-minimizing quantity of an input rises (falls) with output, then it is a “normal” (“inferior”) input.

• Compare: income-consumption curve.

Factor Price Change: L(w; Q) gives labor that minimizes cost for each wage rate – • increase the price of one input (e.g., wage). • factor substitution: All else equal, an increase in w must decrease labor and increase capital due to diminishing MRTSL,K. • compare: price-consumption curve.

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Short-run costs What is the “short run”?

• period over which one input (e.g., capital) is “fixed”. • short-run production function: Q = f ( L, K). • payment to the “fixed factor” (i.e. K—) becomes a fixed cost.

Short-run Cost: C(Q; K—) = w L(Q; K—) + r K—

•variable cost: just the variable/labor expense SRVC = w L(Q; K— ) •fixed cost: unavoidable expense of “fixed factor” SRFC = r K— •input demand functions are the solutions to the short run cost minimization problem • So demand for variable inputs depends on availability of “fixed factor”

Short run average costs

SRATC = C(Q; K) /Q = [w L(Q; K) + r K] /Q Decomposed into fixed and variable components

• variable: SRAVC = w L(Q; K) /Q • fixed: SRAFC = r K/Q

Properties • SRAVC typically has the “U shape” • since TC > VC, SRATC > SRAVC (where difference is SRAFC) • SRAFC falls to 0 as Q increases Short run marginal cost

• addition to cost of producing last unit of output SRMC = ∆C/∆Q = ϑC/ϑQ • note that any fixed cost is irrelevant to marginal cost: SRMC = ∆VC / ∆Q Properties • diminishing marginal product => SRAC and SRMC rising • when SRMC > SRATC, then SRATC rising (and vice versa)

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• consequently, SRMC = SRATC when SRATC minimum, similarly SRMC = SRAVC when SRAVC minimum • compare with marginal product: SRMC = ∆(wL(Q,K)) / ∆ Q = w (∆Q/∆L)-1 = w / MPL Comparing short and long run Recall

• SRTC = w L (Q; K—) + r K— (i.e., one input fixed) • LRTC = w L(Q) + r K(Q) (i.e., all inputs vary freely)

Consequences of Flexibility • SRTC > LRTC and SRATC > LRATC for all Q • SRMC steeper than LRMC

Scaleability The problem:

• business model works for limited market: certain “lot size,” geographic area, customer type, and so on.

• can it be replicated for broader market?

Success Stories:

• geographic expansion: McDonald’s, Domino’s, Starbucks, AOL • product expansion: GE, Dell, Staples • both: Walmart

Failures:

• professional services, video rentals • grocery delivery (viz., WebVan)

Summary II.

1. Opportunity cost is the relevant notion of economic cost. 2. A profit-maximizing firm will minimize the cost of producing its chosen

level of output. 3. Costs are minimized when the MRTS equals the input price ratio. 4. The input demand functions show how the cost minimizing quantities of

inputs vary with the quantity of the output and the input prices. 5. The short run cost minimization problem solves the firm’s problem when

one or more inputs are fixed. Returns to scale have a counter part in the shape of the cost function captured by degree of “economies of scale.”

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Criticisms of neoclassical economics

Neoclassical economics is sometimes criticised for having a normative bias. In this view, it does not focus on explaining actual economies, but instead on describing a "utopia" in which Pareto optimality obtains. Key assumptions of neoclassical economics which are widely criticized as unrealistic include: The focus on individuals in the economy may obscure analysis of wider long term issues, such as whether the economic system is desirable and stable on a finite planet of limited natural capital. The assumption that individuals act rationally may be viewed as ignoring important aspects of human behavior. Many see the "economic man" as being demonstrably different to a real man on the real earth -- they are not human, and are increasingly criticized for not being human. The assumption of rational expectations which has been introduced in some more modern neo-classical models (sometimes also called new classical) may also be strongly criticized on the grounds of realism. Large corporations might perhaps come closer to the neoclassical ideal of profit maximisation, but this is not necessarily viewed as desirable if this comes at the expense of a "locust-like" neglect of wider social issues. Problems with making the neoclassical general equilibrium theory compatible with an economy that develops over time and includes capital goods. This was explored in a major debate in the 1960s - the Cambridge Capital Controversy - about the validity of neoclassical economics, with an emphasis on the economic growth, capital, aggregate theory, and the marginal productivity theory of distribution. There were also internal attempts by neoclassical economists to extend the Arrow-Debreu model to disequilibrium investigations of stability and uniqueness. However a result known as the Sonnenschein-Mantel-Debreu theorem suggests that the assumptions that must be made to insure that the equilibrium is stable and unique are quite restrictive. In the opinion of some, these developments have found fatal weaknesses in neoclassical economics. Economists, however, have continued to use highly mathematical models, and many equate neoclassical economics with economics, unqualified. Mathematical models include those in game theory, linear programming, and econometrics, many of which might be considered non-neoclassical. So economists often refer to what has evolved out of neoclassical economics as "mainstream economics". Critics of neoclassical economics are divided in those who think that highly mathematical method is inherently wrong and those who think that mathematical method is potentially good even though if contemporary methods have problems. The basic theory about downward sloping aggregate demand curve for any product is criticized for its allegedly too big assumption, that individual consumers have identical preferences which do not change when the wealth of individual changes (some critics of neoclassical claim, that these assumptions are not told for young students until their faith in the discipline is strong enough). In general, allegedly too unrealistic assumptions are one of the most common criticisms towards neoclassical economics. For example, many theories assume perfect knowledge for market actors and the most common theory of finance markets assumes that debts are always paid back and that any actor can raise as much loan as he wants at any given point of time.

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The basic theory of production in neoclassical economics is criticized of assuming wrongly rationales for producers. According to the theory, increasing production costs are the reason for producers not to produce over certain amount. Some empirical counter arguments claim that most of producers in economy are not doing their production decisions in the light of increasing production costs (for example, they often may have additional capacity that could be taken into use, if producing more was desirable). Often at individual levels, variables such as supply and demand, which are independent, are (allegedly wrongly) assumed to be independent also at aggregate level. This criticism has been applied to many central theories of neoclassical economics. Theory of perfect competition is criticized by claiming that it wrongly assumes that demand curve for one firm is flat, while as a matter of fact, it has to be (very) slightly bending, since in that theory, the demand curve for individual firm is a part of aggregate demand curve that is not flat. Taking this into account would ruin the theory. The critique of the assumption of rationality is not confined to social theorists and ecologists. Many economists, even contemporaries, have criticized this vision of economic man. Thorstein Veblen put it most sardonically: lightning calculator of pleasures and pains, who oscillates like a homogeneous globule of desire of happiness under the impulse of stimuli that shift about the area, but leave him intact. Herbert Simon's theory of bounded rationality has probably been the most influential of the heterodox approaches. Is economic man a first approximation to a more realistic psychology, an approach only valid in some sphere of human lives, or a general methodological principle for economics? Early neoclassical economists often leaned toward the first two approaches, but the latter has become prevalent. Neoclassical economics is also often seen as relying too heavily on complex mathematical models, such as those used in general equilibrium theory, without enough regard to whether these actually describe the real economy. Many see an attempt to model a system as complex as a modern economy by a mathematical model as unrealistic and doomed to failure. Famous answer to this criticism is Milton Friedman's claim that theories should be judged by their ability to predict events rather than by the realisticity of their assumptions. Naturally, many claim that neoclassical economics (as well as other branches of economics) has not been very good at predicting events. Critics of neoclassical models accuse it of copying of 19th century mechanics and the "clockwork" model of society which seems to justify elite privileges as arising "naturally" from the social order based on economic competitions. This is echoed by modern critics in the anti-globalization movement who often blame the neoclassical theory, as it has been applied by the IMF in particular, for inequities in global debt and trade relations. They assert it ignores the complexity of nature and of human creativity, and seeks mechanical ideas like equilibrium: And in Poinset's Elements de Statique..., which was a textbook on the theory of mechanics bristling with systems of simultaneous equations to represent, among other things, the mechanical equilibrium of the solar system, Walras found a pattern for representing the catallactic equilibrium of the market system. (William Jaffe).

