Microeconomics Lecture Notes 2014

ECON1001Foundations of Microeconomics

Lecture Notes

Maksymilian Kwiek∗

30th September 2014

∗University of Southampton

Contents

1 Introduction - positive statements 11.1 A warm-up: social interaction . . . . . . . . . . . . . . . . . . . . . . 11.2 Examples (using simple game-theoretic setup) . . . . . . . . . . . . . 1

1.2.1 Prisoners’ Dilemma . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.3 Entry game . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Do economists think that free markets are the best? . . . . . . . . . . 31.4 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Scientific method in economics . . . . . . . . . . . . . . . . . . . . . . 3

1.5.1 Economic model . . . . . . . . . . . . . . . . . . . . . . . . . 41.5.2 How are models used? . . . . . . . . . . . . . . . . . . . . . . 5

2 Introduction - normative statements 72.1 Basic assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Ordinal utility and Pareto efficiency . . . . . . . . . . . . . . . . . . . 82.3 Utility Possibility Frontier . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Utilitarianism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.5 Equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5.1 Equity of utilities . . . . . . . . . . . . . . . . . . . . . . . . . 102.5.2 Equity of outcomes . . . . . . . . . . . . . . . . . . . . . . . . 102.5.3 Equity of opportunities . . . . . . . . . . . . . . . . . . . . . . 10

3 Preferences, constraints, choices. 133.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Preferences: Basic definitions and assumptions . . . . . . . . . 133.1.2 Indifference curve . . . . . . . . . . . . . . . . . . . . . . . . . 143.1.3 Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1.4 Marginal utility . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Budget constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.4 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4.1 Change of income - Engel curve . . . . . . . . . . . . . . . . . 173.4.2 Change of price - individual demand . . . . . . . . . . . . . . 183.4.3 Income and substitution effect . . . . . . . . . . . . . . . . . . 203.4.4 Incentives in general . . . . . . . . . . . . . . . . . . . . . . . 20

i

Contents

4 Firm (one variable input) 214.1 Production function with one variable input . . . . . . . . . . . . . . 214.2 Cost functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2.1 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2.2 Cost curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.3 Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.1 Output decision . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3.2 Shutdown decision . . . . . . . . . . . . . . . . . . . . . . . . 26

4.4 Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4.1 Supply of an individual firm . . . . . . . . . . . . . . . . . . . 274.4.2 Market supply . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4.3 Example continued . . . . . . . . . . . . . . . . . . . . . . . . 294.4.4 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Market equilibrium. Exogenous shocks and comparative statics. 315.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1.1 Assumptions of perfect competition . . . . . . . . . . . . . . . 315.1.2 Definition of competitive equilibrium . . . . . . . . . . . . . . 315.1.3 Why we study competitive equilibria? . . . . . . . . . . . . . . 335.1.4 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2.1 Price control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2.2 Unit tax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2.3 Short-run and long-run . . . . . . . . . . . . . . . . . . . . . . 34

5.3 Short-run competitive equilibrium . . . . . . . . . . . . . . . . . . . . 355.4 Long-run competitive equilibrium . . . . . . . . . . . . . . . . . . . . 355.5 Exogenous shock; comparative statics . . . . . . . . . . . . . . . . . . 37

5.5.1 Short-run adjustments . . . . . . . . . . . . . . . . . . . . . . 375.5.2 Long-run adjustments . . . . . . . . . . . . . . . . . . . . . . 38

5.6 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.6.1 Expenditures/Revenue and elasticity . . . . . . . . . . . . . . 395.6.2 Tax incidence and elasticity . . . . . . . . . . . . . . . . . . . 39

6 Normative properties of competitive equilibria 416.1 Measure of agents’ welfare . . . . . . . . . . . . . . . . . . . . . . . . 416.2 Competitive equilibrium and maximization of social welfare. . . . . . 426.3 Welfare Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6.4.1 Price floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.4.2 Price support . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7 General equilibrium – trade and comparative advantage. 477.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477.2 Bilateral trade without production . . . . . . . . . . . . . . . . . . . 48

ii

Contents

7.3 Trade in the economy with production. Comparative advantage . . . 507.4 Example of general equilibrium analysis . . . . . . . . . . . . . . . . . 53

8 Public goods, externalities, asymmetric information 558.1 Public goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

8.1.1 Types of goods. . . . . . . . . . . . . . . . . . . . . . . . . . . 558.1.2 Government and public goods. . . . . . . . . . . . . . . . . . . 56

8.2 Externality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568.2.1 Examples: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578.2.2 Government and externalities . . . . . . . . . . . . . . . . . . 58

8.3 Asymmetric information . . . . . . . . . . . . . . . . . . . . . . . . . 59

9 Monopoly 619.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619.2 Profit maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619.3 Marginal Revenue of the monopoly . . . . . . . . . . . . . . . . . . . 619.4 Graphical illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . 639.5 Welfare properties of the monopoly. . . . . . . . . . . . . . . . . . . . 639.6 Price discrimination. . . . . . . . . . . . . . . . . . . . . . . . . . . . 649.7 Why monopolies exist? . . . . . . . . . . . . . . . . . . . . . . . . . . 64

10 Oligopoly 6710.1 Market structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6710.2 Strategic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6710.3 Application: Cournot model of quantity competition. . . . . . . . . . 6810.4 Application: Bertrand model of price competition. . . . . . . . . . . . 6810.5 Cartel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6910.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

11 Production (many variable inputs) 7111.1 Introduction to firm’s problem . . . . . . . . . . . . . . . . . . . . . . 71

11.1.1 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7111.1.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7111.1.3 The problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7111.1.4 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

11.2 Production function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7211.2.1 One input (Short-run) . . . . . . . . . . . . . . . . . . . . . . 7211.2.2 Two inputs (Long-run) . . . . . . . . . . . . . . . . . . . . . . 7211.2.3 Marginal returns . . . . . . . . . . . . . . . . . . . . . . . . . 7311.2.4 Returns to scale . . . . . . . . . . . . . . . . . . . . . . . . . . 73

12 Costs (many variable inputs) 7712.1 Short-run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

iii

Contents

12.2 Long-run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7712.2.1 Short-run and long-run comparison . . . . . . . . . . . . . . . 7812.2.2 Economies of scale . . . . . . . . . . . . . . . . . . . . . . . . 78

12.3 Equilibrium conditions revisited . . . . . . . . . . . . . . . . . . . . . 80

iv

1 Introduction - positive statements

1.1 A warm-up: social interactionEach of N students “Enters” or “Stays Out”. Staying out generates net payoff ofzero virtual pounds. As far as entering is concerned, there is a benefit and a cost.The cost is equal to the number of students who selected “Enter”. Benefit is equalto some pre-announced value V . What is the number of students who enter, n?A different experiment: let there be an entry fee of F pounds. Otherwise, the

procedure is the same.

1.2 Examples (using simple game-theoretic setup)There are many classes of economic models and you will become experts in usingmany of them. One class is called normal-form games.

1. What is it for? A normal-form game is a model appropriate to analyze situationsin which independent agents interact in a single simultaneous-move encounter.

2. What is it? A normal-form game is a list of

• agents, i.e. independent decision makers• strategies (choices available to each agent), i.e. expressions of scarcity and

trade-offs• payoff functions, i.e. expressions of desires/incentives

3. How is it solved? Solution concept is Nash equilibrium: a list of agents’ choices,with the property that no agent can improve their payoff by switching to adifferent choice, while other agents’ choices are kept the same.

1.2.1 Prisoners’ DilemmaEach of two suspects held by the police can either confess the alleged serious crimeinvolving both, or stay silent. If at least one suspect confesses then the serious crimecan be proven in court. If none confesses, then the serious crime cannot be proven, butthere is a minor offense that can still be proven against the suspects. The detectivestell the suspects that they are going to be sentenced according to this matrix:

1


Prisoner 2Confess Silent

Prisoner 1 Confess −6 −6 0 −9Silent −9 0 −1 −1

Table 1.1: Prisoners’ Dilemma (years in prison)

Confess-Confess is a Nash equilibrium.

Remark: Note that Silent-Silent is a better outcome for the suspects, but it is notan equilibrium.

1.2.2 StandardsRobinson Crusoe and Friday live on an island. They can purchase mobile phones, butthere are two standards to choose from. If they select incompatible standards, theywill not be able to communicate with each other and will receive payoff zero. If theyboth choose standard 1 then they will get payoffs (2, 3). Standard 2 is objectivelyinferior; if they both select it then they will get payoffs (1, 2).

FridayS1 S2

Crusoe S1 2 3 0 0S2 0 0 1 2

Table 1.2: Standards

(S1,S1) is a Nash equilibrium, because if everybody is expected to select S1, thenno player has any incentives to switch to S2 unilaterally. (S2,S2) is a Nash equilibriumtoo.

Remark: Sometimes, there may be more than one equilibrium.

1.2.3 Entry gameLet there be N = 140 students in the room and let V = 70.01.V , N and F are exogenous variables, F being possibly a policy variable. Variable

n, total number of entrants, is endogenous (see the explanation in section 1.5.1).

1. Suppose there is no fee, F = 0. Only if there is n = 70 entrants we have a Nashequilibrium. Proof: Consider the incentives of an entrant: by entering, they getV −n = 0.01. By staying out they get zero. Thus, they should enter. Considerthe incentives of an abstainer: by staying out they get zero, by entering theyget V − (n+ 1) = −0.99. Thus they should stay out. We have an equilibrium.

2

1.3 Do economists think that free markets are the best?

2. Let F = 30. Claim: there is n = 40 entrants in equilibrium. Proof: Considerthe incentives of an entrant: by entering, they get V − F − n = 0.01. Bystaying out they get zero. Thus enter. Consider the incentives of an abstainer:by staying out they get zero, by entering they get V − F − (n+ 1) = −0.99.Thus stay out. We have an equilibrium.

• Comparative statics: comparing outcomes for two situations, F = 0 and F =30. Maybe interpret as “if the fee goes up from 0 to 30 then the number ofentrants goes down from 70 to 40”

• Note also that with F = 0 the total payoff in the economy is close to zero (70entrants, each getting a penny, that is a total of £0.70). When F = 30 thenthe society collects total of 40× 30 = 1200 pounds in taxes and all entrants gohome with a penny. The total gain of the economy is therefore £1200.40.

1.3 Do economists think that free markets are thebest?

These examples suggest an important observation: even if every individual is the bestjudge of what is best for her/him

social outcomes are not necessarily socially the best.

This statement justifies the existence of governments as forces of coercion, applyingpolicies and interventions that are capable of moving equilibrium outcomes closer towhat is socially best. However, first we have to define what we mean by “the bestoutcome”; see next week.

1.4 EconomicsEconomics – social science that studies human behavior as an outcome of an interplayof two factors

• scarcity (of food, time, production factors, other resources etc) and

• desires/incentives (of economic agents such as individuals, firms, institutions,associations etc).

1.5 Scientific method in economics• Positive question - what is? Positive analysis should be free of ethical, religious,

political, or value judgments.

• Normative approach - what ought to be? Norms have to be defined.

3


Scientific method is a collections of rules that allow us to provide a relatively reliableanswer to the positive question. Postulate a hypothesis and investigate how muchconfidence there is that the hypothesis is “true”:

• Theory - what are the necessary implications of the hypothesis?

• Empirics - finding evidence and testing if the implications of the hypothesishold in reality by controlled field or lab experiments, natural experiments, casestudies etc.

Theory is deductive and so the implications are totally reliable. Empirical investiga-tion is inductive, thus it is not totally reliable.

1.5.1 Economic modelHow do we perceive reality? Since the reality is too difficult to understand, we usemodels of reality to represent some of its aspects in a simplified way. You cannotavoid being a theorist!We can talk about two types of errors

• a model contains an internal logical mistake

• a model, being logically correct, is not an adequate representation of the reality.

