Managerial Economics 10/29/2012 8:42:00 AMs3.amazonaws.com/prealliance_oneclass_sample/roVR… ·...
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Managerial Economics 10/29/2012 8:42:00 AM Professor Tariq Nizami Grading - 2 assignments (10%) assignment 1: appendix A and chapters 2, 3, 4 due October 29 and handwritten assignment 2: Chapter 5, 6, 7, 8, 9 and 10
Transcript of Managerial Economics 10/29/2012 8:42:00 AMs3.amazonaws.com/prealliance_oneclass_sample/roVR… ·...
Managerial Economics 10/29/2012 8:42:00 AM
Professor Tariq Nizami
Grading
- 2 assignments (10%)
assignment 1: appendix A and chapters 2, 3, 4
due October 29 and handwritten
assignment 2: Chapter 5, 6, 7, 8, 9 and 10
due last day of class
- Midterm (30%)
Chapter 1, Appendix A, 2, 3 and 4
50 -75 multiple choice questions
November 2nd from 9am-11am
50 % theory, 50% mathematical problems
- Final Exam (60%)
3h closed book
760-755 multiple choice (50%) and 8 problems (50%)
Chapter 4-11
Chap. 1 – Intro to Managerial Economics 10/29/2012 8:42:00 AM
Maximize revenue, minimize costs.
Revenue is not income. Income is the residual. Revenue shows the name of the
account from which you received cash, it is the amount of cash coming in from
each sale.
Managers cannot expect to succeed unless they understand both opportunities
and constraints.
Economic/Market forces of supply and demand in the market place determine:
1. Demand for products
2. Prices of resources and cost of production
3. Number of rival firms
4. Nature of pricing strategies
5. Profitability of business investors
What is managerial economics?
Managerial Economics extract from microeconomic theory. Those concepts and
techniques that enable managers to select strategic direction to allocate
efficiently resources available and to respond effectively to tactical problems.
What does managerial economics provide?
Provides a systematic and logical way of analyzing business decisions which
focuses on economic forces that shape day to day short run decision, as well as
long run planning decisions. Managerial Economics focus on the application of
microeconomic theory to business problems.
ME focuses on the application of microeconomic theory to business problems.
Microeconomics is the study and analysis of the behavior of individual segments
of the economy such as:
- individual consumers
- workers and owners of resources
- individual firms and markets for goods and services
Studies show our subconscious and our rationality influence the way we buy.
Example: when they played French music in the store more people bought
French wine over German wine and vice versa. Advertising agencies aim to
attack you in these ways.
In the pharmaceutical industry, if companies keep their products cheap, not
many people buy. People begin to think they are not as effective if they do not
cost as much. This is evidence of our irrationality.
The focus in microeconomics is at the firm or market level whereas the focus in
ME is on managerial behavior. This managerial behavior provides powerful tools
and frameworks to guide managers to better decisions. It serves to strengthen
all analytical skills. The most important task of managers is to make good
decisions. The objective of ME is to help business students become architects of
business strategy. It develops critical thinking and provides students with a
logical way of approaching business decisions.
In 2008, decisions exports had made failed. The best economists could make
good decisions. Now they aim to look at what happened. ME is powerful and
essential.
All successful business have used the fundamentals of ME to maximize their
profitability. We always use ME to make decisions (trade, time, money etc.).
Most of this decision making is irrational because you are thinking with
emotions.
ME draws on economic analysis for such concepts as demand, supply, cost,
project, competition, pricing, entry strategy and market protection.
ME bridges the gap between theorists and managers.
The chapter provides basic concepts that will be seen in class. We have to make
two decisions to maximize the profit: price to charge and output to produce.
The market you are in will determine how well you make this decision.
Boeing was once the largest producer of commercial aircraft. Airbus now has
the largest aircraft which seats 550 people first class or 800 people. Boeing‟s
approach was to be a low cost of airplanes and to be a technology leader. Years
ago, they had 80% of the market. By 1977, Airbus overtook them. Boeing was
selling their 747 plane for 150 million dollars and profiting 45 million dollars per
aircraft. ME can explain how Airbus was able to dominate. They used the cost
method and they wanted to be technology leaders. Walt Disney used much of
ME. In 1966, after he died they tried to expand their kingdom under CEO
Michael Eisner who was later thrown out by stock markets. Companies with a lot
of money move the cash and base their decisions of the basis of profit.
ME applies microeconomic theory to real world problems. By using optimization
techniques and integral calculus, to make decisions
Microeconomics and Macroeconomics are largely descriptive. Managerial
economics is largely prescriptive – establish rules and techniques to fulfill
specified goals. We will later see how they take care of out. ME is concerned
with how they should price their products. ME has to do with thinking and
predicting behavior not the actual action. ME analyzes the impact of alternative
courses of action using optimization techniques, including differential calculus,
mathematical programming and statistics for decision makers.
Economic Profit vs Accounting Project
Economic profit: = total revenue – explicit costs – implicit costs/ normal profit
the amount by which total revenue exceeds total economic costs
If I close down the business, you only make the value worth the implicit
(normal) profit. This amount never went out, you do not pay interest.
Economic losses: Any negative amount of economic profit.
When economic profits are zero, you are making normal profits. That dollar
amount never left. That is the amount you would make if you were not in the
business.
Total economic costs: the sum of all opportunity costs of each and every
recourse used by a firm.
Business generally utilizes two kinds of recourses:
1. Resources owned by others (i.e. capital equipment rented or leased from
suppliers).
2. Resources owned by the firm/owner (labor services provided by owner of
company, money provided to the company, machinery, equipment and space
provided by owner)
Implicit costs: Dollar amount sacrificed for using the resources in the company.
The company should be able to pay for every penny for the resources it uses. If
not, they would make more renting the resources to others. Example: using a
building that you already own. You should make more than the building‟s value,
otherwise it makes more sense to rent the space out to someone else.
Explicit costs: Dollar amount we pay to outside resources.
Accounting profits = total revenue – explicit costs
Opportunity costs is the next best use of your product.
Theory of the Firm
Theory of the firm describes how the firms behaves and what their goals are. A
firm represents a theory of series of contractual relationships that specify the
rights and responsibilities of various parties such as customers, stock holders,
managers, employees and suppliers. These are also the people directly involved
in the company. This model is called the theory of the firm. The primary goal of
the firm is long term expected value maximization.
Present day theory of the firm assumes that the firm tries to maximize the
value of the firm.
Value of the firm: the present value of its expected future cash flows or profits
in equation form = pi / (1 +i) 1 + pi / (1 + i) 2 ..
This can also be written as n sum t = 1 of TRt – Tct / (1 + 1)n
No company operates without constraints. Managers do not have complete
control over the whole firm because they must cope with the fact that there are
many constraints:
1. Input constraints – Inputs may be limited in the relative meter of
time. Could include specialized equipment, skilled labor, energy etc.
2. Legal and contractual – For example, companies are legally bound
to pay minimum wage. Thus, there is a limit to what they can hire.
They have health and safety standards, federal, provincial and local
taxes, environmental laws and antitrust laws. They also have contracts
with suppliers and customers.
Since there are constraints, the decisions will be analyzed and there will be
constrained optimization methods to incorporate these constraints.
Managerial interest and Principal Agent Problem
Principal is the owner, agent is the manager. Manager wants the best perks for
himself/herself and as such, there is a conflict of profit maximization. This
occurs when these two positions are inhabited by two different people. Owners
want managers to maximize the value of the firm which is usually accomplished
by profit maximization. When managers have little or no interest in the
company, thy are not as concerned with the profits of the owners.
Project reducing objectives are:
Consumption of excess or lavish perquisites: lavish office, membership in
professional clubs, extraordinary levels of life and health insurance,
limousine, chauffeur or even an executive jet.
Pursuit of market share: Some managers are driven to have the firm to be
the largest market share firm rather than the most profitable firm. In many
industries, the largest firms are not the most profitable.
To deal with these problems, corporations/ stockholders give incentives to
managers to pursue objective close to profit maximization. Management is
given stock options and to purchase shares at less than market price. As such,
they are compensated in stock. In some cases, managers are forced to buy
company stock. Firms in which mangers own more than 5% of stocks are
proven by study to be more profitable than companies where owners own less
than 5%. The larger number of stocks is bought by financial institutions.
What is economics?
Economics is the study of how scarce resources are used to produce goods and
services to satisfy unlimited wants and needs. It is the study of decision making
is a world of scarcity. Wants are what people would buy if their incomes were
unlimited. Needs are what people buy to survive like food, shelter and clothing.
Scarcity is the result of not enough goods and services to satisfy all the wants
and needs.
Macroeconomics: Study of the behavior of the economy as a whole of the
interactions of the major groups called household, governments, foreign sector
of the economy.
Microeconomics: Study of decision making by individuals and firms which are
the individual segments of the economy.
What is an economy system?
Economic system describes how a society distributes its resources to produce
goods and services. It is the institutional means through which resources are
used to satisfy human wants.
Economists classify economic systems into four types of models:
1. Agrarian/Traditional Economies (agricultural)
2. Market Economies (capitalism)
3. Command/ Planned Economies (socialism and communism)
4. Mixed Economies
Nowadays, most economies are mixed. The others do not exist as much.
Your competition depends on your product. If your firm is the only one who
makes that profit, you are said to have a monopoly.
Market structure and managerial decision making:
Price takers: Managers who do not have control over price. Price is determined
by forces of supply and demand
Price setters: Managers who have some market power (the power to increase
the price without loosing all the sales).
What is a market?
- A market is composed of firm and individuals who are in touch with each
other in order to buy or sell some good or service.
- It is any arrangement through which buyers and sellers exchange final
good or service, resource used in production.
Market processes: the buying and selling of goods and services. They are
facilitated by the market forces of supply and demand.
What is demand?
Demand is the various quantities of a good or service that people are willing to
purchase at various prices during a specified period of time (week, month, year
etc.) when all other non priced determinants (incomes, tastes, expectations,
prices of related products, population etc.) are held constant. If any one of
these changes, it does hold true. Since price is a part of what we call demand,
demand is a relationship between price and quantity. A change in the price
cannot change the demand but a change in price actually changes the quantity
demanded.
Law of demand says that “quantity demanded of a good is inversely related to
price when all other non-price determinants are held constant.”
Market Demand Schedule: is a table showing a list of possible product prices
and corresponding quantities demanded during a specified period of time.
Price ($) Quantity (#)
5 20
4 40
3 60
2 80
1 100
Market Demand Curve: is a graph showing the inverse relationship between
price and quantity (downward slope).
Shift in Demand: Takes place rightward (increase in demand) or leftward
(decrease in demand) when any of the non price determinants change.
Increase in demand – A change in demand function that causes the increase
quantity demanded at each and every price.
Decrease in demand – A change in demand function that causes the decrease
quantity demanded at each and every price.
Profit = Total revenue – total cost
Total revenue = price x quantity
Non Price Determinants of Demand:
1. Income (normal goods)
2. Tastes and preferences (if these changes, there will be a change in demand.
This means the whole curve shifts to the right or left. This is not a change in
price).
3. Price of related products (complements such as batteries and flashlights,
petroleum and cars etc. substitutes include coffee and tea).
4. Expectations (future prices announced so people start to buy more presently,
product availability also increases people‟s spending‟s)
5. Population (Florida‟s populations doubles in the winter time.
Change in Demand vs Change in Quantity Demanded:
Change in demand: A change in one or more non price determinants will lead to
a change in demand. This is a shift of the demand curve.
Change in quantity demanded: A change in a goods‟ own price leads to a
change in quantity demanded. This is movement along the same demand curve.
Supply: is the various quantities of a good or service, sellers are willing and
able to supply for sale at various prices at a specified period of time (week,
month, year) holding all non price determinants (input costs, technology and
productivity, government taxes and subsidies, price expectations and number of
firms in the industry) constant.
Law of supply: Quantity supplied has a direct relationship to the price. As price
goes up, more is supplied and vice versa.
Market Supply Schedule: is a table showing a list of possible product prices and
corresponding quantities supplied by all firms.
Price ($) Quantity (#)
5 100
4 80
3 60
2 40
1 20
Market Supply Curve: is a graph showing the quantity supplied and price when
all non price determinants are held constant (upward slope graph of price vs.
quantity).
Shift in Supply: is a rightward or leftward shift in the supply curve when any
one or more non price determinants are changed. If you price of labor changes,
technology changes, then people will buy more. Increase in supply is a
rightward shift while a decrease in supply is a leftward shift.
If you want to see the effect of profit, you must hold all non price determinants
constant to be able to measure price and quantity.
Non Price Determinants of Supply:
1. Cost of inputs
2. Technology and Productivity
3. Taxes and Subsidies (municipalities will offer no taxes for big companies to
move into their area and prove jobs to locals)
4. Price expectations (if the firm expects the price to increase in the future,
they will hold some of the products in order to reduce current supply)
5. Number of firms in the industry (if they increase, more of that good will be
supplied at each price resulting in a rightward shift)
Change in Supply vs Change in Quantity Supplied:
A change in one or more non price determinants will lead to a change in supply.
This is a shift of the supply curve. A change in a good‟s own price leads to a
change in quantity supplied. This is a move along the same curve.
Determination of Market Equilibrium:
Equilibrium price: Price at which quantity demanded equals quantity supplied
(On the graph as price decrease vs quantity demanded and the supply increases
vs quantity demanded it is the intersection of these two lines).
Equilibrium Quantity: Quantity traded
Shortage: is a market situation where the quantity demanded exceeds the
quantity supplied at a price below equilibrium level. There is an upward
pressure on price. As price increases, quantity supplied increases (direct
relationship) so it tends towards equilibrium. In the real world, there exists no
equilibrium. However, we need this to know where we are and help us decide.
Surplus: is a market situation where the quantity supplied exceeds quantity
demanded at a price above the equilibrium level (downward pressure on price).
Let x be quantity (q) and y be price (p). We get P = a – bQ.
Qd is quantity demanded and Qs is quantity supplied.
Pd = a + Qd.
Ps = a + Qs.
When you let Pd = Ps, you can solve for Q.
Appendix A – Optimization Techniques 10/29/2012 8:42:00 AM
Once basic economic relations are understood, optimization techniques may be
applied to find the best course of action.
Economic Optimization Process:
What is optimal decision? Not always the maximize. When alternative courses of
action are available, the decision that produces the result most consistent with
managerial objectives is the optimal decision.
PV of all expected future profits: n Σ t=1: TRt – TRc / (1 +i)t
This is total revenue.
Let Q = output
and TR = total revenue
so TR = f(Q)
This does not a specific relationship, it shows that there exists some
relationship. To make it more expressive: TR = P x Q
Profit is maximized when marginal revenue = marginal costs not when total
revenue is maximized. This is because the slope of the TC line is the same as
the slope of the TR line at this point.
The graph of x vs y shows the relationship between quantity vs price or quantity
vs total revenue.
Functional Relationship
Q = f(P)
Price ($) Number of units
10 150
20 100
30 50
40 0
Using P = a – bQ, solve for a and b.
Q = 200 – 5p
Marginal Analysis
All optimization problems can be solved using the analytical tool of marginal
analysis.
Leads to two simple rules, one for unconstrained decisions and the other for
constrained decisions.
Marginal value of dependent variable is defined as the change in this dependent
variable associated with a one unit change in a particular independent variable.
(change in total revenue of
Number of units sold Total Profits Marginal Profit
0 0 100
1 100 150
2 250 350
3 600 400
4 1000 150
5 1350 150
6 1500 50
7 1550 -50
8 1500 -100
9 1400 -200
10 1200
You need this to tell you where to stop.
The place where marginal profit switches from positive to negative is when
slope of the curve equals 0. This is when total revenue reaches a maximum.
The concept of a derivative (rate of change):
If y is a dependent variable, and x is an independent variable then we say y is
function of x.
A change in y/ A change in x = dY/ dX
How to find a derivative :
1. Derivative of a constant: If y=a then dy=0.
2. Derivative of a power function: If kxn then dy= nkxn-1
3. Derivatives of sums and differences: Suppose u and w are two variables.
and u= g(x) and w = h(x). Y = u+w so dy = du + dw
4. Derivatives of products: If y=uw then dy=wdu + udw
5. Derivatives of quotient
s: IF y= u/w then dy= udw – wdu / w2
If you let the derivative of any function equal 0, then you solve for the
maximum total revenue (when profit is maximized).
First derivative of total revenue is marginal revenue.
(When marginal revenue equals 0, total revenue is maximized).
First derivative of total cost is marginal cost.
(When marginal cost equals 0, total cost is maximized).
First derivative of total profit is marginal profit.
(When marginal profit equals 0, total profit is maximized).
Beyond the point where marginal cost = marginal revenue, your costs decrease.
When profit is maximized, marginal revenue = marginal cost (on the graph of Q
vs P, both slopes of the curved lines are the same).
Partial Differentiation and Maximization of Multi Variable Functions
Exercise 1: Profit = f(Q1Q2)
Profit is a function of the first and second output.
P = -20 + 113.75Q1 + 80Q2 – 10Q12– 10Q2
2 -5Q1Q2
P‟ (Q1) = 113.75 - 20Q1 -5Q2 (holding Q2 constant)
Pi (Q2) = 80 – 20Q2 – 5Q1 (holding Q1 constant)
Let both equations equal 0 (and using systems of equations by subbing Q1 into
Q2), solve for Q1 and Q2.
When we solve, we get Q2 = 2.75 and Q1 = 5.
Exercise 2: Total cost = 4Q12 + 5Q2
2 – Q1Q2
Subject to constraint Q1 + Q2 = 30 (they have to produce 30 of these)
Solve for Q1. We get Q1 = 30 – Q2.
If we substitute Q1 now into the TC equation, we get:
Total cost = 4(30 – Q2)2 + 5Q2
2 – (30 – Q2)Q2
We can solve for TC with respect to Q2: TC = 3600 – 270Q2 + 10Q22
We get Q2 = 13.5 and Q = 16.5
This is how many units of each product we can produce. For the time being,
leave the quantities as decimals.
