01-Agricultural Economics Enj

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Project GCP/SYR/006/ITA Phase II

FAO-ITALIAN GOVERNMENT COOPERATIVE PROGRAM

ASSISTANCE IN CAPACITY BUILDING THROUGH ENHANCING

OPERATION OF THR NATIONAL AGRICULTURAL POLICY CENTER

SYRIA

Intensive Training Program

NOTES OF THE COURSE IN

AGRICULTURAL ECONOMICS

Prof. Alessandro Corsi

(University of Turin Italy)

May-June 2002


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Notes of Agricultural Economics____________________________________________________________

Project GCP/SYR/006/ITA Phase II Intensive Training Program 2

These notes are intended as an handout of the lectures. They do not substitute for more structured

readings of basic textbooks.

The basic references for the contents of the course are:

- Colman D., Young T.: Principles of agricultural economics: Markets and prices in lessdeveloped countries, Cambridge University Press, Cambridge, 1989

- Ellis F.: Peasants economics: Farm households and agrarian development, CambridgeUniversity Press, Cambridge, 1988

An useful additional reference is:

- Harrigan J., Loader R., Thurtle C: Agricultural Price Policy: Government and the Market, FAO,Training materials for Agricultural Planning, N. 31


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1. INTRODUCTION

AGRICULTURE has one basic characteristic in common with other sectors:

- produces (in general) for the market

therefore:

- utilises factors of production:

provided by firms:

- intermediate inputs (fertilisers, seeds, pesticides, fuel, etc.)- capital goods (tractors, harvesters, etc.)

provided by households:

- labour

- capital- land

- and produces:

- consumers goodsfor consumers- production goods (intermediate inputs, e.g. seeds, fibres; capital goods, e.g. dairy cows)for

firms

AGRICULTURE has also specific characteristics of its own:

1. TECHNOLOGICAL SPECIFIC CHARACTERISTICS:

- tight link to land (a scarce and not producible factor)- length of the production process- irreversibility of the production process- dependence on (uncertain) biological cycles- dependence on uncontrolled factors (weather)

As a consequence:- asset fixity- seasonality- difficult standardisation- risk and uncertainty


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2. SOCIO-ECONOMIC SPECIFIC CHARACTERISTICS:

In most countries, agriculture is composed in the largest majority by SMALL FIRMS, FAMILY-OPERATED.

(even the largest farms have a small dimension relative to the overall production)

Two reasons have been indicated for this:- lack of economies of scale- supervision costs of waged labour

Consequences:- agricultural production is highly fragmented- many costs are not explicit (e.g. costs for family labour)

3. HETEROGENEITY OF AGRICULTURAL PRODUCTION

Diversity as to:- farming systems (different location, weather, climate, soil, etc.)- farm structures:

- farm size and size distribution- land tenure system (ownership, rent, sharecropping)- farm/labour relationship (family work, waged work)

4. CHARACTERISTICS OF THE DEMAND FOR AGRICULTURAL PRODUCTION

Agricultural production can be destined for:- food- non-food (fibres, like cotton etc., or raw materials, like rubber etc.)

- self consumption- the market

- fresh product- processing

The different destinations imply different characteristics of the demand, and the short- and long-term trends are different.

For instance, in general the demand for food:- depends on the amount of population- depends also on consumers income, but does not increase much when income increases- the demand for fresh food is less responsive to income than the demand for processed food

The demand for non-food products depends much more on general economic development.


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5. MAIN PROBLEMS CHARACTERISING THE AGRICULTURAL SECTOR

- price fluctuations, due to:- weather, diseases, etc.- effects of international production changes on the local market

- time lags between the decision to produce and the realisation of the final output- income fluctuations- declining long-term terms of trade

- food demand scarcely responsive to income- less concentration in agriculture than in many other sectors, and little market power- sectors outside agriculture (input production, food industry, marketing sectors) are more

concentrated and have more market power- scarce factor mobility (land, machinery, labour): adjustment to market changes are slow- hence: agricultural incomes are often lower than in other sectors

6. ROLES OF AGRICULTURE IN ECONOMIC DEVELOPMENT

Historically, in western countries, agricultural development has been a prerequisite for the industrialrevolution:- providing food for the industrial labour force- providing raw materials for the industry (cotton, wool, etc.)- providing labour for the industry- providing the capitals for the first industries- providing a market for industrial goods (tools, machinery, chemical fertilisers)

In the other countries, agricultural development has important roles too:- provides labour for the other sectors- creates an internal market- may be a source of capital formation- may provide raw materials for a domestic processing industry- may provide foreign currency when the agricultural output is exported

5. MARKET EFFICIENCY AND MARKET FAILURES


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Policy measures change the market conditions. Whenever some change is introduced, most of thetimes someone is losing and someone is gaining.

Is it possible to give an evaluation of the changes from an economic point of view?

In general, economics states that utility is an individual matter, so that gains and losses in terms ofutility among different persons cannot be compared.

Nevertheless, a widely acceptable criterion to evaluate the effects of any change is the fo llowing: ifat least someone is made better off by a change without making anybody else worse off, then thechange is an improvement.

This is a very general criterion of efficiency, called Pareto efficiency.Any change that meets this criterion is called a Pareto improvement.When no change making someone better off is possible without making someone else worse off,

then a situation of Pareto optimality is reached.

- any exchange on a market is a Pareto improvement- if the seller were not made better off by the exchange, he would not sell- if the buyer were not made better off by the exchange, he would not buy- by implementing the exchange, a Pareto improvement is achieved

Nevertheless, any Pareto optimal situation depends on the distribution of resources: there existinfinite Pareto equilibria. If a very rich person trades with a poor person, they may improve theirsituation, but the difference in income may nevertheless be judged as unfair.Therefore, there may exist another reason for intervening with policy measures, a reason that istermed equity criterion: it may be considered that a redistribution is needed, so that necessarilysomeone will gain and someone else will lose.

Apart from equity reasons, it is nevertheless important to explore whether it is possible to improvethe existing situation from a Pareto efficiency point of view.

From this point of view, competitive markets are a powerful tool to reach efficiency.It can be shown that, if some conditions apply, then a competitive market equilibrium is Pareto-optimal since it satisfy 3 conditions:1. it is not possible to increase the utility of any consumer by trading goods among them: this

condition is satisfied if for any consumer the MRS between two prices is equal to the price ratio;since prices are the same for all consumers, none of them wants to change his optimalcombination of goods

2. it is not possible to increase the output by trading inputs: this corresponds to the condition thatthe MRS between two inputs is equal to the price ratio; again, since prices are the same for all

producers, none of them wants to change his optimal combination of inputs3. it is not possible to increase utility by changing the combination of goods produced: since for

every producer the MRT is equal to the price ratio (and the MC is equal to the price), and sincethe price ratio is the same for all consumers, no change in the combination of products mightincrease the utility of consumers.

So, markets are an efficient way to increase the utility associated with the economic activity.


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The above conditions apply to competitive markets. There are nevertheless several cases in whichthe requisites of competitive markets are not met. In these cases, markets fail to allocate efficientlyresources.

The reasons for market failures are:

Existence of a market powerIt is the case of monopoly and of all non-competitive markets. In such markets, operators dont

produce at the point where the MC is equal to the price, but where MC=MR. The result is a loweroutput than in a competitive market (or a lower input use, for a monopsony). So, more could be

produced, and at a lower price.

Lack of marketsMarkets for some goods or resources do not exist or may be incomplete or fragmented. Examplesinclude the land market, the labour market, the capital market.If, for instance, there is no market for labour, then wage is subjective: labour may be cheap for a

poor farmer, and expensive for a wealthy one: the allocation of labour is therefore not optimal.

ExternalitiesExternalities are costs borne by someone other than the one who produces (negative externalities) or

benefits received by someone other than the one who produces.

A typical example of negative externality is pollution: residuals of pesticides are run off with thewater, damaging the activity of fishermen, or making more costly the provision of drinking water.This are cost involved in the agricultural production, but not paid by farmers, but by others.