By studying models we can learn to avoid the first type of error. Deductive methods(i.e. logic) are used to infer the implications from the assumptions. This logic canbe represented algebraically, graphically, or verbally. Empirics helps us to avoid thesecond one, and teaches us that models (a) are contextual and (b) constantly evolve(i.e. hopefully improve).A microeconomic model attempts to draw conclusion about how the whole system

works (like organisations, households, firms, markets, entire economy etc) from theanalysis of incentives of the decision makers in these systems (like consumers, workers,sellers, buyers, managers, owners, etc). An economic model is a set of assumptionsabout how various elements of an economic system relate to and depend on eachother. In practice, any economic model will

1. define a list of variables and

2. assume relationships between them.

Types of variables

1. Exogenous parameters (external, independent, explanatory) - these are parame-ters that the model is not trying to explain. They are given. We can distinguish

• unchangeable parameters of nature,• policy variables - potentially changeable, e.g. by some authority.

4

1.5 Scientific method in economics

2. Endogenous variables - these are variables which are not known at the outset.We can say that the model “explains” these variables. Among endogenousvariables we can distinguish

• decision variables - there is an agent in the economic model, who has thisvariable under their control.

• non-decision variables - an endogenous variable that nobody actually chooses;it is determined by some other force that the model must postulate.

Among the assumed relationships there are equilibrium conditions. There are manytypes of equilibria, but the basic idea is always the same.An equilibrium is a list of the values of all endogenous variables, such that if these

values are realized then there are no reasons in the model that push the endogenousvariables away from the supposed equilibrium.Typically, the equilibrium conditions are:

• an agent should have no incentives to change the decision variable under theircontrol, and

• the forces that control non-decision variables (if any) exactly cancel out.

1.5.2 How are models used?We study equilibria because we believe that if the endogenous variables in the modelare in equilibrium, then the variables that they represent in reality would remain inits vicinity most of the time.The ultimate purpose of the model is to deliver a testable/falsifiable hypothesis,

i.e. a prediction.Comparative statics is a thought experiment - calculate an equilibrium for one set

of exogenous variables and the second one for another set. Interpret the first situationas before the change of exogenous variables and the second as after the change. Orinterpret these equilibria as representing two different locations.

5

2 Introduction - normativestatements

Economists often find themselves in debates involving value judgments. Normativequestion is “what ought to be?” Normative ethics provides framework for this dis-cussion.E.g.:

• Should income tax be increased? If yes, then which income bracket? Shouldthe tax be progressive?

• Who should pay for public goods, such as roads - those who use them, or thosewho can afford it more?

• Should we subsidize, tax, ban, price-control etc. certain goods, such as petrol,housing, drugs, nappies, electricity, alcohol, gambling?

• Who should pay for old-age care, baby-boomers or their children?

• Where should public resources go in health service? I.e. given that someonewill die, who should it be?

2.1 Basic assumptionsAt the outset, we often assume

• Consequentialism - only consequences are the basis for a judgment of what isright and wrong (as opposed to adherence to rules, virtues, etc).

• Non-paternalism - only preferences of the individuals are the basis for a judg-ment of which social outcome is right or wrong (as opposed to someone ease’spreferences, e.g. mine).

Need to define preferences. Utility is a measure of satisfaction/happiness of an indi-vidual from a given outcome. It could be the same as monetary payoff, but it couldalso be a description of subjective desires or preferences unrelated to money.

• Ordinal utility - captures only ranking (and not intensity) of preferences.

• Cardinal utility - its level is treated as an ethically or behaviorally significantquantity.

7

2 Introduction - normative statements

Examples:

1. Suppose raspberry ice-cream gives me utility 2 and chocolate ice-cream givesme utility 3. The meaning of this in ordinal approach is that I prefer chocolateice-cream to raspberry. In cardinal approach numbers 2 and 3 are meaningful,e.g. these could be the maximal prices I am willing to pay for the ice-creams.

2. Consider Standards game. Ordinal utility approach states that Robinson isindifferent between (S1,S2) and (S2,S1), and (S2,S2) is strictly better, while(S1,S1) is better still; beyond that, these payoffs are meaningless. Cardinalutility approach makes the following statement meaningful: Robinson prefers(S1,S1) twice as much as (S2,S2), or his payoff is the same in (S1,S1) as Friday’spayoff in (S2,S2).

2.2 Ordinal utility and Pareto efficiencyPareto improvement - a change from one allocation/outcome to a different one thatmakes at least one agent strictly better off and nobody worse off. An allocation/outcomeis Pareto efficient if no Pareto improvement is possible. I.e. if any change makes atleast one agent worse off.Example. There are five possible outcomes and three agents.

Outcome (Ordinal) utility of Is this outcome Pareto Efficient?Agent 1 Agent 2 Agent 3A 10 20 30 Not PE (e.g. A→ C)B 10 10 10 Not PE (e.g. B → A)C 10 20 80 PE (agent 3 suffers in any change)D 30 35 30 PE (either agent 1 or 3 suffers)E 40 40 20 PE (agent 1 suffers in any change)

Table 2.1: Pareto efficiency

Pareto efficiency is a minimal requirement on what we would think is a rightoutcome. It just says that there is no unnecessary waste.

Remark: There may be many Pareto efficient allocations (and typically there aremany)

Remark: Pareto efficiency has nothing to do with equality or fairness. For instance,allocation C is very unequal but Pareto efficient, while B is equal but notPareto efficient.

8

2.3 Utility Possibility Frontier

�

U2

U1

A

B

C

Figure 2.1: Utility Possibility Sets and Frontiers

2.3 Utility Possibility FrontierAssume cardinal utility. Utility Possibility Set is the set of all utility levels that arefeasible. Utility Possibility Frontier are those utility levels that come from Paretoefficient outcomes (North-East frontier of the UPS). Figure 2.1 shows a hypotheticalUtility Possibility Set for two agents. Point A shows feasible but Pareto inefficientsituation, point B (being on the Utility Possibility Frontier) shows Pareto efficientoutcome, and finally point C shows a configuration of utilities that is not feasible.

2.4 UtilitarianismUtilitarianism proposes that we ought to maximize the sum of utilities.Example. According to utilitarianism, the best allocation in Table 2.1 is C because

it maximizes utilitarian social welfare, 10 + 20 + 80 = 110. For instance, D is nolonger justifiable, because going from D to C generates higher utilitarian welfare.

• Social Welfare function is a way to aggregate individual utilities - from a list,u1, . . . , uN , to a single measure of welfare, W . The utilitarian welfare functionis W = u1 + . . .+ uN .

• Obviously, the best outcome according to this criterion is Pareto efficient, butnot every PE outcome is the best according to this criterion.

• Utilitarianism is particularly justified if utility is transferable. Then the issueof welfare distribution (cutting the cake) is separate from welfare maximization(baking the cake). E.g. with transferable utilities, C is the only Pareto efficientoutcome, i.e. the maximal surplus can be distributed among the agents so thateveryone is happier in C than in any of the remaining outcomes.

9

2 Introduction - normative statements

• Cost-benefit analysis of a proposed change - sum all the payoffs to all the agentsin the economy and subtract all the costs to all the agents and see whetherthe result is positive; if yes, then proposed change is an improvement in theutilitarian sense (again: Pareto improvement if utility is transferable).

2.5 Equity

2.5.1 Equity of utilitiesThe utilitarian welfare criterion puts equal weight on all agents. One can use differentwelfare functions. Consider welfare functions that put more weight on lower utilities.

• Maximin (Rawlsian) welfare function has the strongest concern for equity,W =min {u1, ..., uI}; i.e. the right outcome is the one that selects the greatest benefitof the least advantaged.

• According to Maximin criterion, the best allocation in Table 2.1 is D becausewelfare in this case is the highest possible, min {30, 35, 30} = 30.

• The best outcome according to any such Welfare function is Pareto efficient,but not every PE outcome is the best according to this criterion.

2.5.2 Equity of outcomesA practical approach when thinking about equality is to pick a criterion, calculate ameasure of dispersion and declare it important. For example, one can pick income,or wealth and use Gini coefficient (value of zero for perfect equality, value of one forperfect inequality).

• Note that minimizing such measures of dispersion may generate silly results,e.g. if nobody has anything then perfect equality is achieved.

• More to the point, income is not the same as utility, e.g. some individualsprefer to work less and enjoy life.

2.5.3 Equity of opportunitiesAn allocation is envy-free if no agent would like to exchange her position for thatof another agent. Envy-freeness is a notion of equity. Note that envy-freeness isnot necessarily Pareto efficient (say destroy everything gives us envy-free outcome),neither Pareto efficiency is necessarily envy-free. We want both.Equity of opportunities proposes that initially (i) all agents are given the same

endowment (equal division) and face the same choice opportunities, then (ii) theyare allowed to make life choices according to their heterogeneous preferences, so theoutcomes and even resulting utilities do not have to be the same.

10

2.5 Equity

• Equity concern: Observe that the allocation of equal division of endowment istrivially envy-free. Moreover, the outcome after agents’ choices is also envy-free.

• Efficiency concern: The outcome of equal division is not necessarily Paretoefficient. We will see later (trust me) that in some circumstances the outcomeafter agents’ choices will be Pareto efficient.

Equity of opportunities approach seem to achieve a similar fairness postulate asequity of utilities, except that it does not require cardinal notion of utility. It usesordinal utility approach. Note however, that equity of endowments may be difficultto achieve in case of talents, abilities, etc.

11

3 Preferences, constraints, choices.

� Consumer preferences (define “better”)

Budget constraint (define “affordable”)

Choose the “best” option from those that are “affordable”

Comparative static: How does this choice vary when “best” or “affordable” is altered?

Figure 3.1: Plan

3.1 Preferences3.1.1 Preferences: Basic definitions and assumptions

• A � B means “A is at least as good as B” (or “weakly better”).

• A ∼ B means “A and B are equally good”.

• A � B means “A is strictly better than B”.

Assumption 1. Preferences are rational. I.e. they are

• complete - any two alternatives A and B can be compared and either A � B orB � A.

• transitive - if A � B and B � C, then A � C.

Remark: rational preferences does not mean that they are

• conscious - e.g., I may honestly claim that I prefer a safer car rather than afaster one, but my actions may reveal the opposite

• typical - I may have rational, yet completely abnormal preferences.

• objectively correct - e.g., I may be rational and still derive preference from theassertion that flying is more dangerous that driving.

• egoistic - I may care about others; i.e. altruism is not assumed away (nor issnobbery, status-seeking etc.)

13


�

Water

Food A ∼ B

B

A �

Water

Food

B

A

Nonmonotonic preferences

�

Water

Food

better

Figure 3.2: Indifference curves, A ∼ B

3.1.2 Indifference curve

Indifference curve - a set of bundles that the consumer views as equally good.For convenience we assume

Assumption 2. Monotonicity - more is better.

Assumptions made so far give us a few observations (see Figure 3.2):

1. Indifference curves are downward sloping. If not, then monotonicity is violated.

2. Indifference curves farther from the origin depict better bundles, by monotonic-ity.

3. Distinct indifference curves cannot cross. If they did, the intersection pointwould be indifferent to any point on these two indifference curves.

4. For any point, there is an indifference curve going through it.

14

3.1 Preferences

�

Water

Food A

B

C

�

Water

Food A

B

C

∆f

∆w D

Figure 3.3: Shape of indifference curves

Subjective substitution between goods. Consider a change depicted on Figure 3.3:move from A to B to C. Left - get more and more water, give up food; water becomesvalued more in terms of food. Right - Get more and more water, give up food; waterbecomes valued less in terms of food.The indifference curve on the right seems to describe our typical preferences better.

The Marginal Rate of Substitution of water for food MRSfw says how much foodhas to be given up when the consumer gets one more unit of water, so that he/sheis as well off as before. MRSfw = ∆f/∆w and approximates the slope of a smoothindifference curve.