Exercise 3: If Qd = 50 – 8p and Qs = -175 + 10p
Equilibrium price to quantity: 50 – 8p = - 17.5 + 10p
P = $3.75 and Q = 20.
Total revenue is maximized when marginal revenue shifts from positive to
negative.
Chapter 2 – Demand Theory 10/29/2012 8:42:00 AM
Market Demand Function: q = f (Px, I , tastes, price of market products
population, advertising etc)
Q = b1P + b2I + b3S + b4A
Where
I = per capita disposable income
S = average price of related products
A = amount spent on advertising
b = delta Q / delta P (change in price)
When you change one variable, you have to hold the others constant.
Let Q = -700P + 200I – 500S + 0.01A
E.g. b1: if Price changes by one unit, quantity demanded changes by b1 units
under the condition that all other variables (i.e. price of Software) are held
constant
Price Elasticity of a Demand Function
The price elasticity of a demand function is the percentage change in quantity
demanded in response to a 1 percent increase in price. It measures the
responsiveness or sensitivity of consumers to changes in the price of a good or
service.
It tells us how to price our products. It tells us at what price, we will increase
total revenue or decrease. At the corresponding quantity, marginal revenue is
maximized.
• Typically negative (P and Q are usually opposing signs)
• Price elasticity generally is different at different prices and on different
markets.
It is calculated for movements along a given demand curve or function as price
changes and all other factors affecting Q demanded are held constant.
% change in quantity demanded p
------------------------------------ = ---- (need to know p)
% change in price p – a (a is y intercept)
If delta P changes by -10% and delta Q changes by +30%, the price elasticity is
-3.
Range of Elasticity of Demand
0 ≥ η ≥ –∞
• When η < -1, segment of demand curve is elastic. TR increases with a
decrease in P over the interval of the demand curve. Denominator is lower than
numerator. If this is the case, you decrease the price.
• When η > -1, segment of demand curve is inelastic. Numerator is lower
than denominator. TR decreases with a decrease in P and increase with an
increase in P over this interval of the demand curve. If this is the case, you
increase the price.
• When η = -1, segment of demand curve is unitary. „
Calculation of Arc and Point Elasticity of Demand
When η is calculated over an interval or an arc of the demand curve it is called
arc elasticity of demand. The formula for the arc elasticity is given as:
(Q1- Q2) (Pavg)
= ------------------
(P1-P2) (Qavg)
Point elasticity: a measurement of demand elasticity calculated at a point on the
demand curve rather than over an interval.
If TR = aQ = bQ2 then MR = a – 2bQ
MR = P (1 + 1/η) Applications of this formula: price elasticity, pricing policy
Price Elasticity and Pricing Policy
P = MR
-------
1 + 1/η
Profit is maximized when MR=MC
So, this formula can also be written as P = MC
-------
1 + 1/η
Exercise 1: If η = -2 and MC = $10. What is the profit maximizing price?
P = $10 / (1 + (1/-2)) = $20
Other elasticity: Q = f (P, I, T, Prices of related graph, population).
Income Elasticity of Demand: measures the responsiveness of quantity
demanded to a change in income holding all other variables constant. It is
defined as the percentage change in quantity demanded as a result of a 1%
change in per capita income of consumers.
η = dQ I
---- x -----
dI Q
Exercise: If Q= 1000 – 0.2Px + 05.Py + 0.4I. What is price elasticity when Q –
1600 and I = 10 1000.
η = 0.4 (10 000/1600) = 0.25 This implies a 1% increase in income results in a
.35% increase in quantity demanded.
Cross Elasticity of Demand: measures the responsiveness of quantity demanded
of one good to changes in the price of another good, holding all other variables
constant. It is defined as a percentage change in the quantity demanded of
good x resulting from a 1% change in the price of good y, all other variables
held constant.
ηxy = dQx Py
------ x ------
dQy Qx
Let Q= 1000 – 0.2Px + 05.Py + 0.4I. Let py = $500 and Qx = 2000.
dQx / dQy = 0.5
nxy = (0.5) x (500/2000) = 0.125
Exercise 1: Q = 100 – 0.05P
1. Derive TR and MR
2. Solve for output where TR is the highest.
3. What is the price elasticity at P=1000.
1. Isolate P. P = (100 – Q) / 0.05 . P = 2000 – 20Q
TR = P x Q = 2000Q – 20Q2
MR = 2000 – 40Q (taking derivative of TR)
2. MR = 0 = 2000 – 40Q. Solve for Q.
Q = 50
3. η = p / (p-a) = 1000 / (1000-2000) = -1.
Convert the function into a demand function means solve for Q.
If MC = $5 and η = -4, calculate the profit max price.
MC= P / (1 + (1/n)).
P = 5 / (1 + 1/-.4) = 5/.75 = $6.67.
If price = $12 and η = -1. What is MR?
MR = P (1 + 1/η) = 12 (1 + 1 / -1) = 0.
If MC = $40 and p = $60, what is η?
40 = 60 / (1 + 1/η)
1/3 = 1 + 1/η
-1/3 = 1/η
η = 2.
Chap 3 – Consumers Behavior and Rational Choice10/29/2012 8:42:00 AM
Consumers willingness to buy a product is the most fundamental factor of profit.
Understanding consumer behavior is the first step in making profitable pricing,
marketing, product design and product decisions. This is the economic model of
consumer behavior.
The basic model of consumer behavior focuses on two important factors
influencing consumer behavior
1. Consumers preferences (willingness) and tastes for various combination
of goods.
2. The ability of consumers to acquire goods as determined by income and
prices of goods.
Demand: The amount or quantity a consumer is willing to buy.
Law of demand that the quantity demanded has an inverse relationship with
price.
We need to differentiate between this two. We will study the willingness and we
will study the ability to buy.
We will develop the concepts of utility functions, indifference curves and budget
lines. From this, we will derive the consumer-demand curve.
Consumer preferences and Utility
1. Complete information about the product
2. Preference ordering ability of bundles (combinations of goods)
3. Consumer is Rational (If there are 3 bundles, there are 3 possibilities. A
may be preferred to B or B to A or the individual may be indifferent).
Utility and function: Utility is the benefit or satisfaction consumers obtain from
the goods and services they consume.
U (x,y): u is a function of x and y.
Indifference Curves:
Consumers are willing to make trade offs or substitute among different goods.
(ex: Should we buy the shoes or the dress?). This is determined by the form of
that individuals utility function. An indifference curve is a locus of points
representing different combinations of goods and services each of which
provides an individual with the same level of utility.
All the points on the graphs are joined to form the curve. There are many
points. The points on the curve demonstrate equivalent levels of satisfaction. In
other words, a coordinate of the function curve provide equal satisfaction to
another coordinate. We could say that coordinate (20,40) shows that 20 drinks
and 40 chocolates are satisfying. The cure therefore represents a combination
of goods and services which provide the same level of satisfaction for the
individual.
Properties of indifference curves:
All combinations of goods x and y give the same level of utility along
the same indifference curve
Indifference curves is downward slopping
Indifference curve is convex to the origin (the shape shows that as the
consumption of x increases relative to y, the consumer is willing to
accept a smaller amount of y in order to stay at the same level of
utility). This is the marginal rate of substitution (MRS).
Convex to the origin which implies that consumers marginal rate of
substitution declines as we move down any one of these curves.
Consumers want the highest indifference curve possible (price is
irrelevant).
Marginal Rate of Substitution: The number of units of y that must be given up
for more units of x to maintain the same level of satisfaction. (slope of curve at
a given point)
MRS = - Δy /Δx = Mux / MUy x y
May be calculated for a range or for a specific point. Calculate accordingly. For a
range of values, calculate rise over run x -1. For a specific point, extend the
tangent line at that specific line. Then, y intercept/ x intercept x -1.
Ex: If you chose to increase by 20 units of y by giving up 10 units of x:
Slope = change in y / change in x = 20/ -10 = -2.
MRS = -1 x slope. MRS = 2.
This implies we are willing to give up one unit of x to gain two units of y.
Ex: If the MRS is 2 and the Mux = 20. What is the MUy?
MRS = MUx/ MUy or 2 = 20/ MUy. MUy = 10.
Budget Line: Consumer‟s constraints
Locus of all combinations/ bundles of goods that may be purchased at given
prices if the entire money income is spent.
Ypf + xPc = I
If Income = $600, Food = $3/lb and clothing = $60/piece.
Then y = 3y + 60x = 600
Solve for y. y = 200 – 20x.
Equilibrium Market Basket:
1. Super impose indifference curves on budget line onto one graph.
2. Chose the market bundle on the budget line that is on the highest
indifference curve.
Equilibrium occurs at the point at which the rate at which the consumer is
willing to substitute equals the rate at which the consumer is able to substitute.
MRS = - Δy Px
---- = -----
Δx Py
This can be written as Mux Px
--- = -----
Muy Py
Rearranging, we get Mux Muy
--- = -----
Px Py
This expression means that MU per dollar spent on the last unit of good X is
equal to the MU per dollar spent on the last unit of good y. This is related to the
demand curve because it is defined by the quantity of product that a consumer
is willing and able to purchase.