An example of positive externality is soil protection by farmers in hilly or mountainous areas,connected with agricultural production: by their activity, they prevent soil runoff, and avoid floods,

but they receive no benefit for this action.Since the costs connected with a negative externality are not borne by the polluter, his private costsare lower than the social costs: by equating his private MC to the price, the polluter will produce toomuch as compared with the social optimum. If there is a positive externality, the producer will notreceive a return for it, so that his production is too low as compared to the social optimum.

Public goodsWhat in economics is called a public good is not a good produced by the public sector: a publicgood is such if it is:- non-rival in consumption: if it is consumed by one person, it remains available for other

persons. For instance, the technological knowledge used by one person does not detract from thepossibility for another person to use it

- non-excludable: it is not possible or it is too costly to prevent the use for those who do notpay. An example is a natural landscape: unless it is visible only from one place, there is no wayto have tourists pay for its view

The two characterist ics can be combined, so there are four categories of goods:- pure private goods: excludable and rival in consumption (e.g., a bottle of mineral water)- open access resources: rival in consumption but not excludable (e.g., marine fish resources)

- club goods: excludable but not rival in consumption (e.g., a non-crowded highway)- pure public goods: non-rival in consumption and non-excludable (e.g., controls to preventimportation of animal and plant deseases)


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The problem with pure public goods is that the market would not produce them, though all thosethat might use them would be better off paying for them and having the good provided.This is a problem offree-riding: many would not pay, since there would be no way to exclude themfrom consumption. This is why pure public goods are provided by the public sector, by imposing a

compulsory payment through taxes. This realises a Pareto improvement that the market cannotreach.Even for club goods, which are excludable, a Pareto improvement would be possible, since usersnot willing to pay the price would increase their utility if they were allowed to use them for free,and no one else would be made worse off, since they are non-rival.Finally, for open access resources, the problem is connected with their overuse. If no regulation isintroduced, they will be exploited exceedingly, and there will be a damage for everyone.

Information problemsIf there is not full information, both technical and on the market conditions, operators are not able to

achieve technical and allocative efficiency.Moreover, if there is risk, unless there are insurance markets for all risks, operators may not makethe most efficient choices.

In all these cases, markets fail to efficiently allocate resources. All these problems call for policyinterventions for correcting market failures.

Policy interventions may also be implemented for equity reasons. But all interventions modify thewelfare of some groups, so that someone gains and someone else loses.There is no objective measure for such gains and losses, since utility is subjective.

Nevertheless, another criterion widely used to evaluate changes in social welfare is Kaldorscompensation principle: it states that a change is desirable if the gains of the gainers are largeenough to compensate the losers for their losses.This principle does not require that the compensation be actually paid to the losers. What it impliesis that the policy-maker considers the total welfare of the society , regardless of whom receives gainsor losses.

Gains and losses of welfare by consumers and producers can be measured through consumer andproducer surplus.

Consumer surplusConsider a market with equilibrium price P* and equilibrium quantity Q*.All consumers pay the same price, P*. But some consumers were willing to pay a higher price: forinstance, consumers located at quantity Q1 were prepared to pay a price P1. So, they benefit fromhaving the good at price P*, so that they gain a surplus, equal to the difference (P1 - P*) betweenthe price they were willing to pay and the actual price. In the same way, consumers located atquantity Q2 were willing to pay a price Q2, but actually paid P*, so they gain a surplus P2 P*.Summing up all surpluses for all purchased units results in the triangle AEP*, which represents theconsumer surplus.


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Producer surplusIn a similar way, producer surplus can be identified.All producers receive the same price, P*. The supply curve is the sum of the MC curves of all

producers. At any quantity produced, for instance quantity Q3, the difference between the price P*and the price P3 represents the difference between the additional revenue from the last unit

produced and the additional variable costs for producing it.

Consumer surplus

O

Pric

S

Quant ity

D

P*

Q*

P1

P2

Q2Q1

A

E

Producer surplus

O

Price

S

Quantity

D

P*

Q*

P3

Q3

C

E


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Summing all the differences for all output levels results in the area CEP*, that represents theproducer surplus

Consumer surplus and producer surplus allow evaluating the welfare effects of some change in

market conditions on consumers and producers.

For instance, suppose that the conditions for the wholesaler monopsony described above areremoved, for instance by creating a commercial structure where producers can sell their productdirectly to consumers. A competitive equilibrium can exist, at price P* and quantity Q*. Theincrease in consumer surplus is PsCFP*, the increase in producer surp lus id PpBFP*.

Similar exercises can be done also for any change in market conditions, for instance for analysingthe effects of shifts of the demand or supply curve.2. ECONOMICS OF AGRICULTURAL PRODUCTION

Theory of the firm (revision)

3 problems:- how to produce (optimal combination of inputs)- how much to produce (optimal output level)- what to produce (optimal combination of outputs)

Changes in consumer and producer surpluses

by removing a monopsony

O

Price

Supply

Quantity

Demand

P*

Q*

MFC

MR

Pp

Ps

A

C

B

EF


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Assumptions:- certainty- availability of inputs- divisibility and homogeneity of inputs

- goal of the entrepreneur: profit maximisation (profits = revenues costs)

- (alternative hypotheses will be considered later)

2.1 OPTIMAL COMBINATION OF INPUTS

a) one product, one factor

Starting point: physical factor-product relationship

Production function:

Q = f(X1, X2, , Xn)

Short-term production function (some factors are fixed, e.g. land, machinery):

Q= f(X1, X2, , Xm | Xm+1, Xm+2,, Xn)

Alternative forms: fixed and flexible coefficients- fixed coefficients: the amount of a factor necessary for each unity of product is the same,

regardless of the production level (e.g., iron for producing each car)- flexible coefficients: the amount of a factor necessary for each unity of product depends on the

production level (e.g. fertiliser per each ton of wheat)

We examine now the case offlexible coefficients

How to use one factor (all other factors held constant)

Q= f(X1 | X2, X3,, Xn)


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TOTAL PRODUCT CURVE:

Remark: the total product curve depends on the level of the fixed factors and on the state oftechnology

3 STAGES:- 1

st stage: the product increases more than proportionally to the input increase (may not exist)- 2

ndstage: the product increases less than proportionally to the input increase (must exist)- 3

rd stage: the product decreases when increasing input usage (or remains at the same level)

Law of diminishing marginal returns: given the fixed factors, the product cannot increaseindefinitely increasing just one factor

CONCEPT OF MARGINAL PRODUCT:

Marginal product = the increase in output resulting from a small change in the variable input,expressed per unit of input

For a discrete change:

MPX1= Q/ X1

Or, for an infinitesimal change:

MPX1= Q/X1 (= the slope of the total product curve at the relevant point)

If you imagine to increase input use one unit at the time, then the MP is the output from the last unitof input.

Total product

0100

200

300

400

500

600

700

800

0 5 10 15

Seeds (kg)

Maize(q)

Total product

1st stage 2nd stage 3rd stage


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The three stages correspond to:

- 1st stage: positive and increasing MP

- 2ndstage: positive and decreasing MP

- 3rd stage: negative and decreasing MP

CONCEPT OF AVERAGE PRODUCT:

Average product = the total output resulting on the average from each unit of the variable input, i.e.the total product divided by the amount of variable input:

APX1= Q / X1

If you imagine to increase input use one unit at the time, then the AP is the average output fromeach unit of input.

AP reaches its maximum when it is equal to the MP: if you imagine to increase input use one unit atthe time, if the MP (the product from the last unit) is higher than the AP (the average product of allunits of input), then the average increases; when the product from the last unit (the MP) becomeslower than the average (the AP), then the average decreases.

Graphical representation of the MP and of the AP

Just from a technical point of view, it can be excluded to use the variable input in the 3rdstage (TP

decreases or remains unchanged when using more input).

Marginal and average product

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Seed

Ma

ize

/see

d

AP

MP


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But, to make a decision on how much variable input to use, we need to make an economicreasoning.