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VI. Theory of the firm in perfect competition and monopolistic competition 1. Theory of the firm The “theory of the firm” is a relatively modern economic construct and one with several variants. Firms produce goods and provide services and, as such, they play an important part in the supply/demand interaction that characterizes the economic order of non-socialist societies. A business firm’s costs, prices, and economic power naturally matter to theoretical economists as well as to those shaping practical economic policy. Economists since Adam Smith have been committed to the notion that markets allocate resources better than alternative means do.27 One early and popular perception of the modern firm linked the size and structure of business enterprises to the state of technology. Technological advances make new forms of production and organization possible. The productive genius of Henry Ford, for example, was possible because technology made it feasible to mass produce and market automobiles. Advances in transportation, communications, and production technologies in the late nineteenth century invited, if not compelled, the growth of interstate business firms in the United States. Neoclassical economic models could capture the characteristics of perfectly competitive and monopolistic markets as outlined in chapter 2 and 3. Since most industries fit neither model, however, economists also explored the world of imperfectly competitive markets, oligopolistic industries, and “monopolistic competition.” The behaviour and performance of firms in markets with these characteristics cannot be predicted with the certainty of producers in perfectly competitive markets or its monopolistic alternative, but they can be analyzed using the tools of neoclassical economics.28 1.1 Profit maximization and loss minimization The competitive firm tries to maximise profits, given that he is a price taker.29 Price is therefore exogenous and the firm just chooses quantities. It therefore tries to maximise π = pq - c(q) by choice of q, where c(q) is the (total) cost function for the firm.30 From this behaviour the optimization rule can be deducted which states that the marginal revenue of each action must be equal to its marginal cost. Or in other words: At the profit-maximizing level of output, marginal revenue and marginal cost are exactly equal.

27 Garvey, G. E. (2003), page 525-540

28 In many sectors of the economy markets are best described by the term oligopoly - where a few producers dominate the majority of the market and the industry is highly concentrated. In a duopoly two firms dominate the market although there may be many smaller players in the industry.

29 Meaning that the price of the firm’s output is the same regardless of the quantity that the firm decides to produce.

30 A firm’s costs reflect is production process.

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To extend this analysis of profit maximization the cost curves can be considered: The firm’s marginal-cost curve (MC) is upward sloping31, the average-total-cost (ATC) curve is U-shaped. And the marginal-cost curve crosses the average-total-cost curve at the minimum of average total costs.

P = AR = MRP=MR1

MC

Quantity0

Costsand

Revenue

ATC

AVC

QMAX

The firm maximizes profit by producing the quantity at which marginal cost equals marginal revenue.

MC1

Q1

MC2

Q2 Figure 1.1: Profit Maximization for a competitive firm32

The market price (P) equals marginal revenue (MR) and average revenue (AR). At the quantity Q1, marginal revenue MR1 exceeds marginal cost MC1, so raising production increases profit. At the quantity Q2 marginal cost MC2 is above marginal revenue MR2, so reducing production increases profit. The profit maximizing quantity Qmax is found where the horizontal price line intersects the marginal-cost curve.33 1.2 Economies and diseconomies of scale As outlined cost considerations are crucial for a profit maximizing firm. In doing so the considerations of economies of scale are important.34 The shape of the long-run average-total-cost curve (see figure 1.1) conveys important information about technology of producing a good. When long run average cost declines as output increases, there are said to be economies of scale. When long-run average total cost rises as output increases, there are said to be diseconomies of scale. And

31 Under perfect market conditions with the firm being price taker the marginal-revenue equals the

market price. 32 Mankiw, N.G. (1998), p. 296 33 Varian, R. (1984), p. 22-46 34 Adam Smith identified the division of labor and specialization as the two key means to achieve

a larger return on production. Through these two techniques, employees would not only be able to concentrate on a specific task, but with time, improve the skills necessary to perform their jobs and production level increases.

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when long-run average total cost does not change there is said to be constant returns to scale.35

Figure 1.2: Long-run average total cost curve 2. Theory of the firm under perfect competition The degree to which a market or industry can be described as competitive depends in part on how many suppliers are seeking the demand of consumers and the ease with which new businesses can enter and exit a particular market in the long run. The spectrum of competition ranges from highly competitive markets where there are many sellers, each of whom has little or no control over the market price - to a situation of pure monopoly where a market or an industry is dominated by one single supplier who enjoys considerable benefits in setting prices, unless subject to some form of direct regulation by the government. Competitive markets operate on the basis of a number of assumptions. When these assumptions are dropped - we move into the world of imperfect competition. These assumptions are discussed below:36 1) Many suppliers each with an insignificant share of the market – this means that each firm is too small relative to the overall market to affect price via a change in its own supply – each individual firm is assumed to be a price taker. 2) An identical output produced by each firm – in other words, the market supplies homogeneous or standardised products that are perfect substitutes for each other. Consumers perceive the products to be identical. 3) Consumers have perfect information about the prices all sellers in the market charge – so if some firms decide to charge a price higher than the ruling market price, there will be a large substitution effect away from this firm.

35 Mankiw, N.G. (1998), page 284 36 E.g.: Mankiw, G.N. (1998), page 291 following

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4) All firms (industry participants and new entrants) are assumed to have equal access to resources (technology, other factor inputs) and improvements in production technologies achieved by one firm can spill-over to all the other suppliers in the market. 5) There are assumed to be no barriers to entry & exit of firms in long run – which means that the market is open to competition from new suppliers – this affects the long run profits made by each firm in the industry. The long run equilibrium for a perfectly competitive market occurs when the marginal firm makes normal profit only in the long term. 6) No externalities in production and consumption so that there is no divergence between private and social costs and benefits. 2.1 Short Run Price and Output for the Competitive Industry and Firm In the short run the equilibrium market price is determined by the interaction between market demand and market supply. In diagram 1 is shown, that price P1 is the market-clearing price and this price is taken by each of the firms. Because the market price is constant for each unit sold, the AR curve also becomes the Marginal Revenue curve (MR). A firm maximises profits when marginal revenue = marginal cost. In the diagram below, the profit-maximising output is Q1. The firm sells Q1 at price P1. The area shaded is the economic profit made in the short run because the ruling market price P1 is greater than average total cost.37

Figure 2.1: Economic Profit38 Not all firms make supernormal profits in the short run. Their profits depend on the position of their short run cost curves. Some firms may be experiencing sub-normal profits because their average total costs exceed the current market price. Other firms may be making normal profits where total revenue equals total cost (i.e. they are at the break-even output). In diagram 2, the firm shown has high 37 Varian, R. (1984), p. 22-46 38 Mankiw, G.N. (1998), page 285 following

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short run costs such that the ruling market price is below the average total cost curve. At the profit maximising level of output, the firm is making an economic loss.

Diagram 2.2: Economic Loss39

2.2 The Effects of a change in Market Demand Figure 2.3 describes the increase in market demand. This causes an increase in market price and quantity traded. The firm's average revenue curve shifts up to AR2 (=MR2) and the profit maximising output expands to Q2, with the MC curve as the firm's supply curve. Higher prices cause an expansion along the supply curve. Following the increase in demand, total profits have increased. An inward shift in market demand would have the opposite effect.40

Diagram 2.3: Increased Market Demand

39 Mankiw, G.N. (1998), page 285 following

40 The effect of a change in market supply (perhaps arising from a cost-reducing technological innovation available to all firms in a competitive market) is a ceteris paribus consideration not further outlined in this work.