Derivation of Individual Demand Curve:
Market Demand Curve: Summation of all quantities for all participants
Ex: 4 budget lines plotted on one graph.
Y = I / Py – (Px / Py) (x)
YLZ = 10 – x
YLr = 10 – 2.5x
Ykz = 5 – 0.5X
YMN = 4 – 0.5X
For line LX, if income is $200, what is the price of y and x.
Py = 200/10 - $20. Px = 200/ 10 - $20.
Chap. 4 – Production Theory 10/29/2012 8:42:00 AM
Learning to price and learning the effect of price on your total revenue. If you
sell more, your costs go up. This affects revenue. We want to find out the
output level at which we sell. Beyond that, the total profit will go down.
Managers know that profit is determined not only by revenue that a firm
generates, but also by the cost that is associated.
Barriers to trade have almost vanished. In the late 1990‟s, early 2000‟s,
globalization of market made it much more difficult to increase profits by
sampling selling more units and charging more. A lot of companies took their
production to Asian countries and now export to Canada for our demands.
Global competition has intensified the need to manage productivity and reduce
costs to satisfy stockholders.
This chapter deals with: how structure of firm‟s cost is determined by the nature
of the production process that transfers input to goods and services.
Cost itself has evolved out of production. Cost does not tell you the optimal
quantity. Production function tells you the combination of labor, capital etc. that
will yield the lowest cost. We do not deal with dollar amounts in this chapter. As
productivity increases, cost decreases. As productivity reaches a maximum, cost
reaches a minimum (inverse relationship).
Managers make production decisions in two different decision making time
frames:
1. Short run production decisions: Manager must produce with at least one or
more fixed input (1 input is fixed in quantity plant and equipment).
2. Long run production decisions: Concerns the same kinds of decisions as short
run except all inputs are variable quantity. The usage of all inputs can be
increased or decreased.
Economists think of short run as the time period during which actual production
takes place and long run as the planning horizon over which future production
will take place. A production function specifies the efficient relationship between
inputs and outputs.
Production: the creation of goods and services from inputs like labor,
machinery, capital equipment, raw material, land etc.
Production function: for a product, is a table, a graph and an equation showing
the maximum amount of output that can be produced with any specified set of
inputs given the existing technology or that time or the state of the art
production. Physical relation between input and output. In our simple model, we
will restrict attention to the product with only two outputs; labor (L) and capital
(K) so that Q = f (K,L).
Short run production decisions: Capital (K) will be the fixed input, so our
function is Q = f(L). The output therefore depends on the usage of labor only.
Amount of Labor Amount of Capital Output
0 5 0
1 5 49
2 5 132
3 5 243
4 5 236
5 5 525
6 5 624
7 1 1
8 1 1
9 1 1
10 1 1
Graph: Production function shows total output
x axis amount of labor
y axis amount of capital
Q = 30L + 20 L2L3
The production function provides basic information concerning the nature of the
firm‟s technology.
Differential concepts in production theory:
Total Product (TP): the maximum output that can be produced by using each
combination of quantities of inputs (labor and capital). TP rises, reaches a
maximum, and then decreases.
Average Product (AP): of an input is equal to the total product divided by the
total input (labor) used to produce this amount of output. AP first rises, reaches
a maximum then declines.
Always pulled up by average of marginal product.
AP = Q / L
Marginal Product (MP): of an input is equal to the addition of total output
resulting from the addition of the last unit of input (labor) when the amount of
other inputs used were held constant.
MP = dQ / dL = change in Q / change in L
On a graph, marginal product is drawn above average product because every
additional unit, the productivity is going up until it reaches AP‟s maximum.
Crowding effect occurs when MP reaches a maximum – but it really refers to the
entire section of MP which has a negative slope. After this point, MP decreases
exponentially. MP is below AP when AP is declining (do not mix up negative MP
and diminishing MP). MP is equal to AP at the highest point of the AP. When MP
increases, TP increases until MP becomes negative, at which point, TP begins to
decrease. The reason it decreases is because one input is fixed. This only occurs
in the short run. In the long run, all inputs are variable which does not occur in
productivity.
Law of Diminishing Marginal Return (LDMR):
As number of units of the variable input (labor) increase in equal increments,
other inputs held constant, a point is reached beyond which the MP of the
variable input (labor) decreases. This law is a direct result of one or more inputs
being fixed and the other input being variable (only applies in the short run).
Optimal level of utilization of a variable input:
The optimal condition is MRPh = MEL
MRPh = Marginal Revenue Product of labor. It is also written as MRPh = MR(MPh)
Not to be mixed up with MP. An individual does not produce only one unit, they
produce multiple.
MRPh = Marginal expenditure of labor
If Q =98L – 3L2 and price = $20 and MEL = $40/day
MP = dq / d L = 98 – 6L
Since MRPh = MEL
then as MR(MPh) = MEL
(20)(98 – 6L) = 40.
Solve for L = 16.
SUPER NOTES BEGIN HERE
Long term production decision: long term is a planning decision over which
future production will take place
Q=f(k,L) k=capitol L= labour
IsoQuants (quant is for quantity)is a curve which shows all possible (efficient)
combinations of inputs that are capable of physically producing a certain
(constant) quantity of outputs
Holding Q constant gives a curve of K vs L. different values of Q will shift curve
away from (0,0) or towards (0,0)
*insert 1/x looking graph here* k on y axis and L on x
this graph is a isoquants map.
each line is a isoquant with a specific Q
characteristicts of IsoQuants:
1 all combinations of K and L give the same Q. because Q is held constant Duh
2 a group of isoquants is called a isoquant map
3 isoquants can‟t intersect
4 isoquants are generally convex to origin ( look like 1/x)
marginal rate of technical substitution( MRTS)
rate of change of isoquant. Change in K for one unit change of L
MRTS= -dk/dL (it‟s negative because the slope is negative and we want to
cancel that out
Relation of MRTS to marginal products
-dk/dL=MP(L)/MP(k)
why MRTS declines along isoquant?
1 less capital
2 more labour
IsoCost: just like isoquant except we are now keeping cost constant
Curve showing all combinations of inputs that may be purchased for a given
level of total expinditure at given prices.
M=P(k)k+P(L)L M=total cost (expenditure) P(K) price of output
P(L) price of labour
Intersection of isocost and isoquant:
Equilibrium position where MP per dollar spent on last unit of labour is equal to
MP per dollar spent on last unit of captital used (confusing, I would ignore)
MP(L)/P(L)=MP(K)/P(K) ------ important
Examples in Daniel notes.
Note! Capital K is not money. It is equipment and building and stuff.
Chap. 5 - The Analysis of Cost 10/29/2012 8:42:00 AM
Short term cost functions
Some inputs are fixed (plant, equipment, etc)
Assumption:
Firm employs two inputs: Labor and capital.
Operates in short term period. Labor is variable and capital is fixed
These inputs are used to make a single product
Level of technology is constant
Firm operates in the most efficient way at all levels of output
Firm operates in perfectly competitive input market (price of inputs is
given by market and is out of our control)( law of diminishing returns)
3 concepts of costs
Total fixed costs
Total variable costs
Total cost
Total fixed costs (TFC) : cost of fixed inputs, output has no affect on it.
Total variable cost (TVC) : cost of variable inputs. Depend on output. Increase
with output rate
Total cost (TC) : TFC+TVC
Average costs
Average fixed cost: AFC = TFC/Q
Average total cost: ATC = TC/Q (total cost divided by output)
Average variable cost AVC = TVC/Q or AVC=w/AVP
(w is change in cost per one unit)
w
Cost do not have a way of telling you the lowest combinations. It is the
arithmetic of the production function. Why does the AVC reach its minimum
before the ATC does?
Marginal Cost: The addition to the total cost resulting from the addition of the
last unit of output.
AVC and ATC reach a minimum when their derivatives equal 0. This is also the
point at which MC intersects those lines.
MC = change in total fixed cost + change in total variable cost / change in
quantity
Since change in total fixed cost is 0 (fixed implies no change).
MC = change in total variable cost / change in quantity.
The MC decreases, reaches a minimum, and then increases. It crosses ATC and
AVC at their lowest points.
MC = w (Δu/ ΔQ) = w (1/MP) = w/MP
Ex: TC = 100 + 50 Q – 11Q2 + Q3
Calculate MC from TC by taking first derivative. You always need a total to
calculate this.
MC = 50 – 22Q + 3Q2
AVC = 50 Q – 11Q2 + Q3 / Q = 50 – 11Q + Q2
Solve for Q at its lowest point. dAVC / dQ = -11 + 2Q = 0
Calculate Q. Q = 5.5
Plug Q in (either in MC or AVC). AVC = 50 – 11(5.5) + (5.5)2 = $19.75
When MC is less than AVC, AVC is decreasing and this adds less to the cost, so
the total cost decreases.
Long Run Cost Function
All inputs are variable, therefore law of diminishing return does not apply (we
would need to have at least one input fixed). Therefore, the shape of the curve
cannot be predicted in the same way.
This curve exhibits 3 common characteristics.
1. When input = 0, cost = 0
2. Cost and input are directly related. LRC increases, as you increase input.
3. LRC first increases at a decreasing rate, and then increases at an increasing
rate. (MC decreases then increases).