We need to know:- the price of the variable input

- the price of the product

- Multip lying the amount of TOTAL PRODUCT by its price we obtain the TOTAL REVENUE(TR): TR = TP * PQ

- Multiplying the amount of MARGINAL PRODUCT by the price of product we obtain theVALUE OF THE MARGINAL PRODUCT (VMP): VMP = MP * PQ

- Multiplying the amount of AVERAGE PRODUCT by the price of product we obtain theVALUE OF THE AVERAGE PRODUCT (VAP): VAP = AP * PQ

The graphical representation of the VMP and of the VAP is the same as MP and AP

The optimal use of one factoris when the VMP is equal to the factor price:- increasing by one unit the use of the factor is profitable if the increase in the total revenue

resulting from the increase in input (= the VMP) is higher than the increase in cost (i.e., theprice PX1 which is paid for one unit of the factor);

- this applies up to the amount of input for which VMP = PX1 (in the decreasing part of the VMPcurve);

- VAP must be higher than p X1 (otherwise, no input use is profitable)

What happens if prices change?- if input p rice decreases:

- it is p rofitable to increase input use (now a one unit increase in input has a lower cost, lowerthan the increase in revenue)

- this applies up to the amount for which the new input price is equal to the VMP- the new optimal input use will be larger than before

- if input p rice increases:- it is profitable to decrease input use (now the decrease in costs resulting from a one unit

decrease in input is larger than the decrease in revenue resulting from the lower production)- this applies up to the amount for which the new input price is equal to the VMP- the new optimal input use will be smaller than before- if input price becomes higher than the maximum VAP, no input use is profitable (the cost

for using each unit of input exceeds the revenue that results from each unit of input)

This defines thefirms demand curve for that input(= the amount of that input that is bought by thatfirm for each input price, holding all other things constant). It corresponds to the decreasing part ofthe VMP curve, below the point of crossing with the VAP curve

- if outp ut price decreases:- the VMP and VAP curves shift downward (MP and AP remain unchanged, but they are

multiplied by a lower output price)- it is profitable to use less input (now the decrease in costs resulting from a one unit decreasein input is larger than the decrease in revenue resulting from the lower production)


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- this applies up to the amount for which the input price is equal to the new VMP- the new optimal input use will be smaller than before- thefirms demand curve for that inputis shifted to the left- the maximum VAP is now lower; the firm will now buy no input (its demand of input is

zero) for a lower input price than before

- if outp ut price increases:- the VMP and VAP curves shift upward (MP and AP remain unchanged, but they are

multiplied by a higher output price)- it is profitable to use more input (now the increase in revenue resulting from a one unit

increase in input is higher than the additional cost of that unit)- this applies up to the amount for which the input price is equal to the new VMP- the new optimal input use will be larger than before- thefirms demand curve for that inputis shifted to the right

Therefore, thefirms demand for that inputis:

- negatively related to its own price- positively related to output price(for instance, it is expected that fertilisers demand decreases if their price increase, but that itincreases if the price of crop increases)


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Exercise

Here is one example of calculation of MP, AP, VMP, and VAP.Check what is the optimal use.You will be given an Excel file with the data on input and output .You have to:

Calculate MP, AP, TR, VMP and VAP using Excel (you can check the results on this table).Find the optimal use when py = 100 and px = 6425

Find the optimal use when py = 120 and px = 4075

Total product, marginal and average

product

Optimal use of one

input

PHISICAL

RELATIONS HIPS

ECONOMICAL

RELATIONSHIPS

COSTS AND

PROFITS

Py(SP/q.)=

100

Seed Maize Px= 3200

x TP MP AP TR VMP VAP COSTS PROFITS(kg) (q.) q.m./kg

seedq.m./kg seed SP SP/kg seed SP/kg seed SP SP

0 0.000

0.5 10.875 21.75 21.75 1087.5 2175.0 2175.0 1600.0 -512.5

1.0 29.000 36.25 29.00 2900.0 3625.0 2900.0 3200.0 -300.0

1.5 53.625 49.25 35.75 5362.5 4925.0 3575.0 4800.0 562.5

2.0 84.000 60.75 42.00 8400.0 6075.0 4200.0 6400.0 2000.0

2.5 119.375 70.75 47.75 11937.5 7075.0 4775.0 8000.0 3937.5

3.0 159.000 79.25 53.00 15900.0 7925.0 5300.0 9600.0 6300.0

3.5 202.125 86.25 57.75 20212.5 8625.0 5775.0 11200.0 9012.5

4.0 248.000 91.75 62.00 24800.0 9175.0 6200.0 12800.0 12000.0

4.5 295.875 95.75 65.75 29587.5 9575.0 6575.0 14400.0 15187.5

5.0 345.000 98.25 69.00 34500.0 9825.0 6900.0 16000.0 18500.0

5.5 394.625 99.25 71.75 39462.5 9925.0 7175.0 17600.0 21862.5

6.0 444.000 98.75 74.00 44400.0 9875.0 7400.0 19200.0 25200.06.5 492.375 96.75 75.75 49237.5 9675.0 7575.0 20800.0 28437.5

7.0 539.000 93.25 77.00 53900.0 9325.0 7700.0 22400.0 31500.0

7.5 583.125 88.25 77.75 58312.5 8825.0 7775.0 24000.0 34312.5

8.0 624.000 81.75 78.00 62400.0 8175.0 7800.0 25600.0 36800.08.5 660.875 73.75 77.75 66087.5 7375.0 7775.0 27200.0 38887.5

9.0 693.000 64.25 77.00 69300.0 6425.0 7700.0 28800.0 40500.09.5 719.625 53.25 75.75 71962.5 5325.0 7575.0 30400.0 41562.5

10.0 740.000 40.75 74.00 74000.0 4075.0 7400.0 32000.0 42000.0

10.5 753.375 26.75 71.75 75337.5 2675.0 7175.0 33600.0 41737.511.0 759.000 11.25 69.00 75900.0 1125.0 6900.0 35200.0 40700.0

11.5 756.125 -5.75 65.75 75612.5 -575.0 6575.0 36800.0 38812.5


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12.0 744.000 -24.25 62.00 74400.0 -2425.0 6200.0 38400.0 36000.0

2.2 OPTIMAL COMBINATION OF INPUTS

b) one product, two (or more) factors

The production function is now:

Q = f(X1, X2 | X3,, Xn)

CONCEPT OF ISOQUANT

The same output level can be achieved with different combination of inputs (e.g., more fertil iser andless irrigation)

Q = f(X1, X2 | X3,, Xn)

There are infinite isoquants (each for every output level)

Moving along the isoquant means achieving the same output level using more of one input and less

of the other: in other words, substituting one input for another, keeping output level constant.

Isoquants

0

2

4

6

8

10

12

0 2 4 6 8

X1

X2

200

351.75

500


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CONCEPT OF MARGINAL RATE OF SUBSTITUTION (MRS):

MRS of X2 for X1 = X2 / X1 = X2 / X1 (holding output level constant)

It can be shown that:

MRS of X2 for X1 = X2 / X1 = - MPX1 /MPX2

The MRS is:- negative (if it is positive, there is technical inefficiency: to keep the output level constant, one

input has to be increased when decreasing the other one)- decreasing in absolute terms (if the MP of inputs are decreasing)

(Other cases: constant MRS for the fix coefficients production function; zero MRS forcomplementary inputs)

How to choose the combination of inputs?This is an economic problem, that can be addressed as the question:Which is the least-cost combination of inputs for a given output level?

(in other words, you want to produce a given output Q at the least cost: how to do?).

If you have a given sum C0 to spend for buying X1 and X2, you can:- spend all the sum for X1 and get C0 / pX1 of it (pX1 is the price of X1)- spend all the sum for X2 and get C0 / pX2 of it (pX2 is the price of X2)- spend the sum for a combination of X1 and X2:

C0 = X1* pX1 + X2* pX2or:X2 = C0 / pX2 (pX1 / pX2 )* X1

This equation represents an ISOCOST: all possible combinations of the inputs that can bepurchased at a given cost.- there exist infinite isocosts (each for any possible cost)- all isocost are parallel, with slope (pX1 / pX2 )- isocosts farther from the origin indicate higher cost s

The problem then becomes choosing the isocost closest to the origin that permits to reach the outputlevel Q . This is the isocost tangent to the isoquant, and the optimal combination is found on the

tangency point.

