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ECO2011 Intermediate Microeconomic Theory Lecture Outline P. W. Liu ON METHODOLOGY 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 • Preference is the primitive concept • Four axions of preference • A1: Complete ordering • A2: Weak monotonicity • A3: Local non-satiation • A4: Closure 1 Utility Function • 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 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 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 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 The demand function shows the effect on the quantity demand when 1. prices and income change by the same proportion; 2. only income changes; 3. own price changes; and 4. other prices change. Homogeneity of Demand Function 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 2 Adding-up Property of Demand Function 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 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 Concepts gross substitutes and complements Concepts of Hicks-Allen substitutes and complements Every good must have at least one Hicks-Allen substitute Expenditure Function 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 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) 3 Consumer Surplus (CS) 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) 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) 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 Demand is the primitive concept and preference is derived to be consistent with demand Definition of revealed preference Weak Axiom of Revealed Preference (WARP) Strong Axiom of Revealed Preference (SARP) Application - Derive negative Slutsky substitution effect without using utility function or indifference curves - Changes in standard of living when prices change Price Indices 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 4 THEORY OF FIRM 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 Two decisions of firms 1. Choose optimal output level 2. At that output level, choose optimal combination of inputs Production function 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 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 Returns to scale: increasing, constant and decreasing Elasticity of scale Examples of increasing returns to scale Homogeneity and returns to scale 5 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 Concept of revealed profitability Weak Axion of Profit Maximization (WAPM) Comparative statics Derive production function using WAPM THEORY OF COST 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 Firm’s choice of optimal output in a perfectly competitive market Definition of perfect competition Short Run Supply Curve Maximization condition: p = MC Second-order condition Inframarginal firm Nature of profit Diseconomies of scale Economies of scale Long Run Supply Curve Constant cost industry Increasing cost industry Decreasing cost industry MONOPOLY Definition of monopoly Maximization condition: MR = MC Why can monopolies exist? Measurement of monopoly power 6 Characteristics of Monopoly 1. No supply curve 2. Non-optimal scale of production 3. Social welfare loss – inefficiency 4. Price discrimination Third degree First degree 5. Taxing monopolies Lump sum tax Profit tax Excise tax Can we reform a monopolist by a combination of tax and subsidy? 6. Multiplant monopoly 7. 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 7 FACTOR DEMAND AND SUPPLY Demand for Labour 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 Supply of labour derived from demand for leisure Substitution effect and income effect Backward-bending labour supply curve - Examples GENERAL EQUILIBRIUM General versus partial equilibrium Exchange Economy 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 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 8 Production Economy Existence of competitive equilibrium Conditions of Pareto Efficiency - consumption efficiency - production efficiency - product mix efficiency Competitive market and efficiency MARKET FAILURE 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 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, and 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 Competition insures efficiency but not equity Criteria for choosing among efficient allocations are normative - Equality criterion - Utilitarian criterion - Rawlsian criterion 9 Social Welfare Function 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 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 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 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 10

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