Assumptions:
1. Firm‟s level of input usage does not affect the price of inputs. Prices are
taken as given by the manager.
2. 2 inputs used are capital (k) and labor (l)
LAC = TC / Q
LMC = ΔTC / ΔQ
Long Run Average Cost + Long Run Marginal Costs
LAC + LMC have essentially the same shape as SAC + SMC but for different
reasons.
1. Short Run Cost functions are affected by law of diminishing returns where
input is fixed.
2. Long Run Cost functions are affected by economics of sale and
diseconomies of scale.
Economies of Scale and Diseconomies of Scale
1. If unit costs decrease as the quantity of production increases and all
resources are variable, we say that these are economics of scale.
2. If unit costs increase as the quantity of production increases and all
resources are variable, we say that there are diseconomies of scale.
3. If the cost per unit of output is constant, as output increases and all
resources are variable, we say that these are constant economies of scale.
Economies of scale: The range of output over which long run average (LAC) falls
as output increases.
Diseconomies of scale: The range of output over which LAC increases as output
increases.
Economies of scale:
1. Specialization and division of labor: division of labor can lead to boredom
2. Technological factors: cost of producing larger machines is lower cost?
3. Financial factors
The range of which average cost goes down, falls as output increases. Implies
declining long run average cost.
Diseconomies of scale
Are attributed to limitations to efficient management. Involves controlling and
coordinating finance, sales etc. If you are inefficient costs go up. To perform
these functions efficiently, a manager has to have accurate information.
- Problems of coordination and control
- Management and staff salary costs increase
- Contact with daily routine of operation is lost
- Increase in red-tape and paper work. (Red tape refers to too many middle
men involved in chain work)
Economies of scope
Is the situation in which joint costs of producing 2 or more products is less than
the sum of the separate costs of producing the goods.
Breakeven Analysis
Analytical tool employed by managers which has to do with cost function. It is
forecasting. Before producing, estimate the breakeven point. You want to find
out the number of units which will give you no profit and no loss.
Breakeven point (BEP) = FC / CM
Where FC is fixed cost and CM is contribution marginal.
NI is net income
CM = SP – VC
Where SP is selling price and VC is variable cost.
Ex: SP = $100, VC = $70, FC = $24000, CM = $100-$30 = $70
Calculate BEP = $24 000 / $30 = $800
Calculate sales at target income ($60,000)
= (FC + NI) / CM
= ($24,000 - $60,000) / $30
= $2800
Income of $60,000 after tax (tax = 50%)
Calculate sales at target income ($60,000 after taxes)
= (FC + NI + taxes) / CM
= (24,000 + 60,000 + 60,000) / 30
= 144,000 / 30
= $4800
If your income after taxes at 40% is $60,000 then it means your income before
taxes was $100,000.
Ex. Your total cost function is TC = 10Q3 – 4Q2 + 25Q + 500
Calculate marginal cost of 25th unit.
MC = 30Q2 – 8Q + 25
MC (25) = 30(25)2 + 8(25) + 25
MC = $18,575
Ex: Average variable cost AVC = 25q + 500
Find marginal cost for 50th unit
Multiply AVC by Q to find TVC because you need to multiply your average
variable cost by the quantity your are producing to find total cost.
TVC = 25Q2 + 50Q
MC = 5Q + 500
MC = 5(50) + 500
MC = $750
Ex: AVC = $25 and FC = $2500. I sell at $75/ unit. What is my BEP.
BEP = FC / CM
Calculate CM = SP – VC = $75 - $25 = $50
BEP = $ 2500 / $50 = 50 units
Ex: TC = 2400 + 100Q and SP = $120. Find BEP.
2400 is TFC and 100 is TVC.
BEP = FC / CM
BEP = 2400 / 20 = 120 units
Chapter 6 – Perfect Competition 10/29/2012 8:42:00 AM
As it turns out, that the nature of the price and output decisions is strongly
influenced by the market structure in which the firm sells its product. Market
structure determines whether a manager will be a price taker or settler.
Market Structure
A system for grouping and analyzing markets according to the degree and types of
competition among sellers. It will depend on the way you make your decisions:
what price to charge and what output to produce?
Economists have divided the market structure into 4 categories.
1. Perfect competition
2. Monopoly
3. Monopolists competition
4. Oligopoly
Markets includes firms that sell similar products or use similar processes, to
compete for the same buyers.
Perfect competition:
1. Each firm takes the market price for the product it sells as given by the market.
Managers are price takers. (The most important characteristic) (Therefore only the
second decision can be made my managers. What price to charge is set so we can
only chose what output to produce).
In this case, demand price = MR. P = MC = MR.
2. All firms produce a homogenous product
3. Each firm is so small it cannot affect price (individual changes go unnoticed).
4. Exit and entry are unrestricted. Firms can enter the market, leave the market.
No artificial restrictions on the number of firms.
5. Each firms has complete knowledge about the product and the market. Each firm
knows best the least costly method of production, input prices etc.
Yellow dot shows equilibrium moment. Before this quantity, we are making profit as
long as profit is above total average cost.
How much output should a perfectly competitive firm produce? We know that
market price given to us is $10.
TR is a straight line because it is a direct relationship between price and quantity.
TC curves upwards due to its equation (i.e: TC = 1 – 2 Q + Q2). Therefore, demand
curve and MR curve are the same. Every time you sell you get 10 more dollars.
If TC = 1 - 2 Q + Q2 and P = MR = MC.
If we know MR = 10.
Then we take MC to be MC = 2 + 2 Q .
So we let 10 = 2 + 2Q
Q = 4
Short Run Average and Marginal Cost Curves
If p is less than variable cost P < AVC, you should shut down.
If there exists an output rate at which P > AVC, it will pay the firm to produce,
despite the fact that the price does not cover AVC.
If there is no output rate at which P exceeds AVC, the firm is better off producing
nothing at all.
To summarize, if the firms maximizes profit or minimizes loses, it sets an output
rate so that short run production = MC and price always above AVC.
Ex. TC = 800 + 6Q + 2Q2
P = MC
MC = 6 + 4Q
P = 6 + 4Q
Let P = $30. $30 = 6 + 4Q so Q = 6.
AVC = TVC / Q
AVC = 6Q + 2Q2 / Q
Plug Q in. AVC = 6 + 2(6) = $18.
Therefore, yes stay in business because P > AVC ($30 > $18).
Long Run Equilibrium of firm under Perfect Competition:
Long run means markets have time to adjust to economic profits and economic
losses. The only way you can have a long run theory, you must have entry and exit
be unrestricted. Just as in the short run, firm attempts to maximize profits. The
firm takes market price as given (defined as MR). In the long run, how much will a
competitive firm produce?
If P > ATC, any firm enter the industry. This increases supply thereby driving prices
down and hence profits.
If P < ATC for own prices, that firm will exit the industry. As firms exit the industry
supply falls, causing price and profits to rise.
Only when economic profits are zero ( P = LAC) is the firm in equilibrium.
Many companies that are flushed with cash that sit on sidelines. They wait to see
which industries are making economic profits. Once they go in, other companies
follow. If there are few firms operating, supply increases as number of firms
increase and there is a downward pressure on price. Once all economic profits are
wiped out. Market price you have no control over. New firms continue to enter,
price continues to fall, firms continue to adjust. Profits diminish as price decreases.
As price falls, profits fall, eventually P = LAC.
Only when economic profits are zero is a firm
in equilibrium. This optimal point is when P =
LAC (long run equilibrium point). This is at
lowest point of average cost (when LAC‟ = 0).
At this point, there is no entry or exit of
companies.
The firm maximizes profits where P = LMC and
therefore LAC = LMC.
If two points can be satisfied simultaneously, we have an equilibrium point.
1. P = LAC where profits are zero.
2. P = LMC where profits are maximized.
(Therefore LAC = LMC at the lowest point)
Ex: If AC = 200 – 4Q + 0.05Q2
What is the lowest point of average cost?
AC‟ = -4 + 0.1Q
0 = -4 +0.1 Q
Q = 40
What price does this correspond to?
AC = 200 – 4 (4c) + 0.05 (40)2
AC = 200 – 160 + 80
AC = $120.
TC = AC(Q) = 200Q = 4Q2 + 0.05Q3
MC = 200 – 8Q + 0.15Q2
MC = 200 – 8(40) + 0.15(40)2
MC = 120
Ex: How many firms are operating in the industry?
TC = 2000 + 20 Q + Q2
Qd = 10,000 – 40P
TC / Q = AVC
(2000 + 20 Q + Q2) / Q = AVC
AVC‟ = -2000/Q2 + 5 = 0
2000 + 5Q2 = 0
Q = 20
Find the price by plugging Q into AC.
AC = 2000/ 20 + 20 + (5x20)
AC = $220.
This the equilibrium price.
Qd = 10,000 – 40(220)
Qd = 10,000 – 8800
Qd = 1200
Qd / Q = number of firms
1,200 / 20 = 60
There are 60 firms.
Ex: 2000 + 10 Q + 0.02(Q2) and P = $@5.