At the tangency point, the slope of the isocost is the same as the slope of the isoquant; therefore, theoptimal solution is when:

MRS of X2 for X1 = (pX1 / pX2 )

Since MRS of X2 for X1 = - MPX1 /MPX2, the solution can also be written as:

MPX1 /MPX2 = pX1 / pX2


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or:

MPX1 /pX1 = MPX2 / pX2

The optimal solution is the same if you ask the question: which is the combination of inputs thatresults in the maximum output for a given cost? (in this case, you have to choose the isoquantfarthest from the origin which is compatible with one isocost; again, the solution is the tangency

point between the isocost and an isoquant).

The economic meaning of the optimal solution is as follows:- if one dollar more spent for purchasing X1 results in an increase in production (MPX1 /pX1)

larger than the decrease in production resulting from spending one dollar less for purchasing X2(MPX2 / pX2), it pays to shift one dollar from purchasing X2 to purchasing X1 (the cost is thesame, the output increases);

- by doing so, the MP of X1 decreases, the MP of X2 increases; for the next dollar, the shift is lessprofitable;

- at one point, when MPX1 /pX1 = MPX2 / pX2, no further shift is profitable. This is exactly thetangency point.

Remark that, repeating this exercise, it is p ossible to determine:- the optimal combination of inputs for each output level- the minimum cost associated to each outp ut level

Isoquant-Isocost

0

2

4

6

8

10

12

0 2 4 6 8

X1

X2

200

351.75

500

Isocost


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What happens if input prices change?

- if both prices change by the same proportion (e.g., both increase by 5%):- the slope of the isocost remains the same (p X1 * 1.05 / pX2* 1.05 = pX1 / pX2)- the isocost shifts to the left (at the same cost, it is now possible to buy less inputs)

- the same isocost will be tangent to a lower isoquant (or, the same isoquant will be tangent toa higher isocost)- profits will decrease (same cost for a lower production, or same production at higher costs)- the opposite is true if prices decrease by the same proportion

- if one price change (e.g., pX1 increases):- the slope of the isocost changes (becomes steeper, in this example)- the same isocost will be tangent to a lower isoquant (or, the same isoquant will be tangent to

a higher isocost)- profits will decrease (same cost for a lower production, or same production at higher costs)- theproportion between the inputs will change: the ratio X2 / X1 will increase

- the opposite is true if the price decreases

More generally, a change in the proportion results from any change in relative prices (pX1 / pX2): forinstance, if pX1 increases by 5% and pX2 by 3%, there will be an increase in the ratio X2 / X1.

2.3 OPTIMAL OUTPUT LEVEL

(one product)

Solving the problem of the optimal combination of inputs, it is possible to determine the minimumcost (for variable costs) associated to each output level.

Costs on the short run:

- fixed costs (FC): are not influenced by the level of output (e.g. rents, depreciation, etc.)- variable costs (VC): depend on the level of outp ut (e.g. fertilisers, fuel, etc.)- total costs (TC) are the sum of variable and fixed costs: TC = FC + VC

Fixed costs, by definition, are constant for all output levels

Variable costs:- in afirst phase, they increase less than proportionally to production (due to increasing returns)

- in a second phase, they increase more than proportionally to production (due to decreasingreturns), and become very high when the output level approaches the limit given by the plant


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CONCEPT OF MARGINAL COST:Marginal cost is the increase in variable (or total) cost associated to a unit (or infinitesimal) increase

in production:

MC = TC / Q = VC / Q = the slope of the TC curve = the slope of the VC curve

If you imagine to increase production one unit at the time, then the MC is the cost of the last unitproduced.

The two stages correspond to:- 1st stage: decreasing MC- 2nd stage:increasing MC

CONCEPT OF AVERAGE COST:Average cost is the cost associated with each unit of production.One needs to distinguish between Average variable cost (AVC) and Average total cost (AT):

AVC = VC / QAC = TC / Q

If you imagine to increase production one unit at the time, then the AVC is the variable cost of eachunit produced up to then, and the AC is the overall cost of each unit produced up to then.

AVC and AC reach their minimum when they are equal to the MC: if you imagine to increaseproduction one unit at the time, if the MC (the cost of the last unit) is lower than the AC (the

Fixed, variable, total costs

020

40

60

80

100

120

140

0 5 10 15

Output

Costs

VC

FC

TC


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average cost of all units produced), then the average decreases; when the cost of the last unitproduced (the MC) becomes higher than the average (the AC), then the average increases.

Marginal and average costs

0

10

20

30

40

50

60

0 5 10 15

Output

Un

itcos

ts MC

AVC

AC


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The economic problem is: which is the output level for which profits are maximised?

Lets assume that the firm isprice-taker, i.e. cannot influence the market p rice, but can sell anyquantity of the product at the current market price (this is true if the firm is small in relation to thewhole market, which is almost always true for farms).

In this case:- Total Revenue (TR) is equal to output multiplied by the market price: TR = Q * P- Marginal Revenue (MR, i.e. the increase in revenue resulting from a unit increase in output, MR

= TR / Q) is equal to price: MR = P (note: this is true only if the firm is a price-taker!)

The optimal outputis when the MC is equal to the output price:- increasing by one unit t he output is profitable if the resulting increase in total revenue (the MR

= the price) is higher than the increase in cost (i.e., the MC);- this applies up to the amount of output for which MC = P (in the increasing part of the MC

curve);

- the AC must be lower than P (otherwise, there are losses, not profits)

Marginal and average costs

0

10

20

3040

50

60

0 5 10 15

Output

Un

itcos

ts

MCAVC

AC

output price

optimal output

AC

MC

AVC

profits


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What happens if prices change?- if outp ut price increases:

- it is profitable to increase output (now a one unit increase in outp ut gives a higher increasein revenue, which is now lower than the increase in cost)

- this applies up to the amount for which the new output price is equal to the MC

- the new optimal output will be larger than before

- if outp ut price decreases:- it is profitable to decrease output (now the decrease in costs resulting from a one unit

decrease in output is larger than the decrease in revenue resulting from the lowerproduction)

- this applies up to the amount for which the new output price is equal to the MC- the new optimal output will be smaller than before- if the output price becomes lower than the minimum AC, no output level is profitable (the

cost for producing each unit of output exceeds the revenue that results from each unit ofoutput)

- if the output price becomes lower than the minimum AC, for a firm is already operating it isstill better to produce, until the price falls below the minimum AVC (recovering the variablecosts, and part of the fixed costs, is better than losing all fixed costs)

This defines thefirms supply curve (= the amount of output that is produced by that firm for eachoutput price, holding all other things constant): it is the increasing part of the MC curve, above thecrossing with the AC curve.

- if costs increase (e.g., because input prices increase):- the MC and AC curves shift upward- it is profitable to reduce the output (now the decrease in revenue from a one unit decrease in

output is lower than the resulting decrease in costs)- this applies up to the amount for which the output price is equal to the new MC- the new optimal output will be smaller than before- thefirms supply curve is shifted to the left- the minimum AC is now higher; therefore, the firms supply becomes zero (it produces no

output) for a higher output price than before

- if costs decrease (e.g., because input prices decrease):- the MC and AC curves shift downward- it is profitable to increase the outp ut (now the increase in revenue from a one unit increase in

output is higher than the resulting increase in costs)- this applies up to the amount for which the output price is equal to the new MC- the new optimal output will be larger than before- thefirms supply curve is shifted to the right- the minimum AC is now lower; therefore, the firms supply becomes zero (it produces no

output) for a lower output price than before-

Therefore, thefirms supply is:- positively related to output price- negatively related to input prices

(for instance, it is expected that farmers increase wheat supply if its price increases, but that theydecrease it if the price of fertilisers increases)


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Here is one example of VC, FC, and TC, and of calculation of MC, AVC, AC.Check what is the optimal use.Find the optimal use when py = 15Find the optimal use when py = 20

Optimal output

py=SP13/unit1000 units 000 SP 000 SP 000 SP SP/unit SP/unit SP/unit SP/unit 000 SP 000 SP

y VC FC TC MC AVC AFC AC TR Profits0 0 40 401 10 40 50 10 10.00 40.00 50.00 13 -372 17 40 57 7 8.50 20.00 28.50 26 -313 22 40 62 5 7.33 13.33 20.67 39 -234 26 40 66 4 6.50 10.00 16.50 52 -145 30 40 70 4 6.00 8.00 14.00 65 -5

6 36 40 76 6 6.00 6.67 12.67 78 27 45 40 85 9 6.43 5.71 12.14 91 68 58 40 98 13 7.25 5.00 12.25 104 69 77 40 117 19 8.56 4.44 13.00 117 0

10 105 40 145 28 10.50 4.00 14.50 130 -15

2.4 OPTIMAL COMBINATION OF OUTPUTS

(two -or more- products)

The problem:- a farmer can produce two products (e.g., wheat and maize)

- he has given resources (a certain amount of land, of capital, of machinery, etc.)- how much wheat and how much maize should he produce to maximise his profits?