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2.3 The adjustment process of a perfectly competitive industry towards the long run equilibrium

If most firms are making abnormal profits in the short run there will be an expansion of the output of existing firms and new firms might enter the market. Firms are responding to the profit motive and supernormal profits act as a signal for a reallocation of resources within the market. The addition of new suppliers causes an outward shift in the market supply curve, as shown in figure 2.4.41

Figure 2.4: expansion of output Making the assumption that the market demand curve remains unchanged, higher market supply will reduce the equilibrium market price until the price = long run average cost. At this point each firm is making normal profits only. There is no further incentive for movement of firms in and out of the industry and a long-run equilibrium has been established. The entry of new firms shifts the market supply curve to MS2 and drives down the market price to P2. At the profit-maximising output level Q3 only normal profits are being made. There is no incentive for firms to enter or leave the industry. Thus a long-run equilibrium is established.

Figure 2.5: expansion of output42

41 Mankiw, G.N. (1998), page 285 following 42 Mankiw, G.N. (1998), page 285 following

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2.4 Perfect competition and economic efficiency Perfect competition is used to compare with other market structures (such as monopoly and oligopoly) because it displays high levels of economic efficiency. In both the short and long run, price is equal to marginal cost (P=MC) and therefore allocative efficiency43 is achieved – the price that consumers are paying in the market reflects the factor cost of resources used up in producing / providing the good or service. Productive efficiency occurs when price is equal to average cost at its minimum point. This is not achieved in the short run – firms can be operating at any point on their short run average total cost curve, but productive efficiency is attained in the long run because the profit maximising output is achieved at a level where average (and marginal) revenue is tangential to the average total cost curve. The long run of perfect competition, therefore, exhibits optimal levels of static economic efficiency.44

43 Allocative efficiency defines a state where all resources are allocated to their highest valued use

(no other possibility exist where they would make greater profit). Whereas productive efficiency describes a way of producing in the lowest cost manner.

44 Another form of economic efficiency – dynamic efficiency – relates to aspects of market competition such as the rate of innovation in a market, the quality of output provided over time and is not subject to these considerations.

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3. Theory of the firm under monopolistic competition Monopolistic competition is a common market form. Many markets can be considered as monopolistically competitive, often including the markets for books, clothing, films and service industries in large cities. Monopolistically competitive markets have the following characteristics:

• There are many producers and many consumers in a given market. • Consumers have clearly defined preferences and sellers attempt to

differentiate their products from those of their competitors; the goods and services are heterogeneous.

• There are no barriers to entry and exit. The characteristics of a monopolistically competitive market are almost exactly the same as in perfect competition, with the exception of heterogeneous products, and that monopolistic competition involves non-price competition (based on subtle product differentiation). This gives the company influence over the market; it can raise its prices without losing all the customers, owing to brand loyalty. This means that an individual firm's demand curve is downward sloping, in contrast to perfect competition, which has a perfectly elastic demand schedule. A monopolistically competitive firm acts like a monopolist in that the firm is able to influence the market price of its product by altering the rate of production of the product. Unlike in perfect competition, monopolistically competitive firms produce products that are not perfect substitutes. In the short-run, the monopolistically competitive firm can exploit the heterogeneity of its brand so as to reap positive economic profit. In the long-run, distinguishing characteristic that enables one firm to gain monopoly profits will be duplicated by competing firms. This competition will drive the price of the product down and, in the long-run, the monopolistically competitive firm will make zero economic profit. Unlike in perfect competition, the monopolistically competitive firm does not produce at the lowest attainable average total cost. Instead, the firm produces at an inefficient output level, reaping more in additional revenue than it incurs in additional cost versus the efficient output level.45 3.1 Short run price and output for the monopolistic industry and firm In the short run, the monopolistically competitive firm faces limited competition. There are other firms that sell products that are good, but not perfect, substitutes for the firm's own product. In other words: every firm has a monopoly of its own product. When the product is differentiated, that means the firm has some monopoly power, and that means we must use the monopoly analysis, as in Figure 3.1 below.

45 Luis M. B. (2000), page 84-85

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Figure 3.1: short run monopolistic revenues46 We see that, the marginal revenue is less than the price. The firm will set its output so as to make marginal cost equal to marginal revenue, and charge the corresponding price on the demand curve, so that in this example, the monopoly sells 1000 units of output (per week, perhaps) for a price of $85 per unit. But this is just a short run situation. We see that the price is greater than the average cost (which is $74 per unit, in this case) giving a profit of $11,000 per week. This profitable performance will attract new competition in the long run. 3.2 Long Run Price and Output for the Monopolistic Industry and Firm In monopolistic competition, when one firm or product variety is profitable, it will attract more competition -- more substitutes and closer substitutes for the profitable product type. Thus, demand will shift downward and costs will increase. This will go on as long as the firm and its product type remain profitable. A new "long run equilibrium" is reached when (economic) profits have been eliminated. This is shown in Figure 3.2:

Figure 3.2: Long run equilibrium47

46 Mankiw, G.N. (1998), page 291 following 47 Mankiw, G.N. (1998), page 291 following

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In this example, the firm can break even by selling 935 units of output at a price of $76 per unit. The profit -- zero -- is the greatest profit the firm can make, so profit is being maximized with the output that makes MC=MR. Zero (economic) profit is also the condition for long run equilibrium in a p-competitive industry. But this equilibrium is not the ideal that the long run equilibrium in a perfectly competitive industry is. 3.3 Critique of monopolistic competition While monopolistically competitive firms are inefficient, it is usually the case that the costs of regulating prices for every product that is sold in monopolistic competition by far exceed the benefits; the government would have to regulate all firms that sold heterogeneous products - an impossible proposition in a market economy. Another concern of critics of monopolistic competition is that it fosters advertising and the creation of brand names. Critics argue that advertising induces customers into spending more on products because of the name associated with them rather than because of rational factors. This is refuted by defenders of advertising who argue that (1) brand names can represent a guarantee of quality, and (2) advertising helps reduce the cost to consumers of weighing the tradeoffs of numerous competing brands. There are unique information and information processing costs associated with selecting a brand in a monopolistically competitive environment. In a monopoly industry, the consumer is faced with a single brand and so information gathering is relatively inexpensive. In a perfectly competitive industry, the consumer is faced with many brands. However, because the brands are virtually identical, again information gathering is relatively inexpensive. Faced with a monopolistically competitive industry, to select the best out of many brands the consumer must collect and process information on a large number of different brands. In many cases, the cost of gathering information necessary to selecting the best brand can exceed the benefit of consuming the best brand (versus a randomly selected brand). 4. Concluding considerations Based on the assumption of profit maximizing companies was shown that it is impossible for a firm in perfect competition to earn abnormal profit in the long run, which is to say that a firm cannot make any more money than is necessary to cover its costs. If a firm is earning abnormal profit in the short term, this will act as a trigger for other firms to enter the market. They will compete with the first firm, driving the market price down until all firms are earning normal profit. On the other hand, if firms are making a loss, then some firms will leave the industry, reduce the supply and increase the price. Therefore, all firms can only make normal profit in the long run. Perhaps the closest thing to a perfectly competitive market would be a large auction of identical goods with all potential buyers and sellers present. By design, a stock exchange closely approximates this, though there is no way to guarantee

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atomicity. As perfect competition is a theoretical absolute, there are no real-world examples of a perfectly competitive market. Therefore the described model of monopolistic competition is by far closer to reality although it brings suboptimal results. Mainly because the rule of P= MR = MC (price equals marginal revenues equals marginal costs) holds true for a competitive firm only, whereas for a monopoly firm price exceeds marginal costs (P > MR = MC). Concluding it can be said that this theoretical approach assumes profit maximization, but can also be used to show how a change in objectives48 (for example from profit maximisation to revenue maximisation) affects the price and output of a business.

48 Other objectives can be: (1) Satisficing: Satisficing behaviour involves the owners setting minimum acceptable levels of achievement in terms of business revenue and profit e.g. a target rate of growth of sales, or an acceptable rate of return on capital. (2) Sales Revenue Maximisation : Annual salaries and other perks might be more closely correlated with total sales revenue rather than profits. Revenue is maximised when marginal revenue (MR) = zero. (3) Constrained Sales Revenue Maximisation - Shareholders of a business may introduce a constraint on the decisions of managers.