P = MC
10 + 0.04Q = 25
Q = 375
Profit = TR – TC
Profit = (25)(375) – (2000 + 10 (375) – 0.02(375)2)
Profit = $812.50
Chap. 7 – Monopoly and Monopolistic Competition10/29/2012 8:42:00 AM
Temporal monopoly (time wise) such as a restaurant being the only one all night.
Only newspaper in a city, only flight to one location are other examples.
Natural monopoly is for the good of a whole such as Hydro Quebec.
Market power is the ability of a firm to raise price without loosing all its sales (might
loose some sales). All firms with market power have a downward slopping demand
curve (not a straight line like perfect competition does). When they raise price,
sales do not fall to zero but they do decrease due to law of demand.
Monopoly
A firm that produces a product for which there are no close substitutes in a market
that other firms are prevented from entering because of a barrier to entry.
Barriers to entry
1. Economies to scale: some monopoly companies have reached a point where they
have reduced costs to the point where no new competitive companies stand a
chance.
2. Barriers created by government
3. Input barriers: sometimes a company might own all resources to produce a
particular product.
4. Brand Loyalties
5. Consumer lock-ins: contract provided between product and company to ensure
loyalty.
6. Network externalities: when value of product increases as more people buy it
i.e.: cell phones
Ex: If P = 10 – Q and TC = 1 + Q + 0.5Q2
TR = 10Q – Q2
MR = 10 – 2Q
MR = MC
10 – 2Q = 1 + Q
Q =3
P = 10 – 3 = $7
We can calculate price elasticity = P / P –a = 7 / 7 – 10 = -2.33
We can calculate AVC = TVC / Q = Q + 0.5Q2 / Q = $2.5
In perfect competition, demand surce of a firm is a horizontal straight line. In
monopoly, it is downward slopping and to the right.
Ex: If P = 30 – 6Q and TC = 14 + 3Q + 3Q2
MR = 30 – 12Q and MR = MC
So MC = 30 – 12Q
P = 30 – 6(1.5) = $21
30 – 12 Q = 3 + 6Q
-18 Q = -27
Q = 1.5
Cost Plus Pricing
A method of determining price by setting price = ATC plus a percentage of ATC as a
mark up. When it is difficult for a firm to estimate their demand.
Usually involves 2 steps.
1. Firm estimates cost of unit per output of the product at 2/3 or ¾ of capacity
(being the total amount they could potentially produce – firms never operate at full
capacity).
2. The firm adds a mark up as a percentage to the estimated average cost.
Meant to include certain costs that are difficult to allocate and to provide a return
on investments.
Mark up = Price – cost / Cost
Can be expressed as a decimal or as a percent.
To solve for price, multiply both sides by cost. Cost (mark up) = price – cost
Price = cost + cost (mark up)
Price = cost (1 + mark up)
Monopolistic Competition
Developed by Edward Chamberland, economist in the 1930‟s. He found that in
between perfect competition and monopoly, there is another market. At this time,
the market was not defined well. He worked and developed a market structure
called monopolistic competition. It is a market consisting of a large number of firms
selling a differentiating product with low barriers to entry and therefore have some
but not much market power. The firms have some market power but are not
monopolies. Firms under monopolistic competition have a downward slopping
demand curve.
Market power:
Monopoly > oligopoly> Monopolistic competition > perfect competition (0 power)
Higher market power, greater slopping demand curve. If market power is zero,
demand curve is straight horizontal line.
Characteristics of monopolistic competition:
1. Firms sell differentiated products – products that are similar to but somewhat
different form one another (most distinct characteristic).
2. Large number of relatively small firms.
3. Unrestricted entry and exit of firms into and out of the market.
4. Firms act like independent firms.
Difference between monopolistic competition and perfect competition, under
monopolistic completion, firms sell a differentiated product. Under perfect
competition, they sell a homogenous product.
Monopoly is not a long run theory. There is no entry and no exit. Both perfect
competition and monopolistic competition are long run theory, because entry and
exit are there.
Monopoly maximizes the profit by actually putting up equilibrium condition so that
MC = MR. this is the same condition for monopolistic competitors in short run that
act like monopolists by maximizing profits. But in long run, we have entry and exit.
This tell us in short run, we will always make profits. But in long run, due to entry
and exit, we may not make profits.
We frequently find ourselves as buyers in monopolistic competition (coffee shops,
retail etc).
Price and output decision under monopolistic competition
Short run: will look like a monopoly operation. MR = MC.
Long run: demand increase, MR increases. Equilibrium point on graph is different.
There is two conditions for long run.
1. Price = LAC (profits are zero) (not equal to MC or MR in this case)
2. MR = MC profits are maximized.
Because of conditions under perfect competition, you can only have equilibrium
under these two conditions.
Demand curve is labeled as AR in the two graphs above.
As companies enter the market, your demand curve shifts to the right of the graph
until it becomes tangent to ATC. At this point, it is at equilibrium. At equilibrium, we
are only making normal profit (implicit costs).
Ex: For monopoly: TC = 40 + 2Q + 2Q2 and MC = 2 + 4Q
Q = 80 – P. Find project maximizing output?
Find P first. Since MR = MC.
TR = P x Q = 80 Q - Q2 and MR = 80 – 2Q
80 – 2Q = 2 + 4Q
Q = 13
Find P using Q = 13.
P = 80 – 13 = $67
Ex: For perfect competition (in short run)
TC = 20 + 20Q + 5Q2
Qd = 1400 – 40P
Qs = -400 + 20P
What is the project maximizing output of this from P = MC.
1400 – 40 P = -400 + 20 P
P = $40
MC = P
MC = 20 + 10Q
20 + 10Q = P
20 + 10Q = $40
Q = 1
Ex: If monopoly MC = 80 – 4Q and P = 200 – 2Q
Find perfect maximizing output and price.
MR = MC
200 – 4Q = 80 – 4Q
- 8Q = - 120
Q = 15
P = 200 – 2(15)
P = $170
Ex: In perfect competition short run MC = 4 + 3Q and P = $3.
Should the firm continue to operate or shut down in the short run?
* Recall P > AVC; keep operating or P < AVC; shut down.
MC = 4 + 3(1)
MC = $7
They should shut down since P < AVC.
Ex: In monopoly, if TC = 100 + 3Q and MC = $3
and Q = 200 – P and MR = 200 – 2Q
What is the profit max price and quantity?
200 – 2Q = 3
Q = 98.5
P = 200 – 98.50
P = 101.50
What is the MR of the 20th unit?
MR = 200 – 2(2o)
MR = $160
Chap. 8 – Managerial use of Price Discrimination10/29/2012 8:42:00 AM
In this chapter, we will show how some
complications (multiple plans, multiple prices,
multiple markets) affect the profit maximizing
competition set in previous chapter. Effect of
these complications does not make their
implementations easier – they get more
complex computationally. We will limit our
attention to firms with market power.
Firms always want to operate when MR = MC
Price Discrimination: A practice whereby a firm charges different prices to different
group of customers for the same goods or service.
A simple monopolist can only maximize profits if MR = MC but creative managers
look at this and realize they can make more profits. Some customers are willing to
pay more than the PM (noted at P1 in graph above).
Reservation price is the highest price a customer is wiling to pay for the product.
Some customers are only willing to pay less than PM. We do not get these
customers. We leave these customers behind (to the right of vertical yellow line).
We do not charge them, we leave them behind. They are considered consumer
surplus. In order to enhance profits, we must charge different prices. Our economic
profit customers are found to the left of the vertical yellow line.
Consumers in top triangle denoted by green, red and yellow border are willing to
pay more but we do not charge them more.
There exist 3 types of price discrimination:
1. First degree price discrimination
2. Second degree price discrimination
3. Third degree price discrimination
In the real world, we cannot do this in all industries. Industries in which we can
include car sales, diamond sales etc.
First Degree Price Discrimination
For the first degree price discrimination to occur, a firm must have a relatively
small number of buyers and it must be able to estimate the maximum prices they
are willing to accept (ex: car dealerships, diamond shops etc).
Second Degree Price Discrimination
Much more common phenomenon. Selling electricity,
gas, water etc. to certain customers is an example.
They also due residential rate.
To the right is the consumer demand curve.
They will charge you price P until unit Q. Amounts in
between Q and Q1 will be charged P1 etc. (should be
read as a step function).
By discriminating, they have been able to increase their TR. If they were only
charging one price, they would have constant TR. By managers discriminating, they
have found ways to increase their profits.
They are also leaving some consumer surplus here (seen as the triangles just below
the demand curve).
In second degree, customers are being charged the reservation price that they are
wiling to pay.
First Degree Price Discrimination
- All customers are charges a price equal to their reservation price
- The firm captures 100% of the consumer surplus
- Equilibrium output and MC is the same
- Firms have a relatively small number of buyers and they are able to estimate
reservation prices.
Second Degree Price Discrimination
- More commonly used by utilities (electricity – gas, water etc)
- Different prices are charged for different quantities of the same good.
Third Degree Price Discrimination
- The most common form of price discrimination
- Demand must be heterogeneous - different demand segments of the market must
have different price elasticity‟s of demand
- Managers must be able to identify the segments
- Markets must be successfully sealed that customers in one segment cannot
transfer the goods to another segment.
