ECO2011 Intermediate Microeconomic Theory
Lecture Outline
P. W. Liu
ON METHODOLOGY
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What is scientific method?
Rationalism
 Descartes
 Deduction
Empiricism
 Bacon
 Induction
Humean Position
 Hume
 Berkeley
Poper's Logical Positivism
 Humean position is asymmetrical.
 The purpose of science is to reject hypotheses.
Fredman's Positive Economics
 Difference between positive science and normative science
 Structure of positive economics
 Hypotheses must have predictions.
 Hypotheses are tested by their predictions.
 Hypotheses cannot be proved. They are either rejected or not rejected.
 Assumptions
 Assumptions are used to abstract from the complexity of reality
 Assumptions are not correct descriptions of reality.
 Hypotheses should not be tested on the basis of whether their assumptions are "realistic".
THEORY OF PREFERENCE
Preference
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Preference is the primitive concept
Four axions of preference
A1: Complete ordering
A2: Weak monotonicity
A3: Local non-satiation
A4: Closure
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Utility Function
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Based on A1 to A4, we can prove the existence of utility function
Utility function is a map of bundles in commodity space into real numbers
Utility function is unique up to monotonic transformation
Utility function is ordinal. It does not have to be cardinal
Quasi-concavity of utility function
Constrained Maximization
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A consumer choosing a bundle he/she prefers most is equivalent to choosing a bundle that
gives the largest utility.
Consumer problem becomes a maximization (of utility) problem under income constraint.
A constrained maximization problem with linear constraints is a classical linear
programming which can be solved by applying the Lagrangian Theorem.
The Lagrangian multiplier represents the marginal change in the maximized objective
function when the constrained constant is marginally relaxed.
Demand Function
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A Marshallian demand function x = x ( p , y) is derived from solving the consumer
problem
Demand curve is obtained from the Marshallian demand function when income and other
prices are held constant in the demand function
Monotonic transform of a given utility function does not alter the derived demand function.
Corner Solution vs Interior Soulation
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Corner solution arises when xi = o
There are goods consumers do not buy because their relative price is higher than the
marginal rate of transformation.
Properties of Marshallian Demand Function
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The demand function shows the effect on the quantity demand when
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prices and income change by the same proportion;
only income changes;
own price changes; and
other prices change.
Homogeneity of Demand Function
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Demand function is homogeneous of degree zero with respect to prices and income
when prices and income change by the same proportion, the quantity demand is not
affected
Homogeneous function satisfy the Euler’s Theorem
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Adding-up Property of Demand Function
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The weighted income elasticity of demand of all goods equals 1
Luxury vs necessity
Superior vs normal vs inferior goods
Negative Substitution Effect of Demand Function
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The concept of income compensation
Hicks’ compensation vs Slutsky’s compensation
Gross price effect as a sum of substitution effect (compensated effect) and income effect
(effect of taking away compensation)
Hicks-Slutsky equation
Marshallian demand curve vs Hicks’ demand curve vs Slutsky’s demand curve
Symmetrical Cross – Substitution Effect
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Concepts gross substitutes and complements
Concepts of Hicks-Allen substitutes and complements
Every good must have at least one Hicks-Allen substitute
Expenditure Function
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The minimum expenditure necessary for a consumer to achieve a specified level of
utility
Primal problem – consumer maximizes utility subject to cost (budget constraint)
Dual problem – consumer minimizes cost subject to a utility constraint
Expenditure function can be derived from solving the dual problem
The primal problem can be solved to get indirect utility which can be inverted to give
the expenditure function
Indirect utility is the maximum utility attainable at given prices and income
Expenditure function and indirect utility function are dual to each other
Use Shephard’s Lemma and Young’s Theorem to prove symmetry of cross
substitution effect.
Consumer Welfare Measures
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A consumer’s welfare is his utility
Even though utility is not directly measureable we can measure a consumer’s utility
(welfare) change indirectly by his monetary valuation of the change
Three common measures of consumer welfare
- consumer surplus (CS)
- compensating vairation (CV)
- equivalent variation (EV)
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Consumer Surplus (CS)
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CS is the difference between the maximum a consumer would be willing to pay (for a
consumption or in general any economic change) and the amount he actually pays
For a normal (inferior) good the Marshallian demand curve overestimates (underestimates)
CS.
