1General Equilibrium and General Equilibrium and Market EfficiencyMarket EfficiencyProduction EconomyProduction EconomyPlanPlan••Pure exchange economiesPure exchange economies––Definition of a Pareto Efficient allocationDefinition of a Pareto Efficient allocation––Competitive equilibrium allocationCompetitive equilibrium allocation––First Welfare TheoremFirst Welfare Theorem––Second Welfare TheoremSecond Welfare Theorem••Production EconomiesProduction Economies––Production Possibilities frontierProduction Possibilities frontier––Equilibrium AllocationEquilibrium Allocation––First Welfare TheoremFirst Welfare TheoremPareto EfficiencyPareto Efficiency••An allocation of goods in an economy is An allocation of goods in an economy is Pareto Pareto efficientefficientif there is no other allocation that will if there is no other allocation that will make at least one individual in the economy make at least one individual in the economy better off without worsening the wellbetter off without worsening the well--being of being of the others.the others.••There may be several Pareto efficient allocations There may be several Pareto efficient allocations of goods.of goods.The Big QuestionsThe Big Questions••Will free markets allocate goods efficiently?Will free markets allocate goods efficiently?––It depends on production technology and It depends on production technology and preferencespreferences––11ststWelfare TheoremWelfare Theorem••Can distributional equity and economic Can distributional equity and economic efficiency issues be separated?efficiency issues be separated?––The answer again, depends on technology and The answer again, depends on technology and preferencespreferences––22ndndWelfare TheoremWelfare TheoremA simple exchange economyA simple exchange economy••Imagine an economy with two consumers, Elizabeth Imagine an economy with two consumers, Elizabeth and Geoffreyand Geoffrey••They consume two goods, apples and raspberriesThey consume two goods, apples and raspberries••Suppose that total quantities of raspberries and apples Suppose that total quantities of raspberries and apples are fixed in the economyare fixed in the economy••Each one of the consumers has an endowment of Each one of the consumers has an endowment of apples an raspberries.apples an raspberries.••Let Elizabeth and Geoffrey trade. Will the resulting Let Elizabeth and Geoffrey trade. Will the resulting allocation be Pareto Efficient?allocation be Pareto Efficient?The The EdgeworthEdgeworthBoxBox2Conditions determining Pareto Conditions determining Pareto Efficient AllocationEfficient Allocation••Assume that Elizabeth’s and Assume that Elizabeth’s and Geoffrey’s preferences are Geoffrey’s preferences are (strictly) monotonic and convex(strictly) monotonic and convex••Then in a Pareto optimal Then in a Pareto optimal allocation the marginal rates of allocation the marginal rates of substitution between the two substitution between the two goods (apples and raspberries) goods (apples and raspberries) of Elizabeth and Geoffrey of Elizabeth and Geoffrey should be equal.should be equal.()()GGGAREEEARARMRSARMRS ,,,,=Assume E. is ready toexchange at most 5 units of raspberries for 1 unit of apples, but G’s MRS between raspberries and apples is 3Then a benevolent planner can offer to take 4 units of raspberries from E. and give it to G. in exchange for 1 unit of apples. Both will agree, as the will be happier under the new allocation. Thus, the initial allocation was not Pareto optimalUtilityUtility--Improving TradesImproving TradesContact CurveContact Curve••Contract Curve is a Contract Curve is a set of all Pareto set of all Pareto efficient allocationsefficient allocations••It also describes all It also describes all allocations that may allocations that may result from a result from a voluntary contracts voluntary contracts between rational between rational informed economic informed economic agents.agents.Contract Curve Contract Curve ••Contract Curve is a set of All Pareto efficient allocations.Contract Curve is a set of All Pareto efficient allocations.••Note it is independent of prices and of distribution of initial Note it is independent of prices and of distribution of initial endowments.endowments.• Describe the Contract Curve: use the condition determining Pareto efficient allocations (equality of the marginal rates of substitution) as well as the two resource constraint (describingtotal amounts of goods in the economy). Depict the contract Curve in the Edgeworth box.() ( )100;100;,;,Example\=+=+==GEGEGGGGGEEEEERRAAARARUARARUCompetitive Equilibrium Competitive Equilibrium AllocationAllocation••Consider a Consider a WalrasianWalrasianAuctioneer who announces prices Auctioneer who announces prices for apples and raspberries in the economy.for apples and raspberries in the economy.••Both agents behave as Both agents behave as priceprice--takerstakers..••Once the prices are announced, Elizabeth and Geoffrey Once the prices are announced, Elizabeth and Geoffrey announce their supply (amount they will sell) and announce their supply (amount they will sell) and demand (amount they will buy) of apples and demand (amount they will buy) of apples and raspberries.raspberries.••The procedure continues till the markets for apples and The procedure continues till the markets for apples and raspberries clear (supply for each good equals to the raspberries clear (supply for each good equals to the demand)demand)Competitive Behavior: GeoffreyCompetitive Behavior: Geoffrey3Competitive Behavior: ElizabethCompetitive Behavior: ElizabethElizabeth and Geoffrey are Price Elizabeth and Geoffrey are Price TakersTakers••Assume that Elizabeth’s and Geoffrey’s MRS Assume that Elizabeth’s and Geoffrey’s MRS between apples and raspberries are as followsbetween apples and raspberries are as follows••Assume that Elizabeth initially holds 50 units Assume that Elizabeth initially holds 50 units of raspberries and 80 units of applesof raspberries and 80 units of apples••Geoffrey’s endowment is 50 units of Geoffrey’s endowment is 50 units of raspberries and 20 units of applesraspberries and 20 units of apples••What are the market clearing prices that will What are the market clearing prices that will be announced by the auctioneer? Set price for be announced by the