Evidence of price discrimination is when there is on differences in cost. As such, the
following conditions must be present. Ex: An airline charges more for tickets to
business rather than to students.
When you have two markets, and two types of price elasticity‟s, to price
discriminate, we should ask:
1. How much output should a price discriminating firm allocate to each class of
buyers?
2. What price should it charge each class of buyers?
If the output is given, then the firm should try to transfer the output from the lower
MR market segment to the higher MR segment. In other words, if the output is
given, a price discriminating firm will decide how they have to allocate to each
market and how much to charge. Assume that there are only two classes and the
firm already knows the total output. The firm will maximize profits by allocating
outputs by making MR of one class = MR of one class. If MR1 = $5 and MR2 = $10,
they will transfer output from first class to second class. As you keep sending more,
price will keep dropping. If MR in one segment is lower than in another, you need to
keep sending until MR1 = MR2.
MR1 = MR2
MR1 = P1 (1 + 1/ η)
P 1 (1 + 1/ η)
--- = -------------
P 2 (1 + 1/ η)
More realistic case is when the firm decides both profit maximizing price and output
by discrimination. The price discriminating firm will choose the output where the MC
of its entire output is equal to the common value of the MR of the two classes.
In this case, the profit of a firm:
Total profit = TR1 + TR2 – TC
TR is simply the horizontal summation of the MR in each market.
We look at the intersection of line MR (total) and MC because this is where MR =
MC. The value on the x axis tells you the quantity to produce. If you draw a
horizontal line you see where it intersects MR1 and MR2. This tells you how much in
each market should be sold (Q1 and Q2).
Ex: TC = 100 + S (QM + QT)
QM = 70 – 2PM
QT = 55 - PT
Isolate P.
PM = 35 – 05.QM
PT = 55 - QT
Profit = TR + TR – TC
Profit = (35 – 0.5QM)QM + (55 - QT)QT – 100 – 5QM – 5QT
Profit‟ = 30 – QM = 0 so QM = 30
Profit‟ = QT = 25
PM = 35 – 0.5 (30)= $20
PT = 55 – 25 = $230
So we get QM = 30 and QT – 50
Total profit = (35 – 0.5(30))(30) + (55 - 25)(25) – 100 – 5(30) – 5(25)
Total profit = $975
No price discrimination
QM = 70 – 2PM
QT = 55 - PT
Q = QM + QT = 70 – 2P + 55 – P = (125 – Q)/ 3
P = 41.7 + 1/3 (Q)
TR = 41.7Q – 1/3 (Q)2
MR = 41.7 – 2/3 (Q)
Profit = 41.7(55) – 1/3 (55)2 – 100 – 5(55)
Profit = 2293.5 – 1008.3 – 100 – 275
Profit = $910.
Ex: What is the price elasticity if MC = $9 and Price = $18
MC = P (1 + 1/ η)
η = -2
Ex: What is the price elasticity if MC = $9 and Price = $27
MC = P (1 + 1/ η)
η = -1.5
Using coupons and rebates for Price Discrimination
In order to implement price discrimination, you can implement coupons and rebates
as a strategy. Why don‟t managers simply reduce prices? Coupons are used to price
discriminate. If they reduce the price, it will be the same for everyone. This will not
be what they want since they want price discrimination which always yields profit.
Not all consumers use coupons (about 20-30%). This demand segment of people
who use coupons is more price sensitive. People with inelastic demand, do not use
coupons.
Ex: What is the project maximizing profit and output in 2 markets?
MR = MC
If MC = 10Q = 10(Q1+Q2)
Q1 = 20 – 0.1P1 – Mk1
Q2 = 20 – 0.2P2 - Mk2
P1 = 200 – 10Q1
TR = 200Q2 – 10Q12
MR = 200 – 20Q2
P2 = 100 – 5Q2
TR = 100Q – 5Q22
MR = 100 – 10Q2
MR1 = MC
200 – 20Q1 = 10Q1 + 10Q2
Q2 = 20 – 3Q1
Substitute the value of Q2 in equation 2
MR2 = MC
100 – Q2 = 10Q1 + 10Q2
Q1 = 6 and Q2 = 2
P1 = 200 – 10Q1 = 200 – 10(6) = $140
P2 = 100 – 5Q2 = 100 – 5(2) = $90
2 Markets
1. Market R – more affluent
2. Market S – less affluent
(People who are more price sensitive will be in the more elastic portion)
Coupon = $X.
P = Nominal / posted price: The price that everyone pays. Buyers without coupon
pay this price.
Buyers with coupon pay $ = $P - $X
What is the
1. the posted price?
2. the price of the coupon?
3. the price paid by consumers S (with a coupon)?
MRR = MRS = MC
If MC = $2, and calculate $P if MRR η = -5 and MRS η = -2
P (1 + 1/ ηR) = (P – x) (P (1 + 1/ ηS)
P ( 1 + ½) = 2
½ P = 2
P = $4
(P – x) x (1 + 1/ -5) = 2
(4 – x) (0.8) = 2
X = $1.5
1. The posted price is $4
2. The price of coupon is $1.5
3. The price paid by consumers with a coupon are $4- $1.5 = $2.5
Coupons and rebates are used to sequent a market. Consumers using coupons and
rebates have a more elastic demand. Coupons and rebates lead people to self select
their market segments.
Peak Load Pricing
The demand for some goods in their sensitive or seasonal – demand can shift with
the time of the day.
Demand for highway and transit services is greatest in the morning and at rush
hour. Roads to resort areas are likely to have a greater demand on the weekend.
Demand for electricity is higher in winter for heating and in summer, for air-
conditioning.
There are leaders and followers in the market for goods and services. Companies
have figured out how to charge higher prices to the leaders.
Peak Load Pricing
- Electricity generation
- Roadways
- Resorts
- Hotel rooms in particular seasons
Cost keeps increasing during high periods due to expensive resources. Firms should
equate MR = MC separately in the two time periods to determine the appropriate
prices because the MR differs in either case. You can do this by showing both
seasonal demand curves on one graph.
2 Part Tariffs: When managers set prices so that consumers pay an entry fee for
each unit of the product they consumer. You cannot consume the product until you
pay the fee. This is a way to operationalize first degree price discrimination. A
monopolist sometimes requires the consumer to pay an initial fee (called entry fee)
for the right to buy its product as well as usage fee for each unit of the product that
he/she buys.
Disney used managerial economic pricing to become one of the most profitable
companies in the world.
An example of a 2-Part tariff graph for a phone
company. $2 represents the entry fee to have a
phone. The consumer surplus is seen by the
darkened triangle. These are extra fees that
consumers may be paying (ex: for voicemail).
2 Part Tariffs examples:
- Golf clubs
- Costco
- Wireless phone companies
- Ski clubs
- Razor and blades
- Computer printers (always buying ink)
Chap. 9 – Bundling and Intrafirm Pricing 10/29/2012 8:42:00 AM
A firm has a bundle of goods (3-4 items) that they want consumers to buy
together. If you like 2/3 or ¾ you will still buy it. This is because your reservation
price is higher than the price for the bundle. Bundling explains how managers can
use it and time strategies to increase profit when customers have heterogeneous
tastes. There are companies that has multi divisions. These divisions are profit
setters. When they sell the product to the other division, they set the same price.
This is called the transfer of goods. Some places have been sued for charging the
same prices in multiple countries with different taxes. Internationally, there are a
lot of accountants to sovle this problem. What pricing is to be used? There are
goods that cannot be bought outside because there is no firm outside. The door
making division asks the assembly division the price for the doors of their cars
needed. This is called upstream and downstream.
Bundling:
1. Simple/pure bundling: this is when managers offer products or services as
one package. Consumers do not have an option to purchase package
components separately. For instance, inclusion of service contract with product
(it is tied with it). You used to have to buy the CD to get one song, now you can
download an individual song. This was an early example of pure bundling.
2. Mixed bundling: Allows consumers to purchase package components either
as a single unit separately. The bundle price is generally less than the sum of
the prices of the individual components. For instance, you can get season tickets
to sporting events or get the table d‟hôte on the restaurant menu.
Bundling is best used when there is a wide variance in consumer‟s price sensitivity
and when market conditions make it difficult to price discriminate. Managers form
bundles so as to increase profits by creating negative correlations across
consumers.
Negative correlation: when some customers have higher reservation prices for one
item and lower reservations prices for another item in the bundle.
Manager can make a higher profit rather than selling the products separately.
Economists separate between the two types of bundling. If you are a manager and
you are asked for creative ways to increase profits, bundling is often used. Fast
food restaurants, sports team and entertainment practice mixed bundling.
Mechanisms of bundling (advantages)
1. Bundling can increase the seller‟s profit if their customers have varied tastes.
There is negative correlation.
2. Can emulate first degree price discrimination (firm is capable of extracting
100% customer surplus) when it is not otherwise possible (because
individual reservation prices cannot be calculated). The law might also
prohibit it.
3. Bundling does not require to have knowledge of individual reservation prices
but only the distribution of reservation prices but only the distribution of
individual reservation prices (they just want to know in which area they have
people have varied taste).