There are two production functions, for wheat and maize respectively:

Qw = f1(X1, X2, , Xn)Qm = f2(X1, X2, , Xn)

With given resources, a f armer can:- produce only wheat (a quantity w0)- produce only maize (a quantity m0)- produce a combination of wheat and maize

All combinations of wheat and maize technically feasible with the given resources form theproduction-possibility frontier(ortransformation curve).


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Along the production-possibility frontier, if the farmer produces more maize, he has to reduce theproduction of wheat. The quantity of wheat he has to give up to produce one more unit of maize isthe MARGINAL RATE OF TRANSFORMATION (MRT) of maize for wheat:

MRT of maize for wheat = Qw / Qm = the slope of the production-possibility frontier

It can be shown that: MRT of Qm for Qw = Qw / Qm = - MCQm / MCQw

Production possibili ty fr ontier

-1

0

1

2

3

4

5

Maize

Wheat


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The MRT:- is negative (to increase maize p roduction, wheat p roduction has to be decreased, and vice versa)- is increasing in absolute terms (if the MCs are increasing)- represents the opportunity costof producing maize in terms of wheat: i.e., what is the cost of

producing one more unit of maize, in terms of wheat given up

If the resources are given, their cost is given too; then, the maximum profit is found by maximisingtotal revenue.Total revenue is the sum of the revenue from wheat and of the revenue from maize:

TR = Qw * pw + Qm *pm(pw is the price of wheat, and p m is the price of maize)

To reach a particular TR0, the farmer can:- produce only wheat (a quantity TR0/pw)- produce only maize (a quantity TR0/pm)

- produce a combination of wheat and maize

All combinations of wheat and maize which yield the same revenue TR0 form an ISOREVENUELINE:

TR0 = Qw * pw + Qm *pmor:

Qw = - (pm / pw)*Qm + TR0 / pw

- there exist infinite isorevenue lines (each for any possible revenue)- all isorevenue lines are parallel, with slope (pm / pw)- isorevenue lines farther from the origin indicate higher revenues

The problem then is to choose the isorevenue line farthest from the origin which is compatible withthe production-frontier curve. This is the isorevenue line tangent to the production-frontier curve,and the optimal combination is at the tangency point.

Product-product equilibrium

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4y1

y2

isorevenue lines

tangency point


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At the tangency point, the MRT is equal to the slope of the isorevenue line:

MRT of Qm for Qw = Qw / Qm = (pm / pw)

Or:

Qw*pw = - Qm*pm

The economic meaning of the opt imal solution is as follows:- if producing less Qm results in a decrease in r evenue (- Qm* pm), but allows an increase in Qw

(Qw) which gives a larger increase in revenue (Qw*pw), then it is profitable to shift resourcesfrom producing maize to producing wheat (the cost is the same, the revenue increases);

- by doing so, the MRT decreases: for a further equal decrease in Qm, the increase in Qw is

smaller, and the shift is less p rofitable;- at one point, when Qw*pw = - Qm*pm, no further shift is profitable. This is exactly the

tangency point.

What happens if output prices change?

- if both prices change by the same proportion (e.g., both increase by 5%):- the slope of the isorevenue remains the same (pm* 1.05 / pw* 1.05 = pm / pw)- the isorevenue shifts to the left (it is now possible to reach the same revenue producing less)- the transformation line will be tangent to a higher isorevenue- profits will increase (same cost, and a higher revenue)- the opposite is true if prices decrease by the same proportion

- if one price change (e.g., pm increases):- the slope of the isorevenue changes (becomes steeper, in this example)- the transformation line will be tangent to a higher isorevenue- profits will increase (same cost, and a higher revenue)- theproportion between the products will change: the farmer will produce more maize and

less wheat, and the ratio Qm / Qw will increase- the opposite is true if the price decreases

More generally, a change in the proportion between the products results from any change in relativeprices (pm / pw): for instance, if pm increases by 5% and pw by 3%, there will be an increase in theratio Qm / Qw.

This is why the supply of a product is inversely related to the price of alternative products: e.g., ifthe price of wheat increases, the farmers will produce more wheat, and the supply of maize willdecrease.2.5 PRODUCTION FUNCTIONS

Talking of the production function:

Q= f(X1, X2, , Xn)


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we defined the short-term production function (some factors are fixed, e.g. land, machinery):

Q= f(X1, X2, , Xm | Xm+1, Xm+2,, Xn)

and we talked of alternative forms: fixed and flexible coefficients

We examined the case offlexible coefficients- flexible coefficients: the amount of a factor necessary for each unity of product depends on the

production level (e.g. fertiliser per each ton of wheat)- flexible coefficients production functions can have an algebraic formulation

We examine now the case offixed coefficients- the amount of a factor necessary for each unity of product is the same, regardless of the

production level (e.g., iron for producing each car)- there is a limited substitutability of one factor for another: i.e., there is a limited number of

techniques

- each technique is characterised by specific coefficients for each factor: this means that forproducing one unit of output with a particular technique it is necessary to use fixed amounts ofeach variable factor

It is often convenient to use fixed coefficient production functions even when (like in agriculture)flexible coefficients production functions are theoretically more appropriate:- farmers may know only few techniques, even if there are many others- fixed coefficient production functions are easily tractable on personal computers

Here is an example of how 3 p ossible techniques are listed in a matrix, corresponding to 3 differentmachines:

TechniquesFactors T1 T2 T3

Seeds 5 5 5Fertiliser 3 3 3Fuel 4 3 2Labour 2 4 7

Output 1 1 1

Each column lists the production coefficients: for example, to produce 1 unit of output with the firsttechnique, one must use 5 units of seeds, 3 of fertiliser, 4 of fuel, 2 of labour. To produce 2 units ofoutput, one must use 10 units of seeds, 6 of fertiliser, 8 of fuel, 4 of labour; and so on.With the second technique, 5 units of seeds, 3 of fertiliser, 3 of fuel, and 4 of labour are needed to

produce one unit of output, the double to produce 2 units, and so on.


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Assume you are using technique 2. You have 12 units of labour available, and 20 units of fuel, andall the fertiliser and the seeds you need. Here are the results of using more inputs:

Technique 2

Factors Unitsavailable

Usedamounts

Usedamounts

Usedamounts

Usedamounts

Usedamounts

Usedamounts

Usedamounts

Seeds all 5 10 15 20 25 30 35Fertiliser all 3 6 9 12 15 18 21Fuel 20 3 6 9 12 15 18 20Labour 12 4 8 12 12 12 12 12Output 1 2 3 3 3 3 3

When 3 units of output are produced, all available labour is used:- it is then impossible to increase the production, even if more fuel and other inputs are available- fuel, seeds and fertilisers are useless if the labour required together with them is not available- labour is in this case a limiting factor.