Assumption 3. MRS is diminishing (along a smooth indifference curve, moving tothe right, in absolute terms)

3.1.3 Utility

Utility can be interpreted as satisfaction, happiness. A � B translates to “A yieldsa strictly higher utility than B”. Suppose one has utility u (x1, x2) = √x1 + √x2,where x1 is quantity of the first good, etc. Then e.g. (16, 1) � (4, 4).It is a mathematical fact, that if preferences are rational (plus some minor technical

assumptions) then there is some utility function that captures these preferences.From now on we are going to spell out preferences in terms of utility functions.

3.1.4 Marginal utility

MU - extra utility generated by extra unit of a commodity.

15


Number of apples Utility Marginal Utility, MUapple

0 1011 110 92 114 43 116 24 117 15 116 −1

Table 3.1: Marginal utility

Consider again Figure 3.3. Slope of a smooth indifference curve is MRSfw =∆f/∆w (such that we stay on the same i.c.). But also, the move from A to B canbe decomposed into two steps, A→ D → B.

1. If A→ D, then utility goes down roughly by ∆f ×MUf .

2. If D → B, then utility goes up roughly by ∆w ×MUw.

3. In order to stay on the same indifference curve the total utility must not change,hence these two changes must cancel each other, −∆f ×MUf = ∆w ×MUw,or (

∆f∆w =

)MRSfw = −MUw

MUf

Conclusion: The MRS can be easily expressed in terms of MUs.

3.2 Budget constraintExpenditures ≤ Income. Let pw, pf and Y be prices and income. Then pww+ pff ≤Y . Budget line is where this condition holds with equality and can be written asf = (Y/pf )− (pw/pf )w. One can see that this is a straight line with a slope −pw/pf

and an intercept of Y/pf . Bundles P and R are affordable, S is not. R requires allthe income.

�

Water

Food

S

R

P

Slope −pw/pf

Intercept Y/pf

Y/pw

Figure 3.4: Budget constraint

16

3.3 Choice

3.3 ChoiceTake the best bundle from these that are affordable. Preferences are given (eitherMUf and MUw, or indifference curves, or utility, or MRS), market conditions aregiven too (pw, pf and Y ). Optimal choice of a consumer is represented by pointD. Points like A, B and C are affordable but still, there are better affordable op-tions; point E is not affordable. An interior point like D must satisfy the tangencycondition:

Slope of indifference curve = Slope of budget line

MRSfw = −pw

pf

In other words, consumer does not rest in adjusting her bundle until her subjec-tive rate of substitution between two goods (MRS) is equal to the market rate ofsubstitution (price ratio).

�

Water

Food

C

B

A

Y/pw

D E

Figure 3.5: Optimal choice

Alternatively, this can be written as

MUw

pw

= MUf

pf

.

3.4 Comparative statics3.4.1 Change of income - Engel curveE.g., suppose that the initial income is 9 and that it falls to 6; graphically, this doesnot affect the slope of the budget line; parallel shift of budget line inward. Engel

17


�

9/pw 6/pw

9/py

Water

Water

6

9

Food

Income

Water is normal

Engel curve for normal goods

6/py

�

9/pw 6/pw

9/py

Water

Water

6

9

Food

Income

Water is inferior

Engel curve for inferior goods

6/py

Figure 3.6: Derivation of Engel curve

curve - How does the quantity demanded change if income varies? Two possiblecases depicted on Figure 3.6: normal goods and inferior goods.

3.4.2 Change of price - individual demandE.g., suppose that the initial price of water is 8 and that it falls to 6. Graphically, thisdoes not affect the vertical intercept Y/py; the budget line “rotates’ around this pointoutward. How does the quantity demanded changes? Two possible cases: Pictureon the left of Figure 3.7 depicts an ordinary situation, where quantity demandedincreases when price falls. But the picture on the right shows that this does nothave to hold: we may have a rational consumer who has preferences satisfying allthe assumptions above, but with a bizarre comparative static: quantity demandedgoes up as the price goes up (while income, preferences and everything else staysunchanged). A good with such property is called a Giffen good.Ordinary situation – the lower price, the higher quantity demanded (negative

slope).

Remark: Demand (function, or curve) is the relationship between price and quantity(the entire curve), quantity demanded is a number of units demanded forone price (point on the curve).

Remark: Quantity demanded not the same as quantity needed (“needs” are notdefined in economics). Quantity demanded not the same as quantity pur-chased.

Effect of a change of price of this good – change of quantity demanded, movementalong the curve. Effect of a change of other factors (income, prices of related goods,

18

3.4 Comparative statics

�

Y/6 Y/8

Y/py

Water

Water

6

8

Food

Price of water

Law of demand �

Y/6 Y/8

Y/py

Water

Water

6

8

Food

Price of water

Giffen paradox

Figure 3.7: Derivation of demand

�

Quantity of apples

Price of apples

�

Quantity of apples

Price of apples

Figure 3.8: Demand curve and its shift

19


tastes, expectations, etc) – change of demand, movement of the curve itself, shifts.Example – income increases, then the demand shifts (maybe to the right so thatquantity demanded is greater for all prices). See Figure 3.8.

3.4.3 Income and substitution effect• Income effect - the change in quantity demanded caused by the change of in-

come, while keeping prices constant.

• Substitution effect - the change of quantity demanded caused by the change ofprice, while keeping the real wealth constant.

When income changes then the only effect is income effect. But when the pricechanges, then both income and substitution effects are present. Firstly - if pricedecreases the consumer becomes “richer” exactly like when income decreases: thisis the income effect of the change of the price. Secondly - the consumer shifts herpurchases towards the cheaper product: this is the substitution effect of the change ofprice. The isolation of income effect from substitution effect when the price changeshinges on the fact how we define real wealth to be kept constant.

3.4.4 Incentives in generalHow do individuals react to the environment? Demand and Engel functions couldbe called more generally behavior functions; they show the behavior intended by adecision maker as a function of some factor external to the decision maker - a factorwhich could be called an incentive or an incentive. E.g. the demand curve showshow the quantity demanded reacts to the change of the unit price. One may considerother behavioral functions: quantity demanded changes with other prices, desiredsize of meals changes with content of fat, speed of driving changes with safety of acar, students’ enrollment changes with the difficulty of the exam, etc.

20

4 Firm (one variable input)

This section considers production decisions of firms, but focuses on a simpler version(more complicated will be discussed later).

4.1 Production function with one variable input

Production function is a way to describe technology. It tells how many units of output(production) can be produced at most, for given inputs (factors of production).Assumption about technology in this section: production of the final product re-

quires one piece of equipment and one variable input. We will call them Capital (fixedK̄ = 1) and Labor (variable L).Production function maps labor into output, q = f (L). For instance, production

function may be

Labor L Production q = f (L) Marginal Product of Labor, MPL

0 0 ×1 10 102 30 203 45 154 55 105 60 56 60 0

Table 4.1: Production function and Marginal Product

Marginal Product of labor, MPL = ∆q/∆L is an extra product generated by anextra unit of labor. It approximates the slope of the production function.Fundamental assumption: “Law” of diminishing marginal returns (or product) to

an input.Figure 4.1 shows a typical production function for one variable input. Only the

middle section is interesting, and from now on we are going to assume that theproduction function satisfies MPinput is positive and decreasing.

21


�

L

q

MPL

MPL > 0, or q↑ MPL < 0, or q↓

MPL ↑ law of diminishing marginal returns MPL ↓

L

Figure 4.1: Production function graphically

22

4.2 Cost functions

4.2 Cost functionsCost function describes the minimal cost of producing q units of final output. DenotedC (q). It conveniently summarizes technology and input prices.In general, cost can be written as Cost = rK̄+wL, where the capital K̄ = 1 is fixed

at one unit, and the only variable is labor, L, and parameters r and w are marketprices of a unit of capital and labor, respectively. This, however, is not the “costfunction”. The cost function depends only on q and other exogenous parameters butnot on endogenous variable inputs such as L.As one wants to change q, one must adjust L, according to the production function

q = f (L). Let L (q) be an inverse of this function, telling us the required L, if q isto be produced. Then, the cost function is C (q) = rK̄ + wL (q).One can see that the total cost consists of Fixed Cost plus Variable Cost, C (q) =

FC + V C (q).

�

L

q

Production function q = f(L)

Required labour, L = L(q)

�

∆C(q)

q

C(q)

VC(q) FC

∆q

Figure 4.2: From production function to cost function

4.2.1 ShapeThe cost function becomes steeper eventually, by law of diminishing marginal returnsto a variable input (labor). Note that the V C (q) = wL (q) has exactly the same shapeas the production function, except that it is inverted and multiplied by w.Example: Let the production function be q =

√L. Therefore, “required labor” is

L = q2. Conclusion: the cost function is C (q) = r + wq2. E.g. if wage is w = 2,rental price of capital is 800, then our cost function becomes C (q) = 800+2q2. FixedCost is FC = 800 and Variable Cost is V C (q) = 2q2.

4.2.2 Cost curvesThe above costs C (q), FC, V C (q) are “total”; but one can talk about “unit” costs:

23


�

MC AC

AVC

q

AFC

Cost curves in the short-run

Figure 4.3: Shape of unit cost functions

• Average costs:

– Average cost, AC (q) = C (q) /q.– Average Fixed Cost, AFC (q) = FC/q.– Average Variable Cost, AV C (q) = V C (q) /q.

Obviously AC (q) = AFC (q) + AV C (q).

• Marginal Cost: MC (q) = ∆C (q) /∆q, extra cost required to produce an addi-tional unit of output. It is roughly the slope of the cost function.

Important observations about cost curves so far:

1. MC is eventually increasing, because the cost function becomes steeper even-tually, by law of diminishing marginal returns to a variable input.

2. If AC > MC then AC ↘, if AC < MC then AC ↗, if AC = MC then AC isconstant. In particular, if AC reaches its minimum then AC = MC. Similarly,for AV C.

3. If FC > 0:

AFC AV C

q → 0 →∞ → some positive numberq →∞ → 0 increasing by law of diminishing marginal

returns to variable input

Table 4.2: Shape of Average Cost curves

24

4.3 Profit

�

MC AC

AVC

q 20

80

Figure 4.4: Cost curves in the example

Hence, AC has a U-shape; AFC are overwhelmingly important for “small”productions; AV C are overwhelmingly important for “large” productions.

4. AV C = MC in the limit as q ↘.

Figure 4.4 illustrates the example (continued): AC (q) = 800/q + 2q, AFC (q) =800/q, AV C (q) = 2q. Marginal Cost is MC (q) = 4q, if ∆q is small.

4.3 ProfitThree ways to write profit conveniently

1. π (q) = pq − C (q), by definition.

2. π (q) = (p− AC (q)) q, as per unit profit multiplied by the number of units.

3. π (q) = (p− AV C (q)) q − FC. This is taking Fixed Costs aside and writingprofit as operational profit (a.k.a. quasi-profit, quasi-rent, or producer sur-plus) minus Fixed Cost. Operational profit itself is per unit operational profitmultiplied by the number of units.

Plan: find out what level of production is optimal. There are two sub-problems:

1. Output decision – if produce, then how much?

2. Shutdown decision – whether to produce at all or to shut down to avoid avoid-able losses.

25


�

MC

AC

AVC

Quantity

£

p

Profit

Operational Profit

q

Figure 4.5: Representing profit

4.3.1 Output decisionSuppose that the firm wants to produce a positive quantity – what is the optimallevel of production? Profit is π (q) = pq − C (q), where

• p is the exogenous price of the final product

• C (·) is the cost function summarizing the technology and input prices.

If production increases by one unit then the revenue goes up by p, and cost goes upby MC (q). Whether production should or should not be increased depends on thecomparison between these two forces, p and MC (q). Let’s compare them on Figure4.6.

1. Suppose q1 is proposed. Note that MC (q1) < p and increasing production bya small unit will increase profit, so original q1 is not optimal.

2. Suppose q2. Then MC (q2) > p and decreasing production by a small unit willincrease profit, so original q2 is not optimal.