Pricing strategies:
Assumption: Goods are independent, so the value of the bundle is equal to the sum
of the reservation prices of the goods in the bundle.
1. Separate pricing: Goods are not bundled. Prices are set to profit maximize
monopoly price. This is used when bundling would not yield higher profits.
2. Pure bundling: Bundle price is set to maximize profits.
3. Mixed bundling: Bundle price and individual good prices are set to maximize
profits.
Pricing separately:
Let Ri = the reservation price of good i
Let Pi = the price of good i
Let Pb = the price of the bundle
If R1< P1 and R2 < P2 The consumer buys neither good.
If R1 > P1 and R2 < P2 the consumer buys only good 1.
If R1 < P1 and R2 > P2 the consumer only buys good 2.
If R1 > P1 and R2 > P2 the consumer buys both goods.
Pure bundling:
If (R1 + R2) < Pb the consumer does not buy the bundle.
If (R1 + R2) > Pb the consumer buys the bundle.
Mixed bundling:
If (R1 + R2) < Pb, R1 < P1 and R2 < P2 the consumer buys neither good or bundle.
If R1 + R2 > Pb the consumer buys the bundle.
If R1 > P1 and R2 < P2 and (R1 + R2) < Pb the consumer buys good 1 only.
If R2 > P 2 and R1 < P1 and R1 + R2 < Pb the consumer buys good 2 only.
Definitions of concepts
Credibility of the bundle: when managers correctly anticipate which consumer swill
purchase the bundle or goods separately.
Extraction: When a manager extracts the entire consumer surplus from each
customer. This is also called perfect price discrimination.
Exclusion: When the manager does not sell a good to a customer who values the
good at less than the cost of production.
Inclusion: When a manager sells a good to a consumer who values the good at
greater than the seller‟s cost.
Extraction, exclusion and inclusion are all satisfied by practicing first degree price
discrimination. Pricing separately will satisfy exclusion. Pure bundling will result in
complete extraction. Mixed bundling the profit is always equal to or better then
pure or separate pricing.
Tying: A form if bundling involving complementary products. It is a pricing
technique in which managers will sell a product, the use of which requires the
consumption of a complementary product. The consumer is required generally by
contract to buy the complementary product from the firm selling the product itself.
For instance, Xerox leased copying machines but companies were forced to
purchase Xerox paper. To ensure that their product works properly and to protect
their brand name, firms use tying. For instance, a fast food restaurant is forced to
use all the same meat for every burger they produce.
Transfer pricing: Transfer price is a payment that stimulates a market where no
formal market exists. This refers to intrafirm pricing among wholly owned
subsidiaries or divisions. Goes on in a lot of industries such as car industry which
has a lot of divisions. They treat each division as a profit center where they have to
look at revenues and expenses.
Function:
To encourage profit maximizing or cost minimizing behavior by providing
an incentive.
Measure the performance of semi-autonomous divisions.
If you look at a multi division firm, you have upstream and downstream monopoly.
Selling division: upstream monopoly
Buying division: downstream monopoly
Transfer Price: Price that the selling division (upstream i.e.: car door parts) division
charges the buying division (downstream i.e.: auto making assembly line) for its
product of the same firm. Results from an internal market.
We assume no external markets exists for their product (they only get doors from
one place). Managers must decide how many engines and autos to make. In
downstream, it is subject to market because autos are sold in external market. If
there is no market for the upstream, the transfer payment takes place.
The price charged by the upstream to the downstream for its product should be set
so that the firm as a whole maximizes profit.
The quantity manufactured by the downstream must equal the quantity
manufactured by the upstream. Therefore, the transfer price is set by the company.
Q‟ is the quantity to be produced.
Transfer Price is where price is equal to
marginal cost. PT = MCp (point c on graph)
Once profit maximizing quantity and price
is set, the market department will operate
at:
MRM = MCT
MCT = PT + MCM
Perfectly competitive external market exists for the transferred product :
If the production department produces more Q than the selling department needs,
they can go outside and sell more. If the production department produces less Q
than the department needs, the department can go outside and buy more.
When you have an external market, the product being transferred is in perfect
competition (sell as much as you want).
Production operates where: MCP = PT
Marketing operates when MRM = MCT
In this case, the transfer price was decided
by the market not by the firm.
Ex: Let the market division: TCM = 200 + 10QM and PM = 100 – QM
And production division: TCP = 10 + 2QP + 0.5QP2 and price = $42
MCP = PT
2 + QP = 42
QP = 40
MCT = PT + MCM
MCT = 42 + 10
MCT = 52
TRM = P x Q
TRM = (100 – QM) (QM)
MRM = 100 – 2QM
100 – 2QM = 52
QM = 24
PM = 100 – 24 = $76
Chap. 10 - Oligopoly 10/29/2012 8:42:00 AM
Decisions taken by firms
1. Pricing
2. Advertising
3. Output
4. Expanding production facilities
5. Spending on research and development
Also affects profit of every other firm in the market when there are relatively small
number of firms in the market. Therefore, profits of all firms are interdependent.
These managers under the market where there are few sellers must get into the heads
of the rival managers in order to make conjectures to predictions about their reactions.
Successful managers must learn how to anticipate the action and reaction of managers
in their market. Interdependence among firms require strategic behavior (which
consists of the actions that firms can threateningly take).
Oligopoly: is a market consisting of a few relatively large firms each with a substantial
shape of the market and all recognize their interdependence. It‟s characterized by
interdependence and the need for managers to explicitly consider the reactions of
rivals. Protected by barriers to entry that result from government decrease, economies
of scale or control of strategically important resources. Some oligopoly markets are
competitive, some are not. In some markets, firms cooperate in others they do not.
Some markets are characterized by a great deal of price competition, others have little.
Anything to differentiate their product such as advertising if fiercely competitive.
Because oligopoly markets differ so much in their behavior patterns and their overall
characteristics, economists have not been able to develop a single, general theory
unlike the 3 other market structures.
Collision Agreement: Collision Oligopoly
Conditions in oligopolistic industry encourage collision since the number of firms in
small and all firms are aware of their interdependence. Advantages of collision are:
1. Decrease uncertainty
2. Increased profits
3. Better opportunity to prevent entry
Cartels: open collusive arrangements. Ex: OPEC. Are illegal in North America.
- Cartels maximize profits by restricting the output of member firms to a level that the
MC of every firm in the cartel is equal to the market‟s MR and then charging the market
clearing price. They horizontally add up the MR of all the firms (they can do this
because there are so little firms in oligopoly).
- The need to allocate output among member firms results in an incentive for the firms
to cheat by overproducing and thereby increasing profits.
Price Leadership
Another cooperative solution to oligopoly problem. This solution does not require open
collusion but the firm and the market must agree to the solution. It has been quite
common in many industries (oil, steel, tire, banks etc). The largest firm follows this
rule. Usually the dominant firm in the market will be the price leaders. The price leaders
set the price to maximize profits. All firms in industry compete for sales.
Price leadership is a pricing arrangement in which one firm in an oligopoly market sets
the price that the other firms match.
Assumption:
1. There is a single firm, the price leader that sets the price in the market.
2. There are also follower firms which behave like a price taker.
3. The price leader forces a residual demand that is the horizontal difference between
the market demand curve and the market supply curve.
4. The price leader produces a quantity at which the residual MR is equivalent to the
residual MC. Price is then set to clear the market.
The black spot is the price that is set by the price leader.
V0 = The end point of arrow B. The total demand.
R0 = The end point of arrow A. The demand provided by the small firms.
The residual (between V0 and R0 is provided by the price leader).
To derive residual demand find a few points.
The graph on the left shows the demand curve.
The graph on the right shows the demand curve for the price leader / dominant firm.
Small firms operate where MC = P. They will provide everything they can. The residul is
provided by the price leader. Small firms provide R0.
Ex: Market Q = 100 – 5P
and Small suppliers Q = 10 + P
and Price leader MC = 2Q
Price Leader:
Q for price leader = market quantity – quantity supplied by small firms
Q = (100 – 5P) – (10 – P)
Isolate P. P = 15 – Q/6
Calculate TR = P x Q. TR = 15 Q – Q2/6
Take the derivative of TR. MR = 15 – Q/3
MR = MC
15 – Q/3 = 2Q
Q = 45/7
Market:
Q = 100 – 5P
Q = 100 – 5 (13.93)
Q = 30.35
Small supplier:
Q = 10 + P
Q = 10 + 13.93
Q = 23.93
Chap. 11 – Game Theory 10/29/2012 8:42:00 AM
Game Theory: is an analytical tool or a guide in making decisions in a situation
involving interdependence. A manager‟s optimal decision on what he/she expects
others to do since payoffs are interactive. Other managers are similarly guided so
all are aware of their interdependence. This is called a chain of reciprocal
applications (because we keep going back and forth). Good managers attempt to
influence the behavior of others by systematically evaluating the variables subject
to their control and using their variables to influence expectations.
Game theory is a mathematical framework that can help managers anticipate the
actions of others. It helps managers represent strategic issues by focusing on the
players (other firms) involved, their feasible strategies the possible outcomes and
the playoffs associated with those outcomes.