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VII. The theory of oligopoly and monopoly Considerations about market situations very often go about the question under what circumstances markets come to equilibrium. Which market constellations make demand and supply coming together and what prices are accepted by consumers to clear markets appropriate? It can be clearly assumed that the situation of competition between suppliers definitely is a decisive influencing factor. A lot of considerations and reflections are made about markets under condition of perfect competition where many suppliers act on the market. The following reflections concern the constellations of markets under oligopoly and monopoly conditions where just one or a few actors supply customers demand. 1. Monopoly 1.1 General consideration about monopoly constellation A monopoly is an industry in which there is one seller. Because it is the only seller, the monopolist faces a downward-sloping demand curve, the industry demand curve. The downward-sloping demand curve means that if the monopolist wants to sell more, it must lower its price. (assuming that price discrimination is not possible; that the firm can charge only one price.) Because the monopolist must lower price to sell more, the extra or marginal revenue it gets from selling another unit is less than the price it charges. Thus, its marginal revenue curve lies below its demand curve. In contrast, for a seller who is a price taker, demand is identical with marginal revenue. A first approach to the case of monopoly is shown by the following table. Marginal cost is the value of the additional resources needed to produce another unit of output. The marginal benefit to consumers is the price that consumers are willing to pay for each unit. This column should be recognized as a demand curve. The maximization principle leads to the fact that the economically efficient amount to produce is five, the amount that gives consumers the greatest value. To produce the first unit, the firm takes resources that have a value of 100 and turns them into something with a value of 121. Because this transformation has increased value, producing the first unit is more economically efficient than producing none. By this logic, producing the sixth unit would decrease economic efficiency because the firm would take resources with a value of 100 and transform them into something with a value of only 98. Table: Example of monopoly constellation Output Marginal Cost Marginal benefit buyers Marginal benefit sellers 1 100 121 121 2 100 116 111 3 100 111 106 4 100 108 105 5 100 101 94 6 100 98 95

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The monopolist, however, will find it most profitable to produce only four units because it does not see marginal benefit the same way that buyers see it. For the seller, the extra benefit of the second unit is only 111. It sells the second unit for 116, but to sell the second unit, it had to reduce the price it charged by 5. Thus, it "lost" 5 money units on the first unit, so the net increase in its revenue was only 111. Using the maximization principle, one can see that producing beyond the fourth unit is not in the interests of the firm. The fifth unit brings in added benefits of only 94 to the firm (it sells for 101, but to sell it, the firm lowers price on other units), but costs an added 100. From the point of view of the buyers, however, the fourth unit should be produced. It brings them more added benefits than it uses resources. The discussion above is illustrated below. The seller attempts to set marginal cost equal to marginal revenue, or to produce at q0. From the consumers' viewpoint, the best amount to produce would be q1. The monopolist restricts output because of a divergence between marginal benefit as the firm perceives it and marginal benefit as buyers perceive it. Producing beyond q0 is not in the interests of the firm because the extra benefit it sees, the marginal revenue curve, is less than the extra cost of production, shown by the marginal cost curve. Extra output is in the interests of buyers because the extra benefit they get, shown by the demand curve, is greater than the extra costs of production.

In terms of the production-possibilities frontier shown below, an economy with some industries competitive (all transactors are price takers) and others monopolized (sellers are price searchers) will produce at point b. However, consumers would be better off at point a because the gain of x amount of monopolized goods has a greater value than the loss of y amount of competitive goods. Because a monopolist restricts production from what a competitive industry would do, too many resources are being used in the competitive industry and not enough in the monopolized industry. Thus, the existence of monopoly violates product-mix efficiency. Because marginal rates of substitution are not equal to marginal rates of transformation, the economy produces the wrong mix of products.

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The unexploited value of monopoly leads to two questions. First, one can ask whether people have found ways to capture this value. Because the search for value occupies a great deal of people's talents and energies in a market economy, it should not surprise us to learn that there is a commonly-used way to capture this value. Sellers can capture it with price discrimination. Second, one can ask if the government can eliminate the unexploited value with some sort of intervention. Economists have suggested two important ways for the government to intervene, through antitrust actions and through regulation. 1.2 Amoroso-Robinson equation As shown above the effect of price elasticity gets very important under monopoly constellation, where suppliers manage prices and lead their output to maximum or optimum profit. The supplying company has to think about price elasticity of demand by changing output and output prices. Price elasticity of demand in this case can be seen as aggregated consumption equation. How much does demand increase or decrease if prices are lowered or rose by one percent? So profit can be only upgraded by increased prices if elasticity is not that high to cause a lowered output making the sum of sales shrink below the price-surplus effect. The availability of goods end especially of substitute products always has effect on elasticity so under monopoly constellation (without adequate substitutes) elasticity is lower than under constellation with many suppliers. Essentially price elasticity of demand lies 1 over price elasticity of sales, so price elasticity of sales goes to 0 if price elasticity of demand goes 1. It seems to lead to extreme account of sales if elasticity of sales is 0. Leading to an equation the price (p) elasticity (E) of sales (U) EU,p can be transformed into the following terms:

[1]

[2]

[3]

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[4]

[5]

[6]

[7]

[8]

At last [8] the equation of Amoroso-Robinson leads to the marginal revenue and answers the question how much sales grow with another output unit x. In combination with marginal costs the equation leads to Cournot’s point at the price-sales function which marks companies optimal sales. The price-sales function under monopoly constellation can be seen as function of customers demand for the good supplied by the monopolist. Because of this all theoretical considerations about households demand can be derived.

Because of the monopolists possibility to use prices as variables for action – without risk to lose all turnouts by raising prices like under competition constellation – the monopolist can be seen as price decision maker in comparison (to competitive constellation) to an output decision maker.

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2. Oligopoly 2.1 General consideration about oligopoly (duopoly) constellation An oligopoly is a market form in which a market is dominated by a small number of sellers (oligopolists). The word is derived from the Greek for few sellers. Because there are few participants in this type of market, each oligopolist is aware of the actions of the others. Oligopolistic markets are characterised by interactivity. The decisions of one firm influence, and are influenced by, the decisions of other firms. Strategic planning by oligopolists always involves taking into account the likely responses of the other market participants. An oligopoly is a form of economy. As a quantitative description of oligopoly, the four-firm concentration ratio is often utilized. This measure expresses the market share of the four largest firms in an industry as a percentage. Using this measure, an oligopoly very often is defined as a market in which the four-firm concentration ratio is above 40%. The problem of interdependence has thwarted economists' attempts to develop a good theory of oligopoly. When there are only a few sellers, each recognizes that his decisions affect others who may react to what he does. This problem of interdependence can be shown in terms of game theory in a situation that is identical to the prisoners' dilemma. The table below shows the pricing options of the only two gas stations in an isolated town. The payoffs in the center are profits. If both stations charge high prices, the joint profits are maximized. But then each has a temptation to cut prices to get to a more favorable corner. If one of them gives in to this temptation, it may start a gas price war as the other firm must retaliate. They then end in the least favorable position of lowest joint profits. Table: Oligopoly (Duopoly) as prisoner’s dilemma Supplier 1 Pricing strategy 100% 90%

Opponent 100/100 10/130 Supplier 130/10 20/20

There may be no equilibrium solution in a situation of this sort. Rather, there may be a period of collusion in which firms agree (though it may be an unspoken agreement) to keep prices high. Then, the collusion may disintegrate as firms begin cheating and finally a new period of collusion may begin. Whether sellers collude or compete will depend on many factors that can be difficult to measure and put into a theory, such as the number of sellers, their personalities, whether they have equal or unequal shares of the market, whether their costs are the same, the ease of cheating and of detecting cheating, and whether the sellers can compete on nonprice bases such as service and quality. A thorough examination of the possibilities of oligopolistic strategies and how well they fit observed behavior of real-world oligopolies is a large and controversial subject that is beyond the scope of these readings. The important point concerning economic efficiency is that if oligopolists perceive their demand curves as downward-sloping (that is, if they take into account that the amount they produce will have a significant effect on the price they can charge), their

