1General Equilibrium and Market EfficiencyPlan• Pure exchange economies– Definition of a Pareto Efficient allocation– Competitive equilibrium allocation– First Welfare Theorem– Second Welfare TheoremPareto Efficiency• An allocation of goods in an economy is Pareto efficient if there is no other allocation that will make at least one individual in the economy better off without worsening the well-being of the others.• There may be several Pareto efficient allocations of goods.The Big Questions• Will free markets allocate goods efficiