1Microeconomics: An Integrated ApproachDavid Besanko and Ronald BraeutigamChapter 16: General Equilibrium TheoryPrepared by Katharine Rockett© 2002 John Wiley & Sons, Inc.1. Why do General Equilibrium Analysis I? Partial Equilibrium Bias2. Efficiency and Perfect Competition3. Why do General Equilibrium Analysis II? General Equilibrium and the Efficiency of Competition•A tool: The Edgeworth Box•Analysis of Allocation: A Pure Exchange Economy•Analysis of ProductionIf there are spillover effects from one market to another, then the effects of a change in one market on the economy must be analyzed by examining its effect on allmarketsFurther, many exogenous events (or policy changes) affect many markets simultaneously (example: discovery of a major oil deposit that raises the income of all citizens in an economy and so affects equilibrium in all markets).If we do not take into account all markets in our equilibrium calculation, we induce a bias in our analysis.Definition: is the study of how equilibrium is determined in all markets simultaneously (e.g. product markets and labor markets).Definition: is the study of how equilibrium is determined in only a single market (e.g. a singleproduct market). Partial Equilibrium analysisGeneral Equilibrium analysisExample: Equilibrium in two marketsQ1D= 12 – 3p1+ p2Q1s= 2 + p1Q2D= 4 – 2p2+ p1Q2s= 1 + p2a. What is the general equilibrium level of prices and output in this economy?Market 1 equilibrium:Market 2 equilibrium:12 – 3p1+ p2= 2 + p1p1= 10/4 + p2/44 – 2p2+ p1= 1 + p2p2= 1 + p1/32Substituting condition 1 into condition 2:4 – 2p2+ 10/4 + p2/4 = 1 + p22 = p2e3 = p1eðQ1e= 5ðQ2e= 3Q1P1Market 14.6714Example: Equilibrium in Two MarketsQ1P12 P1= Q1s- 2Market 14.6714Example: Equilibrium in Two MarketsQ1P12 5 P1= Q1s- 2P1= 4 + P2/3 - Q1D/3•3e1Market 14.6714Example: Equilibrium in Two MarketsQ2P21P2= Q2s- 1Market 2Example: Equilibrium in Two MarketsQ2P21 11P2= Q2s- 1P2= 4 + P1/2 - Q2D/25.5Market 2Example: Equilibrium in Two Markets3Q2P21 11P2= Q2s- 1P2= 4 + P1/2 - Q2D/2•25.5e2Market 24Example: Equilibrium in Two MarketsSuppose an exogenous shock increases demand in market 1 to: Q1D= 22 – 3p1+ p2. What is the new general equilibrium?Market 1 equilibrium: p1= 22/4 + p2/4Market 2 equilibrium: p2= 1 + p1/3ð32/11 = p2eð63/11 = p1eðQ1e= 85/11Q2e= 43/11b. Suppose you used the partial equilibrium price and output level in market 2 in order to compute the market 1 equilibrium. What would be the bias in your conclusions for market 1?If we re-solve for market 1 price with the new demand but p2e = 2, we obtain p1e = 11/2 = 5.5…but in part (b), p1e= 63/11 = 5.72. In other words, we would underestimate the true price for good 1.Definition: An economic situation is Pareto Efficient if there is no way to make any person better off without hurting somebody else.Result 1"Production efficiency" : A perfectly competitive market produces a Pareto efficient amount of output…because the price at which someone is willing to buy an extra unit exactly equals the price that must be paid to induce someone else to sell an extra unit…or…Since price equals marginal cost at the competitive equilibrium, consumers value the last unit of output by exactly the amount that it costs to produce (in the sense of opportunity cost) so that no reallocation of consumption towards this good or away from this good could increase the valueobtained from resources in the economy.4•As long as Pi> MCi, the total size of the “economic pie” could be increased by increased consumption of good i since MRireflects the opportunity cost of producing i.•As long as Pi< MCi, the total size of the “economic pie” could be increased by decreased consumption of good i.Result 2 "Allocative efficiency": A competitive market allocates goods in a way that is Pareto efficient …because it equalizes the marginal rates of substitution across consumers.i.e., If all consumers are willing to trade goods at the same rate then it is not possible for any pair to get together and improve their joint utilities by reallocating goods…Summarizing…Perfect competition maximizes the sum of consumers’ surplus plus producers’ surplus (minimizes deadweight loss) and allocates that output in a Pareto Efficient way...•We know that consumers’ surplus is not the “ideal” measure of consumer benefit from consumption when there are income effects…but if income affects the placement of demand, have we calculated our measure of “efficiency” correctly? Where does “income” come from and does our result depend on the allocation of income across consumers?•Producers’ surplus measures producers’ benefits net of costs (i.e., costs affect the placement of supply)…but what determines these “opportunity costs”?•Our discussion has taken “income” and “costs” as, at least partially, given. But these come, in fact, from other markets (labor markets, for example). Further, these concepts are related.•If we wish to make a stronger statement about economic efficiency, we need to measure economic efficiency while allowing income and all costs to be endogenous.Simplifying Assumptions:1. Consumers and producers are price takers.2. There are only two individuals and two goods in the economy.3. Individuals have fixed allocations (endowments) of goods that they may trade. No production occurs for now.4. Consumers maximize utility with usually -shaped indifference curves(and nonsatiation). Utilities are not interdependent.5Good 1Good 2wB2wB1Good 2Good 1Person APerson BwA1wA2Example: An Edgeworth Box DiagramGood 1Good 2wB2wB1Good 2Good 1Person APerson BwA1wA2ICAExample: An Edgeworth Box DiagramGood 1Good 2wB2wB1Good 2Good 1Person APerson BwA1wA2ICAICBExample: An Edgeworth Box DiagramGood 1Good 2•EwB2wB1Good 2Good 1Person APerson BwA1wA2ICAICBExample: An Edgeworth Box DiagramIn an Edgeworth Box…1. The length of the side of the box measures the total amount of the good available.2. Person A’s consumption choices are measured from the lower left hand corner, Person B’s consumption choices are measured from the upper right hand corner.3. We can represent an initial endowment, (wA1,wA2), (wB1,wB2) as a point in the box. This is the allocation that consumers have before any
View Full Document