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marginal revenue curves will lie below their demand curves and they will restrict output relative to what an industry of price takers would. Thus, there will be an efficiency loss involved. Most economists use the term "market power" to describe the ability of any price maker to set price. When the possession of market power is profitable, it should attract new entrants into the industry. If entry is easy, then the existence of very few or even only one firm may not result in economic inefficiency. The threat of potential entry may be enough competition to keep the industry operating at or close to the competitive solution. In this case, the market is a contestable market. However, if entry is not easy but there are significant barriers to entry, the threat of competition is less. Barriers to entry exist when there are sunken costs-expenses that cannot be recovered once a firm has entered the industry. Where these costs are high, the industry probably operates as the theory of monopoly suggests it will. 2.2 Approaches to oligopoly theory (exemplarily Cournot, von Stackelberg) There are two general types of theories for oligopoly. Conjectural Variation Models on one hand and Limit Pricing Models on the other. In conjectural variation models the firms in the industry are taken as given and each firm makes certain assumptions about what the others reactions will be to its own actions. For example, in the Cournot model each firm assumes there will be no reaction on the part of the other firms. In the limit price models one firm chooses its action taking into account the possible entry or exit of competitive to or from the market. In the Cournot Model each firm presumes no reaction on the part of the other firms to a change in its output. Thus, ∂Q/∂qi = 1. Therefore the first order condition for a maximum profit of the i-th firm is: p0 - b*(Qoi + 2qi) = Ci1 where Qoi is the output of the firms other than the i-th. When this is solved for qi the result is: qi = (p0 - Ci1)/2b - Qoi/2 However it is more convenient to represent the first order condition and its solution as: p0 - b*(Q + qi) = Ci1 and qi = (p0 - Ci1)/b - Q. Now we can sum the above equation over the n firms. The result is: Q = n(p0/b) - C1/b - n*Q where C1 is the sum of the Ci1. The solution for Q is: Q = [n/(n+1)](p0/b) - [1/(n+1)]C1/b When this output is substituted into the inverse demand function the result is:

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p = [1/(n+1)]p0 + [1/(n+1)]C1 or if we let c1=C1/n: p = [1/(n+1)]p0 + [n/(n+1)]c1 where c1 represents the average of the marginal costs of the n firms. It can be seen from the last term that as the number of firms increase without bound the market price approaches c1. If one follow through with this model one would have to take in consideration that the firms with above average marginal cost would be making a loss on variable costs and would cease production. Heinrich von Stackelberg proposed a model of oligopoly in which one firm, a follower, takes the output of the other firm as given (a Cournot type oligopolist) and adjusts its output accordingly. The other firm, a leader, takes into account the adjustment which the follower firm will make. The output decision of a Cournot oligopolist is given by the equations above. Thus if a leader firm increases its output qL by 1 unit the follower firm will decrease its output by one half of a unit. The term ∂Q/∂qL = 1/2 for the leader firm so the first order condition for the leader firm is: ∂UL/∂qL = (p0 - b*Q) -b*(1/2)*qL - CL1 = 0 qL = (p0 - CL1)(2/3b) - 2QoL/3. Carrying through with the analysis as shown below indicates that the market price will be: p = [1/(n+2)]p0 + [(n+1)/(n+2)]c1 where c1 is now the weighted average of the marginal costs of the firm with all of the follower firms given an equal weight and the leader firm given a weight of twice that of the follower firms. The leader firm has the effect on the industry of two follower firms. Otherwise the result is the same as in the case of the Cournot oligopoly.

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VIII. Input markets Market Definition: A market is, as defined in economics, a social arrangement that allows buyers and sellers to discover information and carry out a voluntary exchange. Along with a right to own property, it is one of the two key institutions that organize trade. The existence of markets is one of the key components of capitalism. Though markets are often viewed as being located in a physical marketplace that allow a face-to-face meeting, markets may exist in any medium that allows social interaction, such as through mail or over the Internet. Structure: The information function of a market requires, at a minimum, that the buyer and seller are both aware of what is being sold and if a voluntary transaction is possible. Economic models assume that such knowledge is perfect, including in knowledge of alternatives and other factors affecting the proposed sale/purchase. Markets rely on adjustments to price to coordinate individual decision making relating to supply and demand. For example, suppose that more buyers want a certain good than is available from sellers at a given price. The solution requires either that buyer reduce their demand for the good, or that sellers produce more of the good. These results are accomplished by a rise in the price of that good: some buyers will refuse to pay the higher price, while more sellers are willing to offer the good for the increased price. In cases where more of an item is available than people will buy, the reverse effect (a drop in price) will make the choices of buyers and sellers compatible. Markets are thus efficient, in the economic sense, in that the buyers who value a good most highly will buy from sellers most willing to sell. While barter markets exist, most markets require the existence of currency or other form of money. An economic system in which goods and services (and resources required to produce those goods and services) are mediated by markets is called a market economy. Critics of the market economy have tried or proposed a command economy or other non-market economy. The attempt to mix socialism with the incentives created by a market is known as market socialism, which includes the relatively recent socialism with Chinese characteristics, though some argue that socialism and markets are fundamentally incompatible. Input Markets Definition: Input markets are markets for goods and services needed in a production process. On a higher level, there are two different kinds of inputs in a production process: 1. Production factors and 2. Preliminary product; these products have mostly been produced with other

production factors themselves

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Production factors In the classical economics, the factors work, capital, ground and knowledge are designated as production factors (since Adam Smith and David Ricardo) The factor work is represented by the individual human being. Primarily the factor ground referred the farmland. Later it was extended to all kinds of natural resources like crude oil, minerals etc. Because of the increasing shortage of production factors like water and other commodities this production factor is just called nature. The production of all goods starts with the production factor nature. But there are no ready for use goods in the nature; there are just commodities witch have been made converted first and there is work needed for this conversion. Times by time people have learned to multiply their power by using tools and machines. These production factors are called capital. Unlike nature, capital is called a derivative production factor or producing production factor. Some economist means that knowledge and information should also be added to the production factors. The Five Capitals Model The Five Capitals Model of sustainable development was developed by the organization Forum for the Future. The model groups together:

Natural capital Social capital Human capital Manufactured capital Financial capital

Preliminary product Preliminary products are measuring the value of the used, transformed and processed goods and services. Factors of production Factors of production are resources used in the production of goods and services in economics. Classical economics distinguishes between three factors:

Land or natural resources naturally-occurring goods such as oil and minerals that are used in the creation of products. The payment for land is rent.

Labour - human effort used in production which also includes technical and marketing expertise. The payment for labour is a wage.

Capital goods human-made goods (or means of production) which are used in the production of other goods. These include machinery, tools and buildings. In a general sense, the payment for capital is called interest.

These were codified originally in the analyses of Adam Smith, 1776, David Ricardo, 1817, and the later contributions of Karl Marx and John Stuart Mill as part of one of the first coherent theories of production in political economy. Marx refers in “Das Kapital” to the three factors of production as the "holy trinity" of political economy.