3. Suppose q∗. Then MC (q∗) = p and changing production a little will changerevenue and cost at the same rate and hence will not change profit, so this q∗may be optimal.

Hence, to get a candidate for optimal production level, q∗, set MC (q∗) = p.

4.3.2 Shutdown decisionIs the above positive q∗ indeed optimal? Consider three cases illustrated on Figure4.7.

26

4.4 Supply

�

MC

AC

AVC

q

£

p

q1 q* q2

Loss from last unit, when q2 is

produced.

Profit from last unit, when q1 is

produced.

Figure 4.6: Output decision

(a) Suppose that p > minAC. Then profit is positive and q∗ is definitelyoptimal, because shutting down gives profit of π (0) = −FC.

(b) Suppose that price is lower, but not too much, so that minAV C < p <minAC. The profit is negative, but operational profit is still positive. Thisoperational profit can be used to cover some of the Fixed Cost. Hence, thefirm should keep producing q∗ in the short-run to minimize losses.

(c) Suppose that price falls even more, so that p < minAV C. Then notonly profit is negative, but operational profit is negative too. Instead ofproducing q∗, the firm should rather shut down the operations immediately,avoid this operational loss and suffer losses equal only to unavoidable fixedcosts, π (0) = −FC.

Conclusion: Shut down only if operational profit is negative, or if p < minAV C.The key observation is that only FC is unavoidable. Operational profit (positive)can cover part or whole of the FC. If there is operational loss then it is not going tohelp in covering FC, but this operational loss can be avoided by shutting down.

4.4 SupplyWe would like to know how firms respond to market prices.

4.4.1 Supply of an individual firmThe firm supplies zero if price is below the shutdown price of minAV C. If the priceis above this shutdown price, then the firm should supply according to the MC (q)curve, like on Figure 4.8. Conclusion: for this technology, the supply of an individualfirm is upward sloping, essentially by the law of diminishing marginal returns.

27


MC

AC

AVC

q

£

p

q*

minAC

minAVC

Case (a)

MC

AC

AVC

q

£

p

q*

minAC

minAVC

Case (b)

MC

AC

AVC

q

£

p

q*

minAC

minAVC

Case (c)

Figure 4.7: Shutdown decision

�

MC

AC

AVC

q

£ SR Supply

Shutdown price

Figure 4.8: Individual supply

4.4.2 Market supply

It is the sum of individual supplies. For instance, let firm 1 supply q1 and firm 2supply q2 at price p′. Then market supply (if only these two firms are on the market)at this price is q1 + q2.

28

4.4 Supply

� Firm 1

q

£ Market Supply

p’

Firm 2

q1 q2 q1 + q2

Figure 4.9: Market supply

4.4.3 Example continuedRecall that the short-run cost function is C (q) = 800 + 2q2, so that AC (q) =800/q+2q, AFC (q) = 800/q, AV C (q) = 2q, andMC (q) = 4q. Hence, the shutdownprice is zero and the short-run supply function of the individual firm is obtained fromcondition p = 4q, which results in individual supply function q (p) = p/4. If thereare n identical firms like this one the market supply is Qs (p) = np/4. (Parameter nis exogenous for now).

4.4.4 Comparative staticsQuantity supplied - the amount of the good that the firm intends to sell at a givenprice, holding other factors constant. Supply curve - quantity supplied at each price.See Figure 4.10. How do the following changes can be depicted graphically

• Increase of the price of the good produced by this firm

• Increase of the price of the fixed input

• Increase of the price of the variable input

• change in technology (various forms)

29


�

Quantity of corn

Price of corn

�

Quantity of corn

Price of corn

Figure 4.10: Supply curve and its shifts

30

5 Market equilibrium. Exogenousshocks and comparative statics.

5.1 Introduction

5.1.1 Assumptions of perfect competitionPerfect competition will always mean that

1. Goods are private and homogeneous (like corn, but not necessarily cars, andsurely not like public security)

2. No market power (such as monopoly, oligopoly or cartel); we say that all agentsare price-takers. In particular, goods must be traded and have prices.

3. No transaction costs (like search cost, legal fees, transportation etc.)

4. No externalities (like pollution, congestion, or making discoveries that benefitothers)

5. No asymmetric information (i.e. qualities and abilities are known etc.)

Assumptions made here for simplicity: all firms are identical and all input prices andtechnology are constant, even if the entire industry expands or contracts. Note that:

1. Strictly speaking we do not assume that there are many firms and individuals.But since many assumptions above are justified only if there are many agents,me may as well make that de facto assumption.

2. We do not automatically assume that entry to an industry and exit from it isfree. Usually, we will assume free entry/exit in the long-run, but not in theshort-run.

5.1.2 Definition of competitive equilibriumSo far we only illustrated how an external factor affects agents’ behavior. E.g. theprice of corn affects buying and selling intentions of corn consumers and producers.Now we will hypothesize that causality also goes in the other direction: collectivebehavior affects the price.Draw supply and demand on one picture.

31

5 Market equilibrium. Exogenous shocks and comparative statics.

�

Quantity of corn

Price of corn

13

12

10

Excess supply

Excess demand Demand

Supply

Figure 5.1: Competitive equilibrium

• If price is, say, 10 then quantity demanded is much larger than quantity sup-plied. There is excess demand. Imagine a queue of potential buyers chasingsellers. We expect that buyers bid up price, i.e. this price cannot be a part ofequilibrium.

• If price is 13 then there is excess supply, sellers chase few buyers, and price ispushed down.

• If price is 12, then quantity demanded is equal to quantity supplied. Neithersellers nor buyers have an advantage; there is no pressure on price.

Thus, in a competitive equilibrium, optimal behavior of consumers (demand) andoptimal behavior of firms (supply) interact in a process determining the prices whichis called market clearing.Competitive equilibrium is a price and quantity such that:

1. Given prices, every decision maker is behaving optimally and

2. Prices are such that markets clear (quantity supplied is equal quantity de-manded)

Remark: The story motivating this definition refers to a dynamic process of priceadjustments and bargaining, but strictly speaking the concept is static(price & quantity such that. . . ).

Remark: Price is endogenous (for the first time) but it is not a decision variable.

32

5.2 Examples

5.1.3 Why we study competitive equilibria?As in any equilibrium two types of questions are usually asked:

1. How does this equilibrium change when exogenous parameters change? Thisis a positive question that leads us to a comparative statics exercises. (Seeweek 1)

2. What are the welfare properties of equilibria; do they lead to “good” outcomes?This is a normative question. (See week 2)

5.1.4 TypesThere are many versions of competitive equilibrium, e.g.

1. Long-run versus short-run. In our presentation below the difference is thefollowing:

a) In long-run, firms can enter and exit from the market. In the short-runentry/exit is not possible.

b) (to be considered later, when there are multiple inputs: in the long-runall inputs can be changed. In the short-run, some may be fixed)

2. Partial equilibrium versus general equilibrium.

a) Partial equilibrium – examine one market in isolation if it affects and isaffected by other markets in a negligible way.

b) General equilibrium – if interactions between markets are non-negligiblethen one has to “close” a few partial equilibrium models together to cap-ture these cross-market effects. Microeconomics versus macroeconomics –traditional and contemporary sense.

5.2 Examples5.2.1 Price controlConsider housing market represented on Figure 5.2. If market is unregulated, then r0is equilibrium rent and q0 is the quantity of flats rented in equilibrium. Suppose thatthe gov introduces rent control: “the maximum rent is r1”. Under this regulationthe rent would like to go above r1 to eliminate the excess demand, but it cannot.Excess demand of q1− q2 is a permanent feature on this market (if black market canbe eliminated). However, the actual drop in number flats rented is smaller, q0 − q2.

5.2.2 Unit taxRead on your own.

33


�

Quantity of flats

rent

r0

Supply

Demand

q0

r1

q2 q1

Figure 5.2: Rent control

�

Quantity of flats

rent

r0

Supply SR

Demand (after army moves in)

q0

r1

Demand (initial)

�

Quantity of flats

rent

r0 Supply LR

Demand (after army moves in)

q0 q1

Demand (initial)

Figure 5.3: Shape of behavioral functions

5.2.3 Short-run and long-runSuppose that the army builds a new base in a town. Hundreds of new families movein. This shock is depicted on Fig 5.3 as a demand shift.

1. Short-run: it is impossible to add new flats and houses right away; supply isfixed at q0, and initial rent is r0. Higher demand changes only prices (left panelon Figure 5.3).

2. Long-run: this is a town where land and permits for new developments arewaiting for investors, so any number of new flats can and will be built as longas the rent just covers costs equal r0. Higher demand triggers more investments– only quantity changes (right panel).

Conclusion: the same change (the army moves in) can have different effects dependingon the shape of the demand & supply curves (supply in this case).

34

5.3 Short-run competitive equilibrium

�

��

Firm’s output

£ MC

AC

Individual Firm

AVC

qe Market output

Market

£

Qe = nqe

D S

pe

Figure 5.4: Short-run equilibrium

5.3 Short-run competitive equilibrium1. Givens:

a) Market demand, D (p), from week 3.b) Supply in the form of cost curves, MC (q) , AC (q), from week 4.c) Number of firms, n.

2. Conditions that determine the market equilibrium (price pe, individual level ofproduction qe) are :

a) For any market price pe, firms’ supply function is given by the optimalproduction choice: pe = MC (qe) ≥ pSD, where pSD is the shutdown price.

b) Market clears, i.e. quantity supplied equals quantity demanded, i.e. nqe =D (pe)

5.4 Long-run competitive equilibriumEntry and exit is free, so the number of firms, n, is endogenous too.

1. Given:

a) Market demand, D (p).b) Supply in the form of cost curves, MC (q) , AC (q),

2. Conditions

35


�

Firm’s output

£ MC

AC

Individual Firm

AVC pe

qe Market output

Market

£

Qe = neqe

D Old S (Short-run)

S (Long-run)

New S (Short-run)

Figure 5.5: Long-run equilibrium

a) pe = MC (qe) ≥ pSD

b) Market clears, nqe = D (pe).c) Zero profit condition, pe = AC (qe), so that there is no incentive to exit or

enter this market.

3. Short-run equilibrium above is not a long-run equilibrium. Given the price, theprofit can be made by an investor, hence fresh entry occurs. Entry increases(shifts) the short-run supply. This pushes the price down and ultimately elim-inates profits.

4. So what is the long-run equilibrium? Note that the conditions tell us thatAC (qe) = MC (qe) = pe. In other words: There is only one price that does notgive any opportunity for firms to compete by lowering the cost, i.e. minAC.Otherwise, either losses are made or profits could be made. This gives us asimple algorithm to find the long-run equilibrium (see Figure 5.5):

a) Set price pe = minAC.b) Set the individual quantity, qe, so that AC (qe) = pe.c) See how much quantity will be demanded for price pe, i.e. find D (pe).d) Determine how many firms ne must be active on the market so that quan-

tity demanded equals quantity supplied, D (pe) = neqe.

Remark: In the long-run, the prevailing price is the lowest conceivable, by free entry.

Remark: One may consider a market where entry/exit is restricted. It could still becalled competitive, because the agents are price-takers.

36

5.5 Exogenous shock; comparative statics

�

Firm’s output

£ MC

AC

Individual Firm

AVC pe

qe Market output

Market

£

Qe = neqe

D S (Short-run)

p*

q* neq*

Figure 5.6: Exogenous shock and short-run adjustments

Remark: Firms may not be identical. If some firms have an access to better tech-nologies or to cheaper resources (lower AC curves) than others (or if entryis restricted) then these firms may have positive profit permanently. Insuch a case, the profit would often be called “economic rent” rather thaneconomic profit, and would be attributed to access to better resources,technology or to industry with limited entry.

Remark: More to come later, when we consider firms with more than one variableinput.

5.5 Exogenous shock; comparative staticsConsider Figure 5.6, which shows a market in LR equilibrium. The price is pe,individual quantity is qe, and number of firms is ne. Suppose that a close substitutebecomes more expensive so that the demand for this good increases.