To measure CS correctly, we have to use Hick’s demand curve.
Compensation Variation (CV)
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CV is the amount of money we can take away from an individual after an economic change,
while leaving him as well off as he was before it
For a welfare gain, it is the amount he would be willing to pay for the change
For a welfare loss, it is minus the amount he would need to receive as compensation for the
change.
CV assumes a move from state 0 to state 1 (the economic change) and asks what money
should be withdrawn from the individual to restore his utility level to that at state 0.
Equivalent Variation (EV)
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EV is the amount of money we would need to give an individual if an economic change did
not happen, to make him as well off as it did happen.
For a welfare gain, it is the compensation he would need to forego the change.
For a welfare loss, it is minus the amount he would be willing to pay to avert the change.
EV assumes no move from state 0 to state 1 (the economic change) and asks what money
should be given to the individual to shift his utility to that at state 1.
Revealed Preference
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Demand is the primitive concept and preference is derived to be consistent with demand
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Definition of revealed preference
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Weak Axiom of Revealed Preference (WARP)
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Strong Axiom of Revealed Preference (SARP)
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Application
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Derive negative Slutsky substitution effect without using utility function or indifference
curves
- Changes in standard of living when prices change
Price Indices
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Cost of living versus standard of living
Definition of Laspeyres index and Paasche index
Laspeyres index overestimates cost of living increases
Passche index underestimates cost of living increases
Use revealed preference to determine standard of living changes
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THEORY OF FIRM
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Specialization leads to increasing returns
Nature of classical firms
- owner / entrepreneur
- contract for services
- residual income
- transferable property right
Why has the firm become the dominant form of organization for production?
- transaction cost
Why has other forms of organization such as producer co-operatives not become dominant?
- Free-rider problem
Objective of classical firms
- profit maximization
- other social objectives
- separation of ownership and management giving rise to other management
objectives
THEORY OF PRODUCTION
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Two decisions of firms
1. Choose optimal output level
2. At that output level, choose optimal combination of inputs
Production function
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Examples: Cobb-Douglas, Constant elasticity of substitution function (CES)
Quasi-concave
Diminishing marginal rate o f technical substitution (MRTS)
Elasticity of substitution
Special property of production function: homogeneity
MRTS of homogeneous production function depends only on factor ratio (K/L)
Short Run Profit Maximization
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There is a fixed factor (input) in short run
Value of marginal product = factor price of variable input
Comparative statics showing factor demand curve is downward-sloping and supply curve
of output is upward-sloping
Long Run Analysis
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Returns to scale: increasing, constant and decreasing
Elasticity of scale
Examples of increasing returns to scale
Homogeneity and returns to scale
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Long Run profit Maximization
 Maximizing profit under cost constraint
 Maximizing profit under output constraint
 Maximizing profit with no constraint on cost or output
 First-order conditions of the above 3 maximization problems are identical
Revealed Profitability
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Concept of revealed profitability
Weak Axion of Profit Maximization (WAPM)
Comparative statics
Derive production function using WAPM
THEORY OF COST
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Cost function is a derived function
Long run cost minimization problem
Derive input demand function and cost function
Properties of cost function and analogy to expenditure function in consumer demand theory.
Example of cost function
Elasticity of cost
Economies and diseconomies of scale and their relation to returns to scale
Cost curves
PERFECT COMPETITION
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Firm’s choice of optimal output in a perfectly competitive market
Definition of perfect competition
Short Run Supply Curve
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Maximization condition: p = MC
Second-order condition
Inframarginal firm
Nature of profit
Diseconomies of scale
Economies of scale
Long Run Supply Curve
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Constant cost industry
Increasing cost industry
Decreasing cost industry
MONOPOLY
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Definition of monopoly
Maximization condition: MR = MC
Why can monopolies exist?
Measurement of monopoly power
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Characteristics of Monopoly
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No supply curve
Non-optimal scale of production
Social welfare loss – inefficiency
Price discrimination
 Third degree
 First degree
Taxing monopolies
 Lump sum tax
 Profit tax
 Excise tax
 Can we reform a monopolist by a combination of tax and subsidy?