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In the classical analysis, working capital was generally viewed as being a stock of physical items such as tools, buildings and machinery. This view was explicitly rejected by Marx. Modern economics has become increasingly uncertain about how to define and theorise capital. With the emergence of the knowledge economy, more modern analysis often distinguishes this physical capital from other forms of capital such as "human capital" and Intellectual Capital which require intangible management orientated techniques to manage such as Balanced Scorecard, Risk Management, Business Process Reengineering, Knowledge Management, and Intellectual Capital Management Prior to the Information Age the land, labour, and capital were used to create substantial wealth due to their scarcity. Following the Information Age (circa 1971-1991), and the Knowledge Age (circa 1991 to 2002) and the current Intangible Economy (circa 2002+) the primary factors of production today are intangible. These factors of production are knowledge, collaboration, process-engagement, and time quality. According to economic theory, a "factor of production" is used to create value and economic performance. As the four factors of production today are all intangible, the current economic age is called the Intangible Economy. Intangible factors of production are subject to network effects and the contrary economic laws such as the law of increasing returns. It is therefore important to differentiate between convetional (tangible) economics and intangible economics when discussing issues related to factors of production which change according to the economic era that society is experiencing. For example, land was a key factor of production in the Agricultural Age. Some economists mention enterprise, entrepreneurship, individual capital or just "leadership" as a fourth factor. However, this seems to be a form of labor or "human capital." When differentiated, the payment for this factor of production is called profit. This is when entrepreneurs think of ideas, organise the other three factors of production, and take risks with their own money and the financial capital of others. In a market economy, entrepreneurs combine land, labor, and capital to make a profit. In a planned economy, central planners decide how land, labor, and capital should be used to provide for maximum benefit for all citizens. The classical theory, further developed, remains useful to the present day as a basis of microeconomics. Some more means that deal with factors of production are as follows: Entrepreneurs are people who organize other productive resources to make goods and services. The economists regard entrepreneurs as a specialist form of labor input. The success and/or failure of a business often depends on the quality of entrepreneurship. Capital has many meanings including the finance raised to operate a business. Normally though, capital means investment in goods that can produce other goods in the future. It can also be referred to as machines, roads, factories, schools, and office buildings in which humans produced in order to produce other goods and services. Investment is important if the economy is to achieve economic growth in the future. Human Capital is the quality of labour resources which can be improved through investments, education, and training. Fixed Capital this includes machinery, work plants, equipment, new technology, factories, buildings, and goods that are designed to increase the productive potential of the economy for future years.

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Working Capital this includes the stocks of finished and semi-finished goods that we be economically consumed in the near future or will be made into a finished consumer good in the near future. Human capital Human capital is a way of defining and categorizing peoples' skills and abilities as used in employment and as they otherwise contribute to the economy. Many early economic theories refer to it simply as labour, one of three factors of production, and consider it to be a commodity -- homogeneous and easily interchangeable. Other conceptions of labour are more sophisticated. Knowledge and capital The introduction of the term is explained and justified by the unique characteristics of knowledge. Unlike physical labour (and the other factors of production), knowledge is: Expandable and self generating with use: as doctors get more experience; their knowledge base will increase, as will their endowment of human capital. The economics of scarcity is replaced by the economics of self-generation. Transportable and shareable: knowledge is easily moved and shared. This transfer does not prevent its use by the original holder. However, the transfer of knowledge may reduce its scarcity-value to its original possessor. Human capital and labour power In some way, the idea of "human capital" is similar to Karl Marx's concept of labour power: to him, under capitalism workers had to sell their labour-power in order to receive income (wages and salaries). But long before Mincer or Becker wrote, Marx pointed to "two disagreeably frustrating facts" with theories that equate wages or salaries with the interest on human capital. Classical view as the base of microeconomic theory Although it did not deal substantially with complex issues of a sophisticated modern economy, the classical theory is useful as the basis of microeconomics, however many distinctions one cares to make or macro-theory or political economy one chooses to apply to trade them off or set their valuations in society at large. Land has become natural capital, imitative aspects of Labour have become instructional capital, creative or inspirational aspects or "Enterprise" have become individual capital (in some analyses), and social capital has become increasingly important. The classical relationship of financial capital and infrastructural capital is still recognized as central, but there is a wider debate on means of production and various means of protection, or „rights", to secure their reliable use. Resource-based view The Resource-Based View (RBV) is an economic tool used to determine the resources available to a firm, which ought to be exploited in order for that firm to develop a strategy for achieving sustainable competitive advantage. Barney

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(1991) formalised this theory, although it was Wernerfelt (1984) who introduced the idea of resource position barriers being roughly analogous to entry barriers in the positioning school. The key points of the theory are: 1) Identify the firm’s potential key resources 2) Evaluate whether these resources fulfil the following criterion: Valuable - they enable a firm to implement strategies that improve its efficiency and effectiveness 1) Rare - not available to other competitors 2) Imperfectly imitable - not easily implemented by others 3) Non-substitutable - not able to be replaced by some other non-rare resource Definitions Resources: Firm resources include all assets, capabilities, organizational processes, firm attributes, information, knowledge, etc. controlled by a firm that enable the firm to conceive of and implement strategies that improve its efficiency and effectiveness. (Barney) (Resources are inputs into a firm's production process, such as capital, equipment, the skills of individual employees, patents, finance, and talented managers. Resources are either tangible or intangible in nature. (Kay) Competitive advantage: A firm achieves competitive advantage when it is able to implement a “value creating strategy not simultaneously being implemented by any current or potential competitors (Barney) Criticisms Priem and Butler made four key criticisms: 1) The RBV is tautological 2) Different resource configurations can generate the same value for firms

and thus would not be competitive advantage 3) The role of product markets is underdeveloped in the argument 4) The theory has limited prescriptive implications Further criticisms are: It is perhaps difficult (if not impossible) to find a resource which satisfies all of the Barney's VRIN criterion. There is the assumption that a firm can be profitable in a highly competitive market as long as it can exploit advantageous resources, but this may not necessarily be the case. It ignores external factors concerning the industry as a whole; Porter’s Industry Structure Analysis ought also be considered. Cost-of-production theory of value In economics, the cost-of-production theory of value is the belief that the value of an object is decided by the resources that went into making it. The cost can be

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composed of any of the factors of production including labour, capital, land, or technology. Two of the most common cost-of-production theories are the medieval just price theory and the classical labour theory of value. The labour theory of value, which interprets labour-value as the determinant of prices, was first developed by Adam Smith and later expanded by David Ricardo and Karl Marx. Most classical economists (as well as nearly all Marxists) subscribe to it. However, Marx's theory is not a true cost-of-production theory since the value of a commodity contains a component of surplus value unrelated to the physical cost of producing it. The magnitude of this surplus value may be unrelated to production-costs. A somewhat different theory of cost-determined prices is provided by the "neo-Ricardian school" of Piero Sraffa and his followers. The most common counterpoint to this is the marginal theory of value which asserts that economic value is set by the consumer's marginal utility. This is the view most commonly held by the majority of contemporary mainstream economists. The Polish economist Michał Kalecki distinguished between sectors with "cost-determined prices" (such as manufacturing and services) and those with "demand-determined prices" (such as agriculture and raw material extraction). In microeconomics, production is the act of making things, in particular the act of making products that will be traded or sold commercially. Production decisions concentrate on what goods to produce, how to produce them, the costs of producing them, and optimising the mix of resource inputs used in their production. This production information can then be combined with market information (like demand and marginal revenue) to determine the quantity of products to produce and the optimum pricing. Production theory basics In microeconomics, Production is simply the conversion of inputs into outputs. It is an economic process that uses resources to create a commodity that is suitable for exchange. This can include manufacturing, storing, shipping, and packaging. Some economists define production broadly as all economic activity other than consumption. They see every commercial activity other than the final purchase as some form of production. Production is a process, and as such it occurs through time and space. Because it is a flow concept, production is measured as a “rate of output per period of time”. There are three aspects to production processes:

the quantity of the commodity produced, the form of the good produced, the temporal and spatial distribution of the commodity produced.

A production process can be defined as any activity that increases the similarity between the pattern of demand for goods, and the quantity, form, and distribution of these goods available to the market place.

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IX. General equilibrium

General Equilibrium (linear) supply and demand curves. This diagram is based on Walras' analysis.