Remark: if another technique is chosen, the limiting factor may be different; for instance, withtechnique 1, the situation is the following:

Technique 1Factors Units

availableUsed

amountsUsed

amountsUsed

amountsUsed

amountsUsed

amountsUsed

amountsUsed

amounts

Seeds all 5 10 15 20 25 30 35Fertiliser all 3 6 9 12 15 18 21Fuel 20 4 8 12 16 20 18 20Labour 12 2 4 6 8 10 12 12Output 1 2 3 4 5 5 5

With this technique:- a greater production is possible- the limiting factor with this technique is fuel


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The Total product graph is:

Fuel

Output

Technique 2

Technique 1

The Marginal Product is:- constant up to the maximum outp ut (with technique 2, each additional unit of fuel increases the

output by 0.33 units)- equal to zero for further input units (no additional output is possible by increasing the use of

fuel)- equal to the Average Product up to the maximum output (each unit of fuel produces on the

average 0.33 units of output)

The VMP and VAP follow the same pattern.If the price of the input is lower than the VMP (and VAP) the optimal use of the input is the onethat allows the maximum outp ut: in the example, with technique 2 the optimal use of fuel is 9,which allows the maximum outp ut of 3.


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OPTIMAL COMBINATION OF INPUTS (fixed coefficients)

As usual, lets assume two variable inputs

The ISOQUANT in the case of fixed coefficients:

- the same output level can be achieved with different combination of inputs corresponding to thedifferent techniques- the isoquant is formed by different points (one for each available technique), not a continuous

line- the output levels are proportional to the distance from the origin on the half-lines corresponding

to each technique (to get a double production, the double of inputs is needed, and so on)

The ISOCOSTS are the same as in the case of flexible coefficients.

The least-cost combination of inputs for a certain output level will be where the lowest isocost (redisocost 1) passes through a point on the isoquant (point B). This means that one technique (T2) is

chosen.

What happens if an input p rice change?- the slope of the isocost changes- the profits increase when the input price decreases, and vice versa- it is possible that the optimal combination remains unchanged (and the same technique is

chosen), if the lowest new isocost still passes through the same point (blue isocost, number 2)- or, a new technique is chosen, if the lowest new isocost passes now through a point of the

isoquant corresponding to another technique (green isocost, number 3; point C)

O timal combination of in uts - fixed coefficients

A

BC

T1

T2

T3

X2

X1

1

2

3


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OPTIMAL OUTPUT LEVEL (fixed coefficients)

- Variable costs are proportional to output (to get a double production, the double of inputs isneeded, and, hence, variable costs double)

- the Marginal Cost is constant

- the Average Cost is decreasing

If the output price is higher than the marginal cost, the maximum profit is achieved with themaximum output.

The production for which TC is equal to TR is called the break-even point: for a larger production,there are profits; for a lower production, there are losses.

Break-even po int

TC

TR

Output

Profits,cost

Maximum output

Break-even point

Losses

Profits


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OPTIMAL COMBINATION OF OUTPUTS (two -or more- products -fixed coefficients )

The problem is the same as in the case of flexible coefficients:

- a farmer can produce two products (e.g., wheat and maize)- each of them is produced with a particular technique- the farmer has given resources (a certain amount of land, of capital, of water, of labour etc.)- how much wheat and how much maize should he produce to maximise his profits?

These are the techniques for producing wheat and maize:

Factors Wheat Maize

Land Ha / ton 0.25 0.125Water m3 / ton 300 1,500Capital $ / ton 30 35

Labour days / ton 4 6

Output Tons 1 1

For instance, the first row means that to produce 1 ton of wheat, 0.25 ha are needed (i.e., the yield is4 tons/ha); and, to produce 1 ton of maize, 0.125 ha are needed (i.e., the yield is 8 tons/ha).

- Assume the farmer has available 10 ha of land, 60,000 m3 of water, 1,800 $, and 400 labourdays.

- Each of these resources can be used to produce only wheat, only maize, or a combination of

both.- If the resources are used for only one product, the maximum outputs allowed by each resourceare indicated by the following table:

Maximum

outputFactors Units

available

Wheat Maiz

eLand Ha 10 40 80Water mc 60,000 200 40Capital $ 1800 60 51.4Labour Days 400 100 67

- all factors must be used according to the proportions indicated by the technique- there is therefore a limiting factor for each product:- for instance, if only wheat is produced, there is enough water to produce 200 t. of wheat, but not

enough land: with the available land, it is only possible to produce 40 t. of wheat- likewise, if only maize is produced, the maximum output is 40 t., due to available water


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It is also possible to produce a combination of the two products:- in this case, the resources are allocated to the two products:- the possibilities are indicated by the constraint lines:

- for land: 10 = 0.25 * Qw + 0.125 * Qm- for water: 60,000= 300 * Qw + 1,500 * Qm

- for capital: 1800 = 30 * Qw + 35 * Qm- for labour: 400 = 4 * Qw + 6 * Qm

The production-possibility-frontier line is the broken line ABCD formed by the lowest constraintlines (i.e., by the combinations that are compatible with all constraints); remark that in this examplelabour is never a limiting factor.

With given resources (i.e., with a given cost), the maximum profit is reached by maximising totalrevenues.TR are given by the sum of the revenue from wheat and from maize.

All combinations of wheat and maize which yield the same revenue TR0 form an ISOREVENUELINE (this is the same as in the case of flexible coefficients):

TR0 = Qw * pw + Qm *pmor:

Qw = - (pm / pw)*Qm + TR0 / pw

The problem then is to choose the isorevenue line farthest from the origin which is compatible withthe production-frontier curve. The optimal combination is the vertex of the production-frontier

broken line touched by the isorevenue line farthest from the origin.

Production-p ossibility fronti er (fixed coeffic ients)

50

50 100 150 200

100

w ater

land labour capital

Maize

Wheat

AB

C

D


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There is not an analytical solution to this problem (at the tangency point, it is NOT t rue that theMRT of Qm for Qw = (pm / pw)).

To solve this problem, a method called LINEAR PROGRAMMING is employed.

LINEAR PROGRAMMING is a more general tool:- it is based on the maximisation of a goal function (in this case, total revenue), subject to

constraints (in this case, the constraint lines corresponding to the given resources)- it is possible to take into consideration factors not subject to constraints (e.g., fertilisers that can

be freely p urchased)- it is possible to take into consideration relationships internal to the farm (e.g., production of

fodder to be used in livestock production).

2.6 PEASANT AND AGRICULTURAL HOUSEHOLDS

The preceding analysis of the farm assumes a profit-maximising behaviourThis implies an entrepreneur who is looking for profit, and purchases labour, land and capitals onthe market.In reality, the situation is quite different:- farms are mostly operated as family farms;- there are often limitations in the availability of resources (e.g., credit const raints)

This has several implications:- much, or all of the basic resources are contributed by the household: labour, land, capital- the household is in the same time a production unit and a consumption unit- if there are constraints in resource availability, the farm has to rely on household resources

Hence the economic definition of peasant:

ptimal combination o products ixed coe icients

50

50 100 150 200

100

water

land labour capital

Maize

Wheat

AB

C

DIsorevenue


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- farm households- utilising mainly family labour- partially integrated in imperfect markets

Is the behaviour of peasants different from the behaviour of classical firms?

- in the past, a view of peasants as irrational, or backward, or traditional, or subject to non-economic rules- more recently, an effort to understand the rationality of peasant behaviour

Different theories:

- the theory of poor but efficient peasants:- peasants are neither irrational nor ineff icient, they maximise profits- several studies trying to assess the efficiency of farmers, with mixed results- historically important for further efforts to understand the economic rationale of peasant

behaviour

All alternative theories assume that farmers have goals different from profit.

Partly, this arises from the consideration that farmers cannot know exactly their profits- if some resources are contributed by the farmer, they have no explicit cost (for example, a

farmer owning his land does not explicitly pay a rent)- total revenue minus all explicit costs and depreciation is NET FARM INCOME (NFI)- NFI includes all returns to resources contributed by the farmer, plus profits- returns to own resources means the remuneration of own land (rent for own land), of family

labour (the wage for family labour), of own capital (the interests for own capital)- it is nevertheless impossible to know exactly how much of NFI is rent, wage, interests, and

profits- returns to own resources can be estimated as OPPORTUNITY COSTS (an opportunity cost is

the income foregone by using own resources on the farm):- the opportunity cost of own land is the rent that the farmer would get by renting out his land- the opportunity cost of family labour is the wage that family members would earn if they

worked elsewhere- the opportunity cost of own capital is the interest that would be earned by lending it to

someone else- this is only true if it is actually possible to use these resources off the farm (for instance, if it is

possible to find an off-farm job); if not, then there is no opportunity cost, but a subjective cost.