5.5.1 Short-run adjustmentsThere is an excess demand at price pe, thus the price is bid up. Higher price doestwo things:

• it induces firms to increase the quantity supplied according to their supplyfunction MC (·), so that the total quantity supplied increases,

• it convinces consumers to reduce the level of quantity demanded.

Eventually, price p∗ equilibrates the market, firms produce q∗.

37


�

Firm’s output

£ MC

AC

Individual Firm

AVC pe

qe

Market

£

neqe

D S (Short-run)

p*

q* neq* n*qe

Figure 5.7: Long-run adjustments

5.5.2 Long-run adjustmentsPrice p∗ cannot be a part of long-run equilibrium because it is higher than minAC,so that profit can be made by new entrants. New firms enter and the market supplyincreases, n goes up. Price goes down and individual quantity decreases according tothe MC (·). Eventually, the price is pe, each firm produces qe. New number of firmsis n∗.

5.6 ElasticityIt is important to know how much quantity responds to a change of price for bothdemand and supply. Thus we need a measure of responsiveness of demand and supply.Consider Figure 5.8. The (inverse of) slope of demand could be one measure,

∆q/∆p. But much better measure is price elasticity of demand - the percentagechange of quantity demanded related to the percentage change of price,

ε = ”%∆q””%∆p” = ∆q/q

∆p/p = ∆q/∆pq/p

Example: suppose that if the price goes up from 1000 to 1010, then the quantitydemanded falls from 50 to 47.5. Then ”%∆p” = 10/1000 = 1%, while ”%∆q” =−2.5/50 = −5%. Therefore, the elasticity is −5%/1% = −5.Observation: elasticity has no units, as opposed to slope. Hence, it is irrelevant

whether one uses € versus £, or liters versus pints (which is not the case for theslope).

• Perfectly elastic demand ε = −∞,

38

5.6 Elasticity

�

Quantity

price

∆p

Demand

∆q

q

p

Figure 5.8: Elasticity

• Elastic demand ε < −1,

• Unit elasticity demand ε = −1,

• Inelastic demand ε > −1,

• Perfectly inelastic ε = 0.

Elasticity can be defined for any behavioral function.

5.6.1 Expenditures/Revenue and elasticityTotal consumers’ expenditure (and firms’ revenue) is E = pq. If the price goes up,then there are two offsetting effects, p ↑ and q ↓. Fact: if demand is inelastic ε > −1then total E goes up (as price increases), otherwise it goes down. Graphically, E isthe shaded rectangle on Figure 5.9

5.6.2 Tax incidence and elasticityHow does it depend on price elasticity of demand/supply?

39


�

Quantity

price Demand (inelastic)

q

p

�

Quantity

price

Demand (elastic)

q

p

Figure 5.9: Expenditure

40

6 Normative properties ofcompetitive equilibria

6.1 Measure of agents’ welfare

In this presentation we will use the utilitarian criterion (Pareto efficiency with trans-fers), see week 2.

1. Consumer surplus (CS) – the difference between what a consumer is willingto pay and what she actually pays. This CS is a measure of consumer’s (andconsumers’) welfare. Remark: Our original measure of consumer’s happiness issome abstract utility. Consumer surplus is exactly the same as utility if utilityis measured in monetary units comparable across agents.

2. Producer surplus (PS) – the difference between the price that the firm actuallygets and the minimum that the firm is must receiver just to cover the cost. PSis our old friend operational profit.

3. Social Welfare or surplus (W ) – the total of all surpluses in the economy, W =CS + PS (+Gov Rev + all other surpluses− other costs).

�

p1

p

q

CS

Demand

p1

p

q

Supply PS

Figure 6.1: Measure of agents’ welfare

41

6 Normative properties of competitive equilibria

�

pe

p

q

CS

Demand

Supply

PS

qe

Figure 6.2: Social Welfare in competitive equilibrium

� p

q

Demand

Supply

W

qe

p

q

Demand Supply

qe

Units that should be produced but were not.

Units that should not be produced, but were.

DWL

Figure 6.3: Deadweight Loss

6.2 Competitive equilibrium and maximization ofsocial welfare.

Consider Figure 6.3 and suppose that the production is lower than in competitiveequilibrium qe. Then some units are not produced, even if they should, since they areworth more to the consumers than the minimal amount needed to cover the variablecost.

Suppose that the production is more than qe. Then some units are produced, evenif they should not, since they are worth less than the minimal amount needed to coverthe variable cost. Loss of social welfare relative to the maximum is called DeadweightLoss (DWL)

42

6.3 Welfare Theorems

6.3 Welfare TheoremsThis leads us to the observation that the competitive quantity maximizes social wel-fare. This is an example of one of the most celebrated results in all economics. TheFirst Theorem of Welfare Economics

Competitive equilibrium is Pareto efficient.

Competitive price plays a dual role here.

1. Firstly, it “tells” each consumer how much to demand and each firm how muchto produce. This informative role of prices is fundamental for welfare maxi-mization.

2. Secondly, they divide social welfare into parts (CS and PS, in this case).

However, we know that there are many Pareto efficient allocations; some may bemore desirable than others. It turns out that, even if you do not like this divisionof social welfare, you may still use prices in their first role, at least theoretically.The Second Theorem of Welfare Economics states that, if the assumptions of perfectcompetition are satisfied and the economy is convex, then

Any Pareto efficient outcome can be achieved by competitive prices, given theappropriate initial transfers of surplus.

Remark: “Transfer” here is a theoretical possibility. For all practical reasons, trans-fers involve distortionary taxes and hence result in some DWL. But still,DWL from a well-designed tax system may be lower than the loss associ-ated with price manipulation.

Remark: The term “invisible hand”, coined by Adam Smith in XVIII century, isinterpreted today as a prequel to the First Welfare Theorem. But formally,both theorems were proven in their full versions barely 60 years ago.

Remark: There have been attempts to replace price system with a central plan-ner (Soviet Union, Eastern Europe and other places). There are two bigfailures of a central planner.

1. Is the government benevolent? It may be autocratic. Even if not, thecentral planner - like any bureaucracy - is corruptible.

2. Is the government omniscient, and then is it omnipotent? The prob-lem of allocation is fabulously complex.

And this attempt was just to replicate the working of a price system thatsolves for Pareto efficient allocations automatically and instantly.

43

6 Normative properties of competitive equilibria

�

pe

p

q

A

Demand

Supply

qe

B C

D E

Min p

q1

Figure 6.4: Price floor

Let’s recall the definitions

Pareto efficient outcome Competitive outcomeSome social/central planner dictatesthe quantities in order to maximize

the utilitarian social welfare. She mustbe benevolent, omniscient and

omnipotent

Nobody dictates anything.Price-taking economic agents behave

egoistically according to theirindividual incentives (and according tothe postulates of perfect competition)

6.4 ApplicationsAssessment of policies. Two examples

6.4.1 Price floorPrices lower than a certain minimum price are declared illegal. See Figure 6.4.

• No price floor: CS = A+B + C, PS = D + E, W = A+B + C +D + E.

• Price floor: CS = A, PS = B +D, W = A+B +D. DWL = C + E.

Remark: whenever there is excess supply or demand, in principle we need to specifya rationing rule. Here we assume that the rationing rule says that thegoods go to those who value them most from these who can produce themthe cheapest. With alternative assumptions we would obtain even biggerDWL. E.g. if there is a queue, time is lost, or if the firm with higher costgets to sell before the firm with lower cost.

44

6.4 Applications

�

pe

p

q

A

Demand

Supply

qe

B C D

F

p`

q1 q2

E G

Figure 6.5: Price support

Remark: if B > E then producers gain from the price floor relative to no interven-tion. However, by the Second Welfare Theorem, we can still improve thesituation of the producers without creating DWL. Just take the sum of Bfrom consumers and transfer it to the producers, and then let the priceswork in an unrestricted way. As the result CS = A+C, PS = B+D+E,and both producers and consumers are happier than with price floor. Pricesstill play an informative role, but not a distributive role.

6.4.2 Price supportConsider Figure 6.5. Suppose that the Gov wants to support price p′ > pe by buyingexcess supply q2 − q1 from the producers (and then dumping it to the Ocean).

• No price support: CS = A+B + C, PS = E + F , W = A+B + C + E + F .

• Price support: CS = A, PS = B+C +D+E+F , Gov exp = C +D+F +G.W = A+B + E −G. DWL = C + F +G.

45

7 General equilibrium – trade andcomparative advantage.

7.1 IntroductionSo far we ignored the fact that changes on one market may influence other markets.But such link may be relevant, because the changes on other markets may hit backour original market. It is more correct to consider equilibrium on all markets simul-taneously (general equilibrium). If one considers trade – selling one thing in orderto buy another – then general equilibrium approach is essential. This approach is aworkhorse of such disciplines as macroeconomics, finance, international trade, etc.Circular model of economy (Figure 7.1) reveals the two-sided nature of every trans-

action.

• People do not work to earn money, but to buy consumption goods

• Likewise, investors do not invest to have profit

• Countries do not export to have hard currency or gold, but to finance imports

Wage, profit, hard currency is only an intermediary

�

Households (Consumers)

Firms

Income versus Expenditures Objective: according to preferences Constraint: budget

Cost versus Revenue Objective: max profit Constraint: technology

Payments (wage, rental price of capital, etc.)

Payments for goods and services

Goods and sevices

Factors of production (labour, capital, land, etc)

Demand

Demand Supply

Supply

Market for final product Market for

factors of production

Figure 7.1: Circular model of economy

47

7 General equilibrium – trade and comparative advantage.

�

10 apples

10

50

90

oranges Robinson �

10 apples

10

50

90

oranges Friday

Figure 7.2: Preferences and endowments

�

10 apples

10

50

90

oranges

Figure 7.3: Edgeworth box

7.2 Bilateral trade without productionExample: Suppose that initially Robinson has an endowment of 40 oranges and 10apples, while Friday has an endowment of 10 oranges and 90 apples. Robinson’s andFriday’s preferences are expressed in terms of indifference curves. See Figure 7.2.

1. Why trade may be beneficial?

• Key observation: Robinson values apples a lot in terms of oranges (highMRS), while Friday values apples a little in terms of oranges (low MRS).Maybe, if Robinson gives up some of his oranges in exchange for some ofFriday’s apples, then both would be happier. . .

• Pareto improving redistribution and Edgeworth box. Any point in theEdgeworth box shows a possible distribution of total endowment of 100apples and 50 oranges. The gray area shows all combinations in which bothRobinson and Friday are better off than in initial endowment. Hence, aPareto improvement exists.

Conclusion: If at certain allocation the MRS are not equal across agents thenthere exists mutually beneficial redistribution. MRS equal across agents anecessary condition for Pareto efficiency.

48

7.2 Bilateral trade without production

�

10 apples

10

50

90

oranges Robinson

∆y ∆x

Figure 7.4: Trading away from the endowment

2. Trade in competitive equilibrium.

• The price as terms-of-trade, expressed not in money but in terms of othergoods. Consider Robinson: without trade he can consume everythingSouth-West of the endowment.

– But suppose that he can sell ∆y oranges in exchange for ∆x apples.Then he can consume everything on or below the blue line. In partic-ular, he can reach a bundle on a higher indifference curve. The rate∆y/∆x is a price of an apple in terms of oranges – graphically this is aslope of a budget line. Let p = ∆y/∆x denote this prevailing marketexchange rate.

– If this slope is steeper than Robinson’s MRS at endowment (ratherthan flatter), then Robinson would also trade to reach higher indiffer-ence curve, but now selling apples to buy oranges.

– The only case when Robinson does not take advantage of trade iswhen the slope of the budget line is exactly equal to MRS, where heis already in optimal point.