Multiplant monopoly
Regulating monopolies
 Rate of return regulation
 Price cap regulation
OLIGOPOLY
 Definition
 Non-cooperative vs co-operative oligopolies
Non-Co-operative Oligopoly
 Cournot model
 Quantity competition
- Cournot-Nash equilibrium
 Chamberlin model
 Stackelberg model
- First mover advantage
 Bertrand model
- Price compeition
Co-operative Oligopoly
 Cartels
(1) Joint profit maximizing cartel
(2) Market-sharing cartel
 Non-price competition
- Clusilers
 Quota
- Free-riders
 Price leadership models
(1) Low cost leader
(2) Dominant firm leader
Limit Pricing
 Barrier to entry
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FACTOR DEMAND AND SUPPLY
Demand for Labour
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Factor demand as derived demand
Competitive product and labour market as labour as the only input
- Value of marginal product curve is the labour demand curve of firm
Two variable inputs case
Example: Derive labour demand function from production function
Supply of Labour
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Supply of labour derived from demand for leisure
Substitution effect and income effect
Backward-bending labour supply curve
- Examples
GENERAL EQUILIBRIUM
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General versus partial equilibrium
Exchange Economy
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Endowment
Definition of excess demand
Definition of equilibrium
Edgenorth box with offer curves
Proposition 1: Homogeneity
Proposition 2: Waltas Law
- Market clearing equations
Lemma: goods with excess supply are free
Existence Theorem (Arrow – Debreu)
Uniqueness of general equilibrium
Example of computing a general equilibrium
Tatonnement process
Optimality of General Equilibrium
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Definition of Pareto efficiency (optimality)
- An allocation is Pareto efficient (optimal) if there is no other
feasible allocation where everyone is at least as well off and
at least one agent is strictly better off.
Pareto efficiency frontier
Conditions for Pareto efficiency
First Theorem of Welfare Economics
Second Theorem of Welfare Economics
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Production Economy
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Existence of competitive equilibrium
Conditions of Pareto Efficiency
- consumption efficiency
- production efficiency
- product mix efficiency
Competitive market and efficiency
MARKET FAILURE
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Conditions of market failure
- Increasing returns to scale
- Uncertainty
- Technological external effects
Classes of externalities
- consumption – consumption
- production – consumption
- production – production
Private vs. social marginal cost
Pigouvian tax as a correction to externalities
Problem of taxing polluters for the social damage done
Example
Coase Theorem
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If costless negotiation is possible, rights are well-specified and redistribution does not
affect marginal values, then
1. the allocation of resources will be identical, whatever the allocation of legal rights,
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2. the allocation will be efficient, so there is no problem of externality
Competitive solution vs socially optimal solution
Irrelevance of property rights as long as they are well defined
Problem of Coase Theorem
Cost of bargaining
Free riding
SOCIAL CHOICE THEORY
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Competition insures efficiency but not equity
Criteria for choosing among efficient allocations are normative
Equality criterion
Utilitarian criterion
Rawlsian criterion
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Social Welfare Function
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Social optimum (bliss point)
Tradeoff between efficiency and equity
Theorem: The socially optimal allocation is Pareto efficient
Since the social optimum is Pareto efficient and any Pareto efficient allocation can be
decentralized as a competitive equilibrium, perfect competition can achieve the social
optimum if factors can be redistributed.
Arrow’s Impossibility Theorem
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Does social welfare function exist?
Are there university accepted moral principles of fairness and justice?
Can we construct social preferences only on the basis of individual preferences which can
be very diverse?
Arrow’s Impossibility Theorem – No rule exists which would satisfy the six criteria and
produce social preference based solely on individual preferences
Condorset paradox of voting
THEORY OF UNCERTAINTY
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Defining a lottery
Four axioms
A1 Complete ordering
A2 Continuity
A3 Ultimate prize
A4 Strong independence
Existence Theorem
Von Neumann Morgenstern utility function and expected utility
Uniqueness – von Neumann Morgenstern utility function is unique up to affine
transformation
Theory of Risk
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Risk aversion
Risk neutrality
Risk loving
Arrow-Pratt measure of absolute risk aversion
Cost of risk (risk premium)
Certainty equivalent
Risk pooling
Law of large numbers
Risk spreading
joint stock companies
Arrow-Lind Theorem on public projects
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