Introduction

General equilibrium theory is a branch of theoretical microeconomics. It seeks to explain production, consumption and prices in a whole economy. General equilibrium tries to give an understanding of the whole economy using a bottom-up approach, starting with individual markets and agents. Macroeconomics, as developed by the Keynesian economists, uses a top-down approach where the analysis starts with larger aggregates. Since modern macroeconomics has emphasized microeconomic foundations, this distinction has been slightly blurred. However, many macroeconomic models simply have a 'goods market' and study its interaction with for instance the financial market. General equilibrium models typically model a multitude of different goods markets. Modern general equilibrium models are typically complex and require computers to help with numerical solutions. In a market system, the prices and production of all goods, including the price of money and interest, are interrelated. A change in the price of one good, say bread, may affect another price, for example, the wages of bakers. If bakers differ in tastes from others, the demand for bread might be affected by a change in bakers' wages, with a consequent effect on the price of bread. Calculating the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the millions of different

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Introduction in general equilibrium theory / The Walras-Cassel system

The "Walras-Cassel" model refers to the general equilibrium model with production introduced in Léon Walras's Elements of Pure Economics (1874). The Walrasian model fell into disuse soon after 1874 as general equilibrium theorists, particularly in the 1930s in the English-speaking world, opted for the Paretian system. The Walrasian model was resurrected in Gustav Cassel's Theory of Social Economy (1918), but even after that, its analysis was confined to the German-speaking world, notably in the Vienna Colloquium in the 1930s, where it was corrected and expanded by Abraham Wald (1936). It only really broke through the English-speaking barrier in the 1950s, when there was a resurgence of interest in general equilibrium with linear production technology and existence of equilibrium questions. However, in the dextrous hands of Arrow, Debreu, Koopmans and the Cowles Commission, the Walras-Cassel model was quickly replaced by the more nimble "Neo-Walrasian" model, which fused aspects of Walrasian and Paretian traditions. As outlined by Walras, the basics of the model are the following: individuals are endowed with factors and demand produced goods; firms demand factors and produce goods with a fixed coefficients production technology. General equilibrium is defined as a set of factor prices and output prices such that the relevant quantities demanded and supplied in each market are equal to each other, i.e. both output and factor markets clear. Competition ensures that price equal cost of production for every production process in operation. Despite its superficial resemblance to some elements of Classical Leontief-Sraffa models (e.g. fixed production coefficients, price-cost equalites, steady-state growth, etc.), the Walras-Cassel model is inherently and completely Neoclassical. Equilibrium is still identified where market demand is equal to market supply in all markets rather than being conditional on replication and cost-of-production conditions. The Walras-Cassel model yields a completely Neoclassical subjective theory of value based on scarcity, rather than a Classical objective theory of value based on cost. Furthermore, in the Walras-Cassel system equilibrium prices and quantites are only obtained jointly by solving the system simultaneously, whereas the Classicals would solve for prices and quantities separately. It might be worthwhile to run down a quick preliminary description of the Walras-Cassel model in order to get up the intuition for what is to follow. Let v denote factors, x denote produced outputs, w be factor prices and p denote output prices. Individuals are endowed with factors and desire produced outputs. They decide upon their supply of factors (which we call F(p, w)) and their demand for outputs (which we call D(p, w)) by solving their utility-maximizing problem. Firms have no independent objective function: they mechanically take the factors supplied to them by consumers and convert them to the produced goods the consumers desire via a fixed set of production coefficients, which we denote B. We face two further sets of equations which form the heart of the Walras-Cassel system: one set makes factor supply equal to factor demand by firms ("factor market clearing") and is written as v = B¢ x; a second set says that the output

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price equals cost of production for each production process ("perfect competition") and is written p = Bw. We shall refer to both of these as the linear production conditions of the Walras-Cassel model. It is important to note that these are not functions, but rather equilibrium conditions. Notice then what is given: consumer's preferences (utility), endowments of factors and production technology. From these components we should be able to derive in equilibrium: (1) factor prices, w*; (2) output prices, p*; (3) quantity of factors, v* and (4) quantity of produced outputs, x*. An equilibrium is defined when these components are such that (1) households maximize utility; (2) firms do not violate perfect competition; (3) factor and output markets clear. The four sets of equations we have outlined connect the entire system together in equilibrium. Their functions can be outlined as follows: (i) D(p, w) connects output prices and output quantities; (ii) F(p, w) connects factor prices and factor quantities; (iii) v = B¢ x connects output quantities and factor quantities; (iv) p = Bw connects output prices and factor prices. To ground our intuition more clearly, we can appeal to Figure 1, where we schematically depict the logic of the Walras-Cassel equations. Heuristically speaking, suppose we have two markets, one for factors (on the left) and one for outputs (on the right). Note that supply of factors F(p, w) on the left is upward-sloping with respect to factor prices w, while demand for outputs D(p, w) on the right is downward-sloping with respect to output prices p. The elasticities of factor supply and output demand curves reflect the impact of prices and wages on household utility-maximizing decisions. [Two caveats: firstly, yes, these are all supposed to be vectors and, yes, Figure 1 makes no sense in that context; but the diagram is merely a heuristic device, not a graphical depiction of the true model; secondly, the output demand function is also a function of w and the factor supply function is also a function of p, so there is interaction between the diagrams which will cause the curves to shift around; for simplicity, we shall suppress these cross-effects by assuming that factor supplies do not respond to p and output demands do not respond to w.]

Figure 1 - Schematic Depiction of the Walras-Cassel Model It is important to note how the factor supply and output demand decisions of households sandwich this entire problem, with the linear production conditions sitting passively in the middle. Fixing any one of the four items (w, p, x or v) at

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its equilibrium value, we can determine the rest [although to do so, we must assume that output demand and factor supply functions are invertible: e.g. given v, we can determine what w is by the factor supply function F(p, w) and given x, we can determine what p by the output demand function D(p, w); naturally, this is a very strong assumption and not a very clear one in the manner it is stated].

It might be worthwhile to go through it "algorithmically" from some starting point (trace this with the arrows in Figure 1). Suppose equilibrium output prices, p*, are given. From p*, we get x* by the output demand function D(p, w) and we obtain w* by the competition condition p = Bw. In their turn, x* gives us v* via the factor market clearing condition v = B¢ x while w* gives us v* via the factor supply function, F(p, w). If this is truly equilibrium, then it had better be that the v*s computed via the two different channels are identical to each other. Equivalently, suppose we start from equlibrium output demands, x*. Thus, given x*, we get p* by the output demand function D(p, w) and v* by the factor market clearing condition v = B¢ x. In their turn, p* gives us w* by the competition condition p = Bw and v* gives us w* by the factor supply function F(p, w). For equilibrium, we need it that both of the w* are the same. We go through analogous stories when we start with equilibrium factor quantities, v*, or equilibrium factor prices, w*. The main lesson is this: in the Walras-Cassel system, there is no necessary direction of determination from one thing to another. The Walras-Cassel system is a completely simultaneous system where equilibrium prices (w*, p*) and equilibrium quantities (v*, x*) are determined jointly. It does not matter whether we say "prices determine cost of production" or "cost of production determines prices", etc. In equilibrium, price equals cost of production, but this is obtained as a solution to a simultaneous system, not by causal direction. The only exogenous data are preferences of households, endowments and technology. Properties and characterization of general equilibrium Basic questions Basic questions in general equilibrium analysis are concerned with the conditions under which an equilibrium will be efficient, which efficient equilibria can be achieved, when an equilibrium is guaranteed to exist and when the equilibrium will be unique and stable. First Fundamental Theorem of Welfare Economics

The first theorem states that any equilibrium is Pareto efficient

The technical condition for the result to hold is the fairly weak one that consumer preferences are locally nonsatiated, which rules out a situation where all commodities are "bads". Additional implicit assumptions are that consumers are rational, markets are complete, there are no externalities and information is perfect. While these assumptions are certainly unrealistic, what the theorem

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basically tells us is that the sources of inefficiency found in the real world are not due to the decentralized nature of the market system, but rather have their sources elsewhere. Second Fundamental theorem of welfare economics

While every equilibrium is efficient, it is clearly not true that every efficient allocation of resources will be an equilibrium. However, the Second Theorem states that every efficient allocation can be supported by some set of prices. In other words all that is required to reach a particular outcome is a redistribution of initial endowments of the agents after which the market can be left alone to do its work. This suggests that the issues of efficiency and equity can be separated and need not involve a trade off. However, the conditions for the Second Theorem are stronger than those for the First, as now we need consumers' preferences to be convex (convexity roughly corresponds to the idea of diminishing marginal utility, or to preferences where "averages are better than extrema"). Existence