• As always in perfect competition, the price of apples, p, is taken by agentsas given, but it is endogenous in the model. Suppose it is too high, i.e.budget constraint is too steep, then Robinson does not want to sell as manyoranges as Friday wants to buy – shortage on orange market, oversupply onapple market (see left panel on Figure 7.5). However, if the price is correctthen there is market clearing and thus the price-quantity configurationforms a competitive equilibrium (right panel on Figure 7.5)

Remark: Observe that in equilibrium we have MRSR = p and MRSF = p.But this implies that MRSR = MRSF . Hence, we have a decen-tralized trade that leads to a Pareto efficient allocation; this is ageneral-equilibrium version of the First Welfare Theorem (competi-tive equilibrium implies Pareto efficiency).

49


�

10 apples

10

50

90

oranges �

10 apples

10

50

90

oranges

Figure 7.5: Competitive equilibrium

Remark: This is still perfect competition, as both Robinson and Friday areprice-takers. The fact that we assume two agents is for convenienceonly; there should be more for price-taking behavior to be justified.

Remark: This is general equilibrium - all markets are solved together.

We are only touching big issues here. Things to remember:

• Pareto improvement generically possible.

• Voluntary trade (leading to competitive equilibrium) possible.

• This equilibrium picks up one Pareto efficient allocation.

• All the above holds in a general equilibrium model of an arbitrarily big andcomplex economy, under some mild assumptions.

7.3 Trade in the economy with production.Comparative advantage

Example: If Robinson works only fishing, then he can catch 20 kilograms of fishper day. Alternatively, if he works only collecting bananas, then he can collect 10baskets of them. Obviously, he can split his day between these activities to get anycombination of these two. Friday is far more experienced. He can catch 30 kilogramsof fish or collect 30 baskets of bananas, or get any combination of the two. In additionto these productivity, assume some preferences; Robinson and Friday want to consumefish and banana in fixed 1 : 1 proportion.Production Possibility Frontier (PPF ) describes what bundles can be produced.

Slope of the PPF is called Marginal Rate of Transformation (MRT ) because it sayshow fish can be “transformed” into bananas. For instance, Robinson needs to giveup two kilograms of fish to get one more basket of bananas. Without trade, Robin-son produces and consumes (bR, fR) =

(62

3 , 623

)and Friday produces and consumes

(bR, fR) = (15, 15). See Figure 7.6.

50

7.3 Trade in the economy with production. Comparative advantage

�

Bananas Bananas

Fish Fish

20

10

30

30

Robinson’s PPF Friday’s PPF

MRT = −2 MRT = −1

1:1 1:1

Figure 7.6: Individual PPF

Bananas

Fish 50

40

(30,20)

Joint PPF

MRT = −2

MRT = −1

(25,25)

(21⅔,21⅔)

Figure 7.7: Joint PPF

1. Why trade may be beneficial? Suppose that Robinson and Friday do not tradeinitially. Total production is (bR + bF , fR + fF ) =

(212

3 , 2123

). Question: Can

we Pareto improve? Consider the following maneuver:

a) Robinson gives up one basket of bananas, which allows him to produce 2additional kilos of fish, i.e. (bR − 1, fR + 2),

b) Friday produces one and a half baskets of bananas more by giving up oneand a half kilo of fish, (bF + 1.5, fF − 1.5).

In total their production of bananas and fish increases by 0.5 unit each, so theyend up with (bR + bF + 0.5, fR + fF + 0.5). This is an authentic free lunch!Formally, this is a Pareto improvement.

Terminology: Robinson has comparative advantage over Friday (but not abso-lute) in fish and Friday has comparative advantage over Robinson in bananas.A fundamental observation is that generically everyone has comparative advan-tage in something!

51


�

Bananas Bananas

Fish Fish

20

10

30

30

−1

−1.5

−1.5

Friday produces bananas

Robinson Robinson produces

fish

Robinson wants to sell fish for

bananas

Friday wants to sell bananas

for fish

−2

Figure 7.8: Markets do not clear at price p = 1.5

2. Trade in competitive equilibrium. Question: Can Friday and Robinson tradewith each other, even if Robinson is less productive in both industries? Answer:Yes.

Let us verify that the following is equilibrium. Let the price be p = 1. Giventhis price, Robinson is producing only Fish (20 kilograms) and intends to sell10 kilograms to Friday in exchange for 10 baskets of bananas. Hence, hisconsumption is (10, 10). Given this price, Friday is indifferent among variousquantities of trade (His marginal rate of transformation is equal to the marketmarginal rate of transformation, MRT = p). So he may as well produce 25baskets of bananas and 5 kilos of fish and sell 10 baskets for 10 kilos of fish. Heends up with consumption bundle (15, 15). To sum up: everyone is behavingoptimally given prices and markets clear.

Total production is (25, 25), which is the best point on the joint PPF .

Remark: we are only touching big issues here. Things to remember:

• Pareto improvement generally possible even if one party is less productivethan others in all industries. It is the comparative advantage that matters.Everyone has comparative advantage in something.

• Voluntary trade at equilibrium price possible.

• This equilibrium picks up a Pareto efficient allocation.

• This is a general equilibrium analysis (even if the economy is tiny) becausemarkets of bananas and fish are interrelated; one cannot exist without theother. This also shows that buying is just another side of selling; importsare another side of exports, e.g. preventing imports hurts exporters, etc.

52

7.4 Example of general equilibrium analysis

7.4 Example of general equilibrium analysisFigure 7.9 shows an example of trade-off. Draw in some indifference curves in thetop-right panel to see what is the best outcome. Suppose that fish industry becomesmore productive for every level of employment. What happens with the productionplan? Is water industry affected?

�

Water (barrels per capita)

Fish (baskets

per capita)

80

20 A

B

C

D

Labour in water industry

Labour in fish industry

Production function in the water industry

Production function in the fish industry

100

100

Distribution of labour between fish and water industry

50

100

50 100

Production Possibility Frontier

Figure 7.9: Production function and Production Possibility Frontier

53

8 Public goods, externalities,asymmetric information

The model of perfect competition is relatively tractable and in many cases reliable asan initial approximation. We obtained a number of testable hypotheses. Now let’sdiscuss some of the situations where we cannot count on perfect competition. Goalis as always two-fold: positive question – how the system works, normative question– is the outcome good and can it be improved?We will discuss:

1. Public goods, commons, free riding,

2. Externalities,

3. Imperfect information,

4. Market power of a monopoly,

5. Market power in imperfect competition, game theory.

8.1 Public goods

8.1.1 Types of goods.

Private goods discussed so far have the properties of rivalry and exclusion.

• Rivalry – one unit of a good cannot be consumed by more than one consumer.

• Exclusion – consumption of a good can be prevented by an owner.

A public good - one unit of this commodity can be consumed by many agents simulta-neously, i.e. there is no rivalry. Pure public good - non-rivalrous and non-excludable.A congestible common property is a good that is accessible to all, i.e. non-excludable,but is not too public, i.e. there is some rivalry, thus ‘congestible’.

55

8 Public goods, externalities, asymmetric information

Exclusion No exclusionRivalry Private goods: apples,

flats, consulting yourGP, toll bridge (if

capacity is an issue).

Commons: publicroads, fishery, publicpark. (if congestible)

No rivalry Public goods withexclusion: cable TV,concert (if capacity is

not exhausted,non-congestible)

Pure public goods:national defense, lawenforcement, cleanair, lighthouse,prevention of

infectious diseases

Table 8.1: Types of goods

8.1.2 Government and public goods.Two ways to supply public goods in without government’s involvement:

1. Paying before production, i.e. voluntary contribution (chipping in). But freeriding among contributors.

2. Paying after production. The good has to be at least excludable. Otherwise,free riding of consumers on the supplier would be rife and it is possible that agood is not provided by a private entrepreneur at all. But obviously exclud-ability alone does not guarantee that the good will be provided by a perfectlycompetitive market in efficient quantities (see natural monopoly, etc).

The question of public goods gives the classical explanation why governments, as aforce of coercion, are needed. Without forced taxation to finance public good - inparticular, pure public goods such as security - the society would have to do withoutit.

8.2 ExternalityAn externality is present whenever an action of an agent (or a voluntary transactionbetween a group of agents) affects another agent’s utility or profit, and the effect isnot mediated by prices. External effect is this extra benefit/cost and contrasts tointernal benefits/costs of agents who are voluntary participants of the transaction.Competitive model incorporates effects mediated by prices.

8.2.0.1 Types of externality

One can talk about consumption externality (consumption generates externality)versus production externality (production generates externality).

56

8.2 Externality

�

MC

Private Demand Social

Valuation

price

q-ty

External benefit

qe qW

Positive externality �

Social MC

Demand

price

q-ty

External cost

qe qW

Private MC

Negative externality

Figure 8.1: Positive and negative externality

More importantly

• Positive externality: effect is beneficial. True social valuation is the sum of twocomponents, private valuation, i.e. inverse demand, and external benefit. Thisis illustrated on Figure 8.1. Competitive market quantity is qe, but sociallyoptimal level is qW > qe. Conclusion: goods with positive externality areunder-supplied by competitive markets.

• Negative externality: effect is harmful. True social MC consists of two com-ponents, private MC and external MC, i.e. marginal damage. Competitivemarket quantity is qe, but socially optimal level is qW < qe. Conclusion: goodswith negative externality are oversupplied by competitive markets.

8.2.1 Examples:• Positive: beekeeping, keeping garden tidy and house painted, education, R&D,

knowledge, charity (i.e. decreasing poverty), network externalities (such asphone, face book, software standard, language), taking a flu jab, commonproject, teamwork,...

• Negative: pollution, CO2 emissions, chatter during class, deforestation, roadcongestion, overfishing, overgrazing, unlicensed radio spectrum, crime (anddrugs that lead to crime), war, voting while not interested or informed, go-ing out while having a flu, sneezing, unprotected casual sex.

Remark: Socially optimal level of pollution typically is not zero! It is just lowerthan the competitive one.

57


Remark: Public good creates a positive externality – say, if someone builds a light-house then all benefit from it. A person who uses public good withoutpaying is free riding.

8.2.2 Government and externalities1. Direct controls such as quotas, industry standards, bans and price controls

2. Pigouvian approach - manipulating incentives. E.g. taxes (Pigouvian tax),subsidies, tariffs. In fact, all policies that affect competitive quantities can beused to bring competitive quantities closer to social optimum.Remark: the Government does not often have enough information.

3. Coasian approach. The government may try to create ownership and marketsfor externalities, to internalize them in prices. Coase Theorem – property rightsand frictionless negotiations will bring the efficient quantities, regardless ofinitial distribution of property rights.

• For instance, suppose Robinson values smoking at +10 and Friday valuespassive smoking caused by Robinson at −7 (negative externality); Paretoefficient outcome (with transfers) is to allow Robinson to smoke. If weestablish property over “air” and guarantee unhindered negotiations thenthis efficient outcome will be achieved for any distribution of propertyrights. Consider two options:

– Option 1: give “air” to Robinson; the outcome is that Robinsonsmokes.

– Option 2: give “air” to Friday; then Robinson buys the right to smokefrom Robinson for a price between 7 and 10 (say 8) and smokes. Theprice is acceptable to both.

• If Robinson valued smoking at +10 and Friday at −15, so that smokingis not Pareto efficient, then again we would face two options and againregardless of the option the outcome is efficient:

– Option 1: give “air” to Robinson; then Friday buys the “air” fromRobinson for a price between 10 and 15 and enjoys breathing.

– Option 2: give “air” to Friday; then Robinson don’t smoke.

Remark: in real life, negotiations are not frictionless and often Friday andRobinson would not come to a Pareto improving agreement. But, anyway,maybe we should try to create markets for pollution and other externalitiesand give up only if this is too cumbersome.

4. An example of a hybrid method: cup-and-trade (total quota with trading) etc

58

8.3 Asymmetric information

8.3 Asymmetric informationBroadly speaking there are two types of problems.

1. Unknown “quality” (unobserved type, adverse selection, pre-contractual asym-metric information). Some examples:

a) A seller knows the quality of the object for sale (say, a used car). A buyerdoes not know it.

b) A job applicant knows her abilities, but the employer does not.c) A buyer knows how much he is willing to pay; a seller does not know how

much she can ask for.d) A mechanic knows if the car needs an engine replacement or just oil change,

but the owner may not know this.e) A person knows her health, an insurer does not.