It is therefore possible to know exactly profits if:- there are markets for all resources- the farmer has no preference for using his resources on the farm rather than off the farm (i.e., if

he evaluates the remuneration of his labour as equal to the market wage, the remuneration of hiscapital as equal to the market interest rate, the remuneration of his land equal to the market rent)

It is moreover not appropriate to assume that farmers try to maximise their NFI:- NFI can be increased by increasing the use of own resources on the farm (for instance, using

more family labour or more capital)- but this has a cost:

- an opportunity cost, if there is a market for these resources- a subjective cost, if there is not a perfect market for these resources, or if the farmer has apreference for using them on his farm


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- the farmer has always to compare the increase in NFI and the increase in the (opportunity orsubjective) cost

Two extreme cases are:

- no external market for own resources- perfect markets for all resources (perfect markets means competitive markets, where everyonecan buy or sell the relevant good at the market p rice, and no one has a market power)

a) no external market (e.g., i t is neither possible to find an off-farm job, nor to hire wagedlabour)

If the other resources are given, then it is possible to increase the output (or income) by increasingfamily labour use till its available quantity . This is the family income curve (curve OSR). Due to thelaw of decreasing marginal product, the increase is less than proportional. The slope of the curve is

the value of marginal product of labour.

More labour therefore implies more income, which makes the farmer happier; on the other hand,work is hard, and working more makes the farmer less happy .There is therefore a trade-off between the satisfaction of income and the pain of work, that can berepresented by income-work indifference curves. An indifference curve depicts all combinations ofwork and income which give the farmer the same welfare. Higher indifference curves indicate anhigher welfare (which in economics is called utility).

The Marginal Rate of Substitution (MRS) of income for work (the slope of the indifference curve)represents the increase in income that is needed to make the farmer indifferent to work one morehour:- it is therefore the subjective wage level- for the same income, it is higher and higher as work increases (when the farmer has worked

much, he needs a larger increase in income to be willing to work one more hour)- for the same amount of work, it is lower and lower as income decreases (when the farmer is

poorer, he strongly needs money, and is willing to work one hour more for a lower increase inincome)

The maximum utility for the farm household is reached where the indifference curve is tangent tothe family income curve. In this point, the MRS (the subjective wage level) is equal to the value ofthe marginal product: in other words, for levels of labour lower than OA, the utility from theincrease in income resulting from an increase of labour is higher than the decrease in utility due tothe increased work; for higher levels of labour, the increase in income would not be worth thedecrease in utility resulting from the additional work.The amount of farm labour is OA, the total family income is OG.


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Changes in the composition and size of the household:- modify the family income curve (for instance, when children grow up and can work, the

available labour is larger)- modify the utility of income: larger families have more income needs, the utility of incomeincreases, and the subjective wage is lower

Changes in output prices (for instance, an increase) have an indeterminate effect on labour use, and,hence, on the output level:- the family income curve is shifted upward, and the tangency is on a higher indifference curve- the VMP is increased, so from this point of view it is more profitable to increase labour use- on the other hand, the household is now richer, and the need for income is lower: this tends to

reduce labour use- the final effect depends on these two contrasting effects (called substitution effect and income

effect, respectively)- implication:

- there is no theoretical prediction of the final effect on supply of an increase in output price- in any case, a situation of isolation from the labour market makes supply less responsive to

prices than when the household is integrated in the labour market

(This theoretical model is called the drudgery-adverse peasant, or non-separable household model)

b) perfect external markets (e.g., it is always possible for family members to find an off-farmjob, and to hire waged labour)

Farm household equilibrium in isolation from the labour market

S

R

I1

OA

I2

I3

G

Total available

family labour


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If the farmer has the possibility to work off the farm, the market wage represents the opportunitycost of family labour.

- if the value of the marginal product of labour on the farm (the slope of the family income curve)is higher than the market wage (the slope of the ww line), working on the farm gives an higher

income than working off the farm- if the market wage is higher than the value of the marginal product of labour on the farm,

working off the farm gives an higher income than working on the farm- with income-work indifference curves as indicated in the graph, the farmer works on the farm

up to the quantity of labour for which the value of the marginal product of labour on the farm ishigher than the market wage; then he works off the farm up to the point for which the marketwage is equal to the MRS of work for income (i.e., to the tangency point of the market wageline ww with an indifference curve I1)

- the quantity of on farm work is OA, i.e., the quantity for which the VMP of labour is equal tothe wage (its price)

- the quantity of off-farm work is AB

- the income from farming is OC, the income from off-farm work is CD- working partly off the farm gives an higher utility (I1) than only working on the farm (I2)

Farm household equilibrium in the labour market: off-farm work

w

w'

S

R

I1

L

OA

B

C

D I2

Total availablefamily labour


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If the farmer can hire workers at the market wage, it is possible than a part of the farm labour iscontributed by hired workers. The farmer has therefore also the choice between working on thefarm and making the hired worker work for him.

- Again, the total amount of farm labour is OA, i.e., the quantity for which the VMP of labour is

equal to the market wage (its price)- with income-work indifference curves as indicated in the graph, the farmer works on the farm

up to the quantity of labour for which the market wage (his opportunity cost of labour) is equalto the MRS of work for income (i.e., to the tangency point of the market wage line ww to anindifference curve I1): the farmers quantity of labour is OB

- the rest of the labour (BA) is contributed by the hired workers- the total farm income is OC, but the farmer has to pay the wage to his workers, which is CD: so,

farmers income is OD- this is a lower income than OC, which is the income he would earn if he hired no worker; but he

is happier to have a lower income, but to work less. This is shown by the indifference curve I2,passing through point S (the work-income combination if the farmer did not hire labour), which

is lower than I1

Changes in output prices (for instance, an increase) have a predictable effect on labour use, and,hence, on the output level:- the family income curve is shifted upward;

- the VMP is increased, and the tangency with the wage line is at larger amounts of labour;- regardless of who contributes the labour (the farmer or the hired workers) the final effect is alarger output level;

Farm household equilibrium in the labour market: hired labour

w

w'

S

R

I1

O AB

I2

C

DE

Total availablefamily labour


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- the amount of labour used on the farm (and, hence, the output level) only depends on the marketwage, not on the preferences of the household (there is separability between farm decisions andhousehold decisions);

- implications:- the farm behaves as a profit-maximising firm, equating the VMP of labour to its price (the

market wage);- the impact of a change in output price is theoretically predictable: an increase in output price

increases the output, a decrease in output price decreases the output;- the preferences and the demographic changes in the household have no impact on the

agricultural production; they only determine the amount of family labour, on the farm andoff the farm.

(This theoretical model is called separable farm household model)


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In the real world, there are many situations that are in between the two theoretical models:- imperfect labour markets (it is possible to find off-farm jobs but only in certain seasons, or for a

certain amount of time; it is not always easy to find hired labour as desired, etc.)- it is also quite possible that certain family members are in the labour market, and others are not

(for example, persons above a certain age cannot easily find a job; there may be discriminations

against womens work, etc.)- in these cases the results are mixed: but in general any situation that isolates partially or totally

the farm household from the labour market makes the farm outp ut less responsive to marketsignals

Finally, remark that in the non-separable model the farmer is assumed to be indifferent betweenfarm and non-farm work. If, by contrast, he has different preferences for any of them (for instance,if he prefers to work on the farm, because on the farm he has no boss) then the behaviour is againnon-separable: preferences do have an impact on agricultural output.2.7 FARMERS AND RISK

All preceding analyses assumed certainty of all variables.

In real life, this is almost never true:- due to the biological nature of agricultural production, there is a variability in the output

resulting from the same amount of inputs- there are also natural hazards (weather, pests, and deseases) which cannot be controlled, or can

be only partially controlled- prices of outputs are almost never known at the time the decision of producing is made; the

problem is more severe for perennial crops and for animal productions that take time from thebeginning of the production process to the final output

- in more general terms, farmers often do not have full information on the variables that areinfluencing their activity

So, farmers operate in an uncertain environment. Although the term uncertainty has been associatedto situations where no objective probability can be associated to events (for instance, there is noknown probability for a war in a particular area), it more generally refers to situations where eventsare uncertain.

The term risk has a narrower sense:- risk include situations where objective probabilities can be attached to events (for instance, if

weather time series show that a drought occurs on the average every 10 years, the probability ofdrought is 1/10);

- but, since what is important is the perception that farmers have, the term risk is also used forsituations where subjective probabilities are attached to events (for instance, when a farmerthinks that a drought can occur every 5 years, his subjective probability for the drought is 1/5)

- the subjective probabilities are more relevant for decision-making of the farmers, since theymake their decisions based on them

If there is a variability in the results of economic activity, the farmer might nevertheless makeefficient choices on the average.For instance, suppose the farmer has to decide fertiliser use. The output results depend also on

weather conditions in the following of the year, that the farmer does not know when he makes hisdecision.


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Assume that weather may only take two possibilities: good year, with higher yields, and badyear with lower yields.The VMP1 and VMP2 curves depict the two situations, respectively: in good years, the yields arehigher, and the VMP curve is therefore higher, than in bad years.In good years, the optimal input use is OA, in bad years it is OB.

Assume that bad years occur every 4 years (or that the farmer believes that a bad year occurs every4 years): then the (objective or subjective) probability of a good year is , the probability of a badyear is .The expected VMP (what it is on the average, or what the farmer expects it to be, based on hisknowledge or beliefs on the likelihood of occurrence of bad and good years) is the weightedaverage of the VMP of good and bad years:

E(VMP) = VMP1 + VMP2

The E(VMP) curve lies between the VMP1 and VMP2 curve. A similar situation applies to VAP.

A rational behaviour for the farmer would be to use the quantity of input (OC) that makes theexpected VMP equal to the input price: by doing so, he would use too much input in the bad years,and too little input in the good years; but, on the average, he would obtain the best profits.

Nevertheless, such an approach neglects some basic points:- farmers may have some income goals that they have to reach first- farmers have their attitudes towards risk

Behaviour of farmers under risk and safety-first approach

VMP1

O AB C

P1

VMP2

E(VMP)

VAP1

VAP2

E(VAP)

Input

VMP,

VAP,

inputpric


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Two approaches to the analysis of farmers behaviour under uncertainty reflect these points:- the safety-first (or disaster-avoidance) approach- the expected utility approach


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The safety-first approach

The idea behind this approach is that farmers have the primary goal to avoid that some variablegoes below a minimum value which would result in a disaster.- for instance, first of all they may want to reach each year at least the minimum output which is

needed for their survival;- even if on the average of the different years they were to get an higher income, if they could not

reach the survival output in one year they would starve to death.

In our example, if the farmer has the constraint of not having losses in any year, he cannot choosethe optimal solution (the amount of input OC for which E(VMP) is equal to input price). If he didso:- he would maximise profits on the average;- but, if a bad year occurs, he would fall below the zero-profits level- in a bad year his VAP would be lower than the input price, and he would suffer losses

As a result, he has to remain in the vicinity of OB, in order to avoid the disaster that would occur inthe bad year.A variant of this model is the assumption that the farmer is unwilling to risk obtaining profits belowa given level, unless the relevant probability is very low.

The expected utility model

The preceding models assume that farmers have a p rimary goal, defined as a constraint.

Another approach assumes that they have positive preferences for income, but negative preferencesfor risk. Therefore, there is a trade-off between more income and the higher r isk that it would entail.

For an example, suppose a farmer can plant a crop which will give an income of 1000 in case of agood year (which occurs 3 years over 4, i.e., with a probability of ), but a loss of 200 in case of a

bad year (which occurs 1 years over 4, i.e., with a probability of ). The expected income (called ingeneral the Expected Money Value, EMV), is the weighted average of the two outcomes:

EMV = 1000 * + (-200) * = 750 - 50 = 700

Now assume that he is given the choice to plant another crop at no risk. If the new crop gives acertain income of 600, and the farmer is indifferent between the certain income 600 and theuncertain outcome of the risky crop, 600 is said to be the certainty equivalent of the uncertainincome: it is the amount of money that would make the farmer as happy, or indifferent, to taking thechance of the two different income outcomes in good and bad years.

In this example, the certainty equivalent is lower than the EMV: this reflects the fact that the farmeris prepared to get a lower income than the one he would get on the average, in order to be sure ofthe income he gets. This farmer is said to be risk-adverse: he prefers to have a lower certain incomethan having on the average an higher but uncertain income.The difference between the EMV and the certainty equivalent is called the insurance premium thatthe farmer is prepared to pay to be certain of his income.

If the EMV is equal to the certainty equivalent, then the farmer is said to be risk-neutral: he isindifferent between a certain income and the same expected value of the two uncertain incomes.


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Finally, if the certainty equivalent for the farmer is higher than the EMV, then he is said to be risk-taker: in other words, he is a gambler, who is willing to accept a lower income on the average than acertain income because he likes risk and prefers to take the gamble. The difference between thecertainty equivalent and EMV is the premium he is prepared to pay to have the chance to gamble.

According to this approach, the farmer makes his choices according to certainty equivalent of eachalternative. Taking again the example of fertiliser use, assume that the choices are only the lowerand higher fertiliser usage (OB or OA). According to the events or states of nature (good or badyear), the following incomes result:- with choice A (more fertil iser), an income of 1000 (area PFEM) in case of good year (when the

actual VAP is VAP1), and a loss of 500 (area PFDT) in case of bad year (when the actual VAPis VAP2);

- with choice B (less fertiliser), an income of 700 (area PLHK) in case of good year (when theactual VAP is VAP1), and a income of 50 (area PLGS) in case of bad year (when the actualVAP is VAP2)

Assume that the certainty equivalent for choice A and B are, respectively, 460 and 500.The following table summarises the outcomes, the EMVs and the certainty equivalentscorresponding to the choices.

Behaviour of farmers under risk and the expected utility approach

VMP1

O AB

P

VMP2

VAP1

VAP2

Input

VMP,

VAP,

inputpric

E

D

F

G

H

L

M

K

S

T


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Analysis of a risky decision

problem

Actions A: More fertiliser B: Less fertiliser

Events Income Probabil ity Income*prob Income Probability Income*probGood year 1000 0.75 750 700 0.75 525Bad year -500 0.25 -125 50 0.25 12.5

EMV 625 537.5

Certainty

equivalent

460 500

In terms of Expected Money Value, choice A would be preferable, since the average income thatthe farmer should expect is 625, as compared to 537.5 with choice B.

Nevertheless, since choice A implies a loss of 500 in case of a bad year, it has a low certaintyequivalent, so that the farmer prefers choice B. In other words, the farmer maximise the utility heexpects from uncertain events.

The result of a risk-adverse behaviour, both within a disaster-avoidance approach and an expectedutility approach, is that the farmer may not use resources at the optimal level.

Several studies support the hypothesis that:- farmers are risk-adverse- cropping pattern are chosen to increase family security rather than maximise profits- risk aversion is stronger among poor farmers

- risk aversion can create an obstacle to the diffusion and adoption of innovations

Policy implications:Several policies can be designed to reduce uncertainty:- irrigation schemes decrease the uncertainty in output due to rainfall variability- diffusion of pest-resistant varieties can stabilise yields- price stabilisation schemes can reduce price variability- spreading technical and market information can reduce uncertainty due to lack of information.

2.8 EFFICIENCY AND TECHNOLOGICAL CHANGE

CONCEPTS OF EFFICIENCY

Two concepts of efficiency are relevant in economics:- technical efficiency- allocative efficiency

Technical efficiency means achieving the maximum level of outp ut for given levels of inputs (or theminimum input usage f

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