Even though every equilibrium is efficient, neither of the above two theorems say anything about the equilibrium existing in the first place. To guarantee that an equilibrium exists we once again need consumer preferences to be convex (although with enough consumers this assumption can be relaxed both for existence and the Second Welfare Theorem). Similarly, but less plausibly, feasible production sets must be convex, excluding the possibility of economies of scale. Proofs of the existence of equilibrium generally rely on fixed point theorems such as Brouwer fixed point theorem or its generalization, the Kakutani fixed point theorem. In fact, one can quickly pass from a general theorem on the existence of equilibrium to Brouwer’s fixed point theorem. For this reason many mathematical economists consider proving existence a deeper result than proving the two Fundamental Theorems. Uniqueness

Although generally (assuming convexity) an equilibrium will exist and will be efficient the conditions under which it will be unique are much stronger. While the issues are fairly technical the basic intuition is that the presence of wealth effects (which is the feature that most clearly delineates general equilibrium analysis from partial equilibrium) generates the possibility of multiple equilibria. When a price of a particular good changes there are two effects. First, the relative attractiveness of various commodities changes, and second, the wealth distribution of individual agents is altered. These two effects can offset or reinforce each other in ways that make it possible for more than one set of prices to constitute an equilibrium. A result known as the Sonnenschein-Mantel-Debreu Theorem states that the aggregate (excess) demand function inherits only certain properties of individual's

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demand functions, and that these (Continuity, Homogeneity of degree zero, Walras' law, and boundary behavior when prices are near zero) are not enough to guarantee uniqueness. There has been much research on conditions when the equilibrium will be unique, or which at least will limit the number of equilibria. One result states that under mild assumptions the number of equilibria will be finite (see Regular economy) and odd (see Index Theorem). Furthermore if an economy as a whole, as characterized by an aggregate excess demand function, has the revealed preference property (which is a much stronger condition than revealed preferences for a single individual) or the gross substitute property then likewise the equilibrium will be unique. All methods of establishing uniqueness can be thought of as establishing that each equilibrium has the same positive local index, in which case by the index theorem there can be but one such equilibrium. Determinacy

Given that equilibria may not be unique it is of some interest whether any particular equilibrium is at least locally unique. This means that comparative statics can be applied as long as the shocks to the system are not too large. As stated above in a Regular economy equilibria will be finite, hence locally unique. One reassuring result, due to Debreu, is that "most" economies are regular. However recent work by Michael Mandler (1999) has challenged this claim. The Arrow-Debreu model is neutral between models of production functions as continuously differentiable and as formed from (linear combinations of) fixed coefficient processes. Mandler accepts that, under either model of production, the initial endowments will not be consistent with a continuum of equilibria, except for a set of Lebesgue measure zero. However, endowments change with time in the model and this evolution of endowments is determined by the decisions of agents (e.g., firms) in the model. Agents in the model have an interest in equilibria being indeterminate: "Indeterminacy, moreover, is not just a technical nuisance; it undermines the price-taking assumption of competitive models. Since arbitrary small manipulations of factor supplies can dramatically increase a factor's price, factor owners will not take prices to be parametric." (Mandler 1999, p. 17) When technology is modeled by (linear combinations) of fixed coefficient processes, optimizing agents will drive endowments to be such that a continuum of equilibria exist: "The endowments where indeterminacy occurs systematically arise through time and therefore cannot be dismissed; the Arrow-Debreu model is thus fully subject to the dilemmas of factor price theory." (Mandler 1999, p. 19) Critics of the general equilibrium approach have questioned its practical applicability based on the possibility of non-uniqueness of equilibria. Supporters have pointed out that this aspect is in fact a reflection of the complexity of the real world and hence an attractive realistic feature of the model. Stability

In a typical general equilibrium model the prices that prevail "when the dust settles" are simply those that coordinate the demands of various consumers for

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various goods. But this raises the question of how these prices and allocations have been arrived at and whether any (temporary) shock to the economy will cause it to converge back to the same outcome that prevailed before the shock. This is the question of stability of the equilibrium, and it can be readily seen that it is related to the question of uniqueness. If there are multiple equilibria then some of them will be unstable. Then, if an equilibrium is unstable and there is a shock, the economy will wind up at a different set of allocations and prices once the converging process completes. However stability depends not only on the number equilibria but also on the type of the process that guides price changes (for a specific type of price adjustment process see Tatonnement). Consequently some researchers have focused on plausible adjustment processes that will guarantee system stability, that is, prices and allocations always converging to some equilibrium, though when there exists more than one, which equilibrium it is will depend on where one begins. Problems and computeable Unresolved problems in general equilibrium

Research building on the Arrow-Debreu model has revealed some problems with the model. The Sonnenschein-Mantel-Debreu results show that, essentially, any restrictions on the shape of excess demand functions are stringent. Some think this implies that the Arrow-Debreu model lacks empirical content. At any rate, Arrow-Debreu equilibria cannot be expected to be unique, or stable. A model organized around the tatonnement process has been said to be a model of a centrally planned economy, not a decentralized market economy. Some research has tried, not very successfully, to develop general equilibrium models with other processes. In particular, some economists have developed models in which agents can trade at out-of-equilibrium prices and such trades can affect the equilibria to which the economy tends. Particularly noteworthy are the Hahn process, the Edgeworth process, and the Fisher process. The data determining Arrow-Debreu equilibria include initial endowments of capital goods. If production and trade occur out of equilibrium, these endowments will be changed further complicating the picture. In a real economy, however, trading, as well as production and consumption, goes on out of equilibrium. It follows that, in the course of convergence to equilibrium (assuming that occurs), endowments change. In turn this changes the set of equilibria. Put more succinctly, the set of equilibria is path dependent... [This path dependence] makes the calculation of equilibria corresponding to the initial state of the system essentially irrelevant. What matters is the equilibrium that the economy will reach from given initial endowments, not the equilibrium that it would have been in, given initial endowments, had prices happened to be just right (Franklin Fisher, as quoted by Petri (2004)). The Arrow-Debreu model of intertemporal equilibrium, in which forward markets exist at the initial instant for goods to be delivered at each future point in time, can be transformed into a model of sequences of temporary equilibrium. Sequences of temporary equilibrium contain spot markets at each point in time.

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Roy Radner found that in order for equilibria to exist in such models, agents (e.g., firms and consumers) must have unlimited computational capabilities. Although the Arrow-Debreu model is set out in terms of some arbitrary numeraire, the model does not encompass money. Frank Hahn, for example, has investigated whether general equilibrium models can be developed in which money enters in some essential way. The goal is to find models in which existence of money can alter the equilibrium solutions, perhaps because the initial position of agents depends on monetary prices. Some critics of general equilibrium modeling contend that much research in these models constitutes exercises in pure mathematics with no connection to actual economies. "There are endeavors that now pass for the most desirable kind of economic contributions although they are just plain mathematical exercises, not only without any economic substance but also without any mathematical value" (Nicholas Georgescu-Roegen 1979). Georgescu-Roegen cites as an example a paper that assumes more traders in existence than there are points in the set of real numbers. Although modern models in general equilibrium theory demonstrate that under certain circumstances prices will indeed converge to equilibria, critics hold that the assumptions necessary for these results are extremely strong. As well as stringent restrictions on excess demand functions, the necessary assumptions include perfect rationality of individuals; complete information about all prices both now and in the future; and the conditions necessary for perfect competition. However some results from experimental economics suggest that even in circumstances where there are few, imperfectly informed agents, the resulting prices and allocations often wind up resembling those of a perfectly competitive market. Frank Hahn defends general equilibrium modeling on the grounds that it provides a negative function. General equilibrium models show what the economy would have to be like for an unregulated economy to be Pareto efficient. Computable general equilibrium

Until the 1970s, general equilibrium analysis remained theoretical. However, with advances in computing power, and the development of input-output tables, it become possible to model national economies, or even the world economy, and solve for general equilibrium prices and quantities under a range of assumptions.

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