This is called adverse selection. Attempts to alleviate these problems: Sig-naling, screening, external expert, warranty, disclosure policy/requirements,reputation. . .

2. Unobservable actions (moral hazard, contract theory, post-contractual asym-metric information). Some examples:

a) Employer can only partially observe the level of his employee’s effort. Em-ployee can shirk. How to design the optimal contract?

b) Insurer cannot observe the lifestyle of an insured person, but this personcan engage in risky behavior after purchasing health or life insurance.What is the optimal contract?

c) Managers’ actions are not fully observed by stock owners. Managers couldspend money on expensive jets or offices, and stock owners have no chancesof seeing if these expenditures are indeed profit-generating.

d) Firms’ collusion not fully observable by market regulating agency.

Attempts to alleviate moral hazard problems: profit-sharing and various otherincentive schemes (in the context of employment), co-payment and deductibles(in the context of insurance), better monitoring, screening, reputation. . .

The central challenge: incentive compatibility (truth telling). A contract (mecha-nism, institution) is incentive compatible (induces truth telling) if all participantshave sufficient incentives to follow the provisions of the contract. Some examples ofmechanism that are not incentive compatible:

• Centrally planned economies of former Soviet Union and Eastern Europe. No-body had incentives to do what they are supposed to do: workers do not haveincentives to work, managers do not have incentives to lower the costs, etc.

59


• A mechanism that says that we clean our kitchen just because we share it.Nobody has incentives to stick to this contract. Rather, everyone would preferto free ride.

• A mechanism that says that we give you insurance premium discount if youdeclare that you do not smoke (without actual medical examination). Everyonewould say that they do not smoke.

• Consider a scheme in which a student may study for free in exchange for afixed fraction of her future income (higher income tax). The hope is that highearners will pay more to cover insufficient contributions of low earners. This isnot incentive compatible: those who are likely to earn a lot will not participate,because they will prefer to take a standard loan and repay fixed interest andprincipal later, rather than pay high income tax. But if the system attractsonly low income graduates, then it is not able to pay for itself.

Whoever designs a contract, scheme or creates an institution, must take this incen-tive compatibility constraint into account. That is, one must make sure that allparticipants receive enough incentives to act as assumed in the contract.

60

9 Monopoly

9.1 SetupMonopoly is a single firm producing a particular commodity. It can affect the marketprice by changing the quantity; via the (inverse) demand function p (q). The trade-off: either sell a lot cheaply, or sell little for a high price. This is the only thing thatis different from the previous analysis of a perfectly competitive firm – in particular,cost curves are not affected. That is, the firm is still perfectly competitive on theinput markets and derives its cost function in the same way as previously.Market structures - monopoly and perfect competition as polar cases:

�

Perfect Competition

Monopoly Imperfect Competition

Oligopoly

Many firms One firm A few firms

Figure 9.1: Market structures

9.2 Profit maximizationThe monopolist follows the same general rules as perfectly competitive firm. First(i) output decision by the comparison of Marginal Revenue (MR) and MC.

• MC < MR then q ↑ increases the profit

• MC > MR then q ↓ increases the profit

• MC = MR then a small change of q will not affect the profit: a candidate foroptimal production level.

Then (ii) shutdown decision – shutdown if operational profit is not positive.The twist is in Marginal Revenue. In the case of a perfectly competitive firm, MR

is equal to price. Not for the monopoly.

9.3 Marginal Revenue of the monopolyAs always, Marginal Revenue is a change of the revenue caused by a unit productionincrease,MR = ∆R/∆q. But now R = p (q)×q. That is, the price that the monopoly

61

9 Monopoly

�

∆q

∆p p(q1)

q-ty

price

A

B

Demand

Initial Revenue

q1

Figure 9.2: Marginal Revenue of the monopoly

can select, depends on the quantity that the monopolist desires to sell. Figure 9.2presents the trade-off of the monopolist. If quantity increases from q1 by ∆q, theninitial revenue goes up by area A because the monopolist sells more, but also goesdown by area B because the price must be lowered from initial price p (q1) by ∆p < 0.Rectangles A = ∆q× (p (q1) + ∆p) and B = −∆p× q1. Since ∆R = A−B, we haveMR = p (q1) + ∆p + (∆p/∆q) q1. If the change of production is “small” then ∆p isessentially zero and we ultimately have p (q1) + (∆p/∆q) q1.

Comparison with perfect competition:

Monopoly Competitive FirmChange of the priceinduced by the firm’sincrease of production

Negative, ∆p/∆q < 0 None, ∆p = 0

Area B There is one There is noneMarginal Revenue MR < p (q1) MR = p

Table 9.1: Monopoly versus perfect competition

Table 9.2 presents a numerical example: First two columns describe the demand,the third column describes total cost. The optimal production level is qm = 3 units(where (i) MR is (almost) equal to MC and (ii) operational profit is not negative,p (qm) > AV C)

62

9.4 Graphical illustration

p q C R MR MC AV C

10 0 10 0 × × ×9 1 14 9 9 4 48 2 18 16 7 4 47 3 22 21 5 4 46 4 26 24 3 4 45 5 30 25 3 4 44 6 34 24 -1 4 43 7 38 21 -3 4 42 8 42 16 -5 4 4

Table 9.2: Numerical example

9.4 Graphical illustrationChoice: (i) Output decision – find a candidate qm fromMC = MR, then use demandto see what price pm is acceptable to consumers. (ii) Shutdown decision – verify thatoperational profit is not negative, pm ≥ AV C.

�

qm q-ty

price

Demand

MR

MC

AVC pm

Figure 9.3: Monopoly decision graphically

9.5 Welfare properties of the monopoly.1. The optimal behavior of the monopoly involves MC = MR < pm. That is, qm

is less than competitive outcome qe with the same cost structure. Hence, thereis DWL. Moreover, Consumer Surplus is lower than if the product is deliveredby perfect competition, because the price is higher.

63

9 Monopoly

2. The above social loss can in fact be greater, if firms actively spend resourcesto become monopolies (for instance, lobbying). Such behavior is called rentseeking.

�

��

��

qm q-ty

price

Demand

MR

MC

AVC pm

��

�� Social Welfare of monopoly

DWL relative to perf. comp.

qe

Figure 9.4: Welfare properties of the monopoly

9.6 Price discrimination.Implicit assumption above: monopolist has to charge a single price for all deliveredunits. It may be justified sometimes – maybe in real world there is arbitrage: con-sumes who buy cheaper may resell to those who would be charged more. But if suchresale is impossible then the monopolist may be able to charge different prices todifferent consumers or for different units. This is called price discrimination. Perfectprice discrimination is when the monopolist knows exactly how much each consumeris willing to pay for each unit. Monopolist may then sell precisely qe units for theprice of the entire Social Welfare (first unit for a very high price, second for slightlylower, etc. until the consumer’s valuation equals MC). Two consequences of suchperfect price discrimination:

• Socially optimal production level is delivered qe, resulting in no DWL. . .

• . . . but Consumer Surplus is zero, captured entirely by the monopolist via per-fectly tailored prices.

9.7 Why monopolies exist?Not only monopolies, but all firms with market power.

1. Cost Advantage. Consider the following exercise: Imagine a perfectly competi-tive market with free exit and entry, with AC that has Minimum Efficient Scaleroughly of the size of the market. Let’s try to find the competitive equilibrium

64

9.7 Why monopolies exist?

according to our notes from week 5: we find that in the long-run the price mustbe pe, because this is where AC has its minimum, and individual productionis equal to MES. Then we proceed to find the equilibrium number of firms,but this is where we realize that total quantity demanded is actually equal toproduction of a single firm and we conclude that equilibrium number of firmsis ne = 1. This however contradicts our assumption that the number of firmsis so great that they all should take prices as given.Conclusion: If MES is “large” relative to the size of the demand, i.e. if firmhas economies of scale for all relevant production levels, then we have a natu-ral monopoly. If the industry is characterized by economies of scale then thestructure with many firms will not be permanent – the bigger one firm becomesthe more cost-efficient it gets, gaining advantage over competitors. Ultimately,only one firm would survive. Examples:

• power plants (say nuclear)• networks such as electricity, gas, water, rail,• intellectual property such as software, movies, music, books, new drugs

etc.

�

q-ty

price

Demand

MC

AC

pe

MES

Figure 9.5: Natural Monopoly

2. Government actions:

• Patents or copyrights – introduced to encourage scientific development andartistic creativity.

• As a result of barriers to entry to assure quality or standards – medicalprofessionals, architects, academic titles, solicitors etc.

• As a result of government procurement contracts, or to assure reliabilityof deliveries – national security, defense industry, energy supplies, food ormedicine stock, etc. (but here the demand side is not a price taker)

65

9 Monopoly

• Selling licenses or rights to operate – to obtain budget revenue.• Licensing, cartels or other less explicit methods due to lobbying, to protect

interests of some political/professional groups or outright corruption.

66

10 Oligopoly

10.1 Market structuresMonopoly and perfect competition are polar cases, but Imperfect Competition is themost interesting.

�

Perfect Competition

Monopoly Imperfect Competition

Oligopoly

Many firms One firm A few firms

Figure 10.1: Market structures

Consider an industry with 2 firms, qi is the production level of firm i, andQ = q1+q2is the market quantity. Inverse demand is p (Q) = 2−Q = 2− q1 − q2, and cost is 1per unit for both firms. Two polar cases (check yourself):

1. Monopoly (cartel) outcome: Qm = 0.5 and pm = 1.5,

2. perfectly competitive outcome: Qe = 1 and pe = 1.

10.2 Strategic behaviorIf firm 1 increases its quantity q1, then this affects

1. Her costs

2. Her revenue, in particular:

a) One more unit brings an additional revenue equal to the price of this unit,b) In order to sell this unit, price may have changed and this affects the

revenue from all other units sold,c) With the different behavior of firm 1, firm 2 may need to adjust its be-

havior, and this hits back firm 1. That is, a change in q1 changes marketquantity, price and then the problem that firm 2 faces. This may triggersome change of q2, and this affects back the market price that ultimatelyaffects firm 1.

67

10 Oligopoly

Effects (1) and (2a) are present in Perfect Competition. In addition to this,the monopolist has to tackle effect (2b). Effect (2c) is only present in thesituation of Imperfect Competition. Notice that effect (2c) is very difficult tocrack conceptually. If the change of behavior of firm 1 triggers the change of theoptimal behavior of firm 2, then the same force works in the opposite direction.Optimal behavior depends on beliefs that firms have about the behavior of theircompetitors. But how about beliefs about beliefs that firms have about eachother, etc?Question: Can we predict that some types of behavior will occur systematically?Strategic situations like the above one are analyzed by non-cooperative gametheory. Recall the normal-form games from the first lecture.

10.3 Application: Cournot model of quantitycompetition.

Problem of firm 2 is to maximize profit given behavior of firm 1, i.e. to let MCequal to MR2. Marginal Cost is equal one. Marginal Revenue of firm 2, given theproduction level of firm 1, is MR2 = (2− q1) − 2q2. Hence optimality conditionMC = MR2 translates into 1 = (2− q1)− 2q2, so that the best response of firm 2 tothe given production level of firm 1 is q2 = 0.5 (1− q1). This is called “best response”because it says what firm 2 should do if it believes that firm 1 chooses q1.Problem of firm 1 is entirely symmetric and its best response to behavior of form

2 is q1 = 0.5 (1− q2). Production profile(qC

1 , qC2

)is a Nash equilibrium (or Cournot

equilibrium) if it satisfies both these conditions. Solution is qC1 = qC

2 = 1/3. Totalmarket quantity is QC = 2/3 and market price is pC = 4/3.We can see how market power gradually increases price, Producer Surplus and

Deadweight Loss and decreases market quantity, Consumer Surplus and Social Wel-fare.

10.4 Application: Bertrand model of pricecompetition.

Suppose that firms choose prices, and all consumers buy from less expensive supplier.If prices are equal then they buy from randomly chosen supplier. Demand and costare like above.Both firms choosing price 1 forms a Nash equilibrium (Bertrand-Nash), because:

• Obeying the plan: profit is zero;

• Deviation: choosing price lower than 1 will attract all consumers but the firmwill sell below costs; choosing price higher than 1 means that all consumers willgo to the competitor and nobody will buy from this firm.

68

10.5 Cartel

There is no profitable deviation if everybody is expected to stick to this plan.

10.5 CartelCartel may be explicit when a number of producers sign a binding contract to restrictproduction (like OPEC). Very often illegal in most developed countries. More inter-esting case is tacit collusion, where there is no communication or contract. Producers“understand” and obey the rules of the cartel without explicit agreement. Cartelsare difficult to maintain because

1. each member of such cartel has incentives to cheat (play a best response), or

2. a new firm may try to enter.

But if firms interact repeatedly, then they may stick to the rules of collusion to avoidfuture punishments (say, price wars). Tacit collusion is more difficult to sustain if

1. there is a threat of new entry,

2. there is a problem with detection of a player who cheats his partners in thecartel (monitoring)

3. decision are infrequent or firms are impatient

10.6 SummaryWhile there is one model of Perfect Competition and one model of Monopoly, thereare a few different market forms of Imperfect Competition between these two polarcases. Cournot, Bertrand and Cartel are three examples.

�

Monopoly, Cartel

Cournot

Perfect Competition, Bertrand

1 2/3 ½

1½ 4/3

1

p

Q

MC

Demand

Figure 10.2: Competition between two firms may lead to a range of outcomes

69

11 Production (many variable inputs)The last two sections are an elaboration on the firm’s problem in week 4.

11.1 Introduction to firm’s problem

11.1.1 GoalQuestions: how do competitive firms operate and make economic decisions? How dotheir decisions depend on long-run and short-run perspective? Ultimately, we wantto derive producer’s supply.

11.1.2 AssumptionsFirms may be enormous in size and complexity, but we are going to assume that

1. They maximize profits, Profit = revenues – costs, π = R− C.

2. The technology is given. For simplicity assume that the firm produces q unitsof a single good or service, but uses two inputs, K units of capital, L units oflabor. Production function f , such that q = f (K,L), tells us what level of q iscreated by the firm employing K and L units of inputs.

3. The firm is perfectly competitive, takes all prices as given: p price of final good,r rental price of capital, w wage or price of labor.

11.1.3 The problemThus the firms’ decision problem may be written as “Knowing all prices (that is p,w and r), choose the level of production and employment (that is q, L and K) sothat the profit π = pq − (rK + wL) is the highest, given that inputs and output arerelated through q = f (K,L).”

11.1.4 ApproachThis problem is complex, it involves finding three variables: q, L and K. Therefore,we are going to divide it into two simpler steps.

71

11 Production (many variable inputs)

1. Step 1 (cost minimization). “Suppose that there is some desired level of finaloutput q. What is the cheapest way to produce this q and how much does itcost? That is, what should K and L be to produce this desired q?” This givesus the correct composition of inputs, K (q) versus L (q), and the cost functionC (q) = rK (q) + wL (q).Here is a new perspective on what is the short-run and long-run:a) in the short-run (SR) capital is fixed, the only variable input is labor.

Hence, this step is trivial – there is no substitution between K and L.b) in the long-run (LR) both inputs are variable. This is where this problem

bites.

2. Step 2. (profit maximization). “Step 1 tells us what the cheapest way toproduce any desired level of final product q is. But what should q be?” Aspreviously this problem consists of two sub-steps: output decision and shut-down decision.

Remark: Confusingly, we use two notions of short-run/long-run. Previously, long-run meant only that firms could enter and exit freely, which was not allowedin the short-run. The second meaning introduced in this section is that inthe long-run firms can change capital in additional to labor, while in theshort-run capital is fixed. Please do not confuse the two meanings. Gen-erally speaking, the meaning of short-run/long-run has to be understoodfrom the context.

11.2 Production functionFirst, however, one has to introduce production function f .

11.2.1 One input (Short-run)This is exactly the problem in week 4.

11.2.2 Two inputs (Long-run)Two inputs – capital is no longer fixed.Isoquant is a set of all combinations of inputs that lead to the same level of output.

Shows flexibility that the firm has in substituting one input for another without givingup output. Properties:

1. Isoquants slope down

2. Isoquants to the north-east represent higher output

3. Isoquants cannot cross

72

11.2 Production function

�

L

K

A, q = 100

B, q = 100

∆K

∆L D

q < 100

Figure 11.1: Isoquants

4. For every point there is an isoquant that goes through it.

Slope of an isoquant - also known as the marginal rate of technical substitution oflabor for capital, MRTSKL = ∆K/∆L, such that production is unaltered. Considera change A→ B as shown on Figure 11.1. This move can be divided into two steps,A→ D → B

• If go A→ D then production goes down by around ∆K ×MPK .

• If go D → B then production goes up by around ∆L×MPL.

• Since total change of production is zero, then −∆K ×MPK = ∆L×MPL. Or

MRTSKL = −MPL

MPK

Observation: If go A→ B then MPL goes down, and MPK goes up, both by the lawof diminishing marginal returns. Hence MRTS becomes flatter (as one moves to theright along an isoquant).

11.2.3 Marginal returnsRecall the law of diminishing marginal returns. It is assumed to hold for all inputsnow.

11.2.4 Returns to scaleIncrease K and L proportionately by a factor a > 1, and see what happens with theproduct. If the product goes up by...

73

11 Production (many variable inputs)

�

q = 10 q = 20

q = 30

L

K

Fixed capital, increase labour

Marginal returns to labour

K

�

q = 10 q = 20 q = 30

L

K

Increase labour and capital proportionately

Returns to scale

Figure 11.2: Comparing the two “returns”

• ... a exactly, then constant returns to scale,

• ... less than a, then decreasing returns to scale,

• ... more than a, then increasing returns to scale.

Note the difference between returns to scale and marginal returns to an input.Remark: One may have a technology that has diminishing marginal returns to all

factors of production (as always assumed), but increasing returns to scale! Considerso-called Cobb-Douglas production function q = AKaLb where parameters a and bare positive and less than 1 and parameter A is positive. Figure 11.3 shows suchfunction for A = 1/7, a = b = 0.75.

• Diminishing marginal returns as indicated by a “parallel” slice for a fixed capitalK̄ = 20,

• Increasing returns to scale, as indicated by a “diagonal” slice, where K = L.

74

11.2 Production function

Marginal returns to aninput

Returns to scale

What is the extra productgenerated by an extra unitof one factor of production,keeping all other factors

constant.

How much output changesif all inputs increased

proportionately

Law of diminishingmarginal returns alwayssatisfied by assumption

Depends on technology –one may have decreasing /

constant / increasingreturns to scale

Table 11.1: Comparing the two “returns”

Figure 11.3: Cobb-Douglas production function with increasing returns to scale

75

12 Costs (many variable inputs)

12.1 Short-runRecall the cost curves in the short-run. Finding the cost function was easy, we hadto invert the production function. The law of diminishing marginal returns impliesincreasing MC and AC.

12.2 Long-runThe question is: given q, what should the composition of K and L be, so thatCost = rK + wL is minimal?Isocost line - all combinations of inputs that are equally expensive: Cost = rK +

wL. Can be written as K = Cost/r − (w/r)L. This is a line with vertical interceptCost/r and slope − (w/r).Optimality condition. Let us superimpose isocosts on isoquants (Figure 12.1).

Given isoquant q let’s minimize cost. Point A is clearly not optimal because q unitscan be delivered cheaper, by employing more capital and less labor. Point B isoptimal. Tangency, where the slope of an isoquant equals to the slope of an isocost,or MRTSKL = −w/r, or MPK/r = MPL/w.Figure 12.2 shows graphically how the cost function emerges from the production

function.Example continued

L

K

Given q

Lower cost

L(q)

K(q) A

B

Figure 12.1: Optimality in the long-run

77


�

L

K

C(q3)/r

q3

q2

q1

C(q2)/r

C(q1)/r

Expansion path (correct composition of capital and labour)

q1 q2 q3

C(q1)

C(q2)

C(q3)

Cost function

q

Figure 12.2: Cost minimization and the cost function

1. Now the production function has both capital and labor variable, q =√K√L.

Believe it or not, but the MPK =√L/2√K and MPL =

√K/2√L. This

means that theMRTS for this production function is −K/L. Hence, the aboveoptimality condition gives us K/L = w/r, describing the correct compositionof factors of production (the expansion path).

2. To get optimal employment K (q) and L (q), one has to solve the system of twoequations (isoquant and tangency condition) with two unknowns (L and K).This solution is L (q) = q

√r/w and K (q) = q

√w/r.

3. To get the cost function just check how much the above solution costs C (q) =rK (q) + wL (q); we obtain C (q) = (2

√rw) q. Recall that w = 2 and r = 800,

so that C (q) = 80q.

12.2.1 Short-run and long-run comparisonLet K̄ be the optimal capital for output q∗, and let this K̄ be fixed in the short-run.Notation: put K̄ in the subscript to indicate that this is the short-run for this levelof capital; add SR or LR to make clear which cost is which.Observation 1: Average Costs, LRAC (q∗) = SRACK̄ (q∗) and LRAC (q) ≤ SRACK̄ (q).

Observation 2: Marginal Costs, LRMC (q∗) = SRMCK̄ (q∗) and LRMC (q) is flatteraround q∗ than SRMCK̄ (q) .

12.2.2 Economies of scaleAs we said before, SRAC is ultimately increasing, by law of diminishing marginalreturns to a variable input. But in the long-run, all input can change, so there are no

78

12.2 Long-run

�

L

K q2 q* q1

q1 q* q2

SRAC

LRAC

LR path

SR path K

SRMC

LRMC

Figure 12.3: Short-run and long-run cost curves

a priori reasons for LRAC to be increasing. LRAC decreasing – economies of scale,LRAC increasing – diseconomies of scale, LRAC constant – no economies of scale.This concept is related to returns to scale (but not equivalent) – increasing returnsto scale in the production function imply economies of scale in the cost function, butare not implied by.

Summary:

Short-run: SRACK and SRMCK are upward sloping eventually (by law of diminish-ing marginal returns to a variable input, labor in this example). SubscriptK denotes level of capital that is fixed in “this” short-run – sometimescalled “scale of operations” or “plant size”. Figure 12.4 shows only threeexamples of short-run costs, for capital levels 1, 2 and 3. There are manymore in between.

Long-run: LRAC may slope upward, downward, be constant, or change its slope.However, U-shaped LRAC is typical for competitive firms. The minimumquantity at which LRAC reaches its minimum is called the Minimum Ef-ficient Scale, MES, or full capacity.

79


�

Firm’s output

LRAC £

SRMC1 SRMC3

SRMC2

SRAC1

SRAC2

SRAC3

U-shaped LRAC

Economies of scale Diseconomies of scale MES

Figure 12.4: Cost curves

12.3 Equilibrium conditions revisited

All the previous equilibrium conditions hold, but there are new ones. In the sort-run,for some fixed K, it is possible to have LRAC < SRACK . But in the long-run,we must also have LRAC = SRACK , for if not, the firm would adjust K to reacha lower average cost. Likewise, at the equilibrium price p = LRMC = SRMCK .Observation 2 now leads to an important implication: individual supply curve of thefirm is flatter in the long-run.

80

12.3 Equilibrium conditions revisited

pe

qe

LRAC

SRMCK

SRACK

LRMC

Figure 12.5: Long-run equilibrium (with restricted entry)

81

Documents

Microeconomics Lecture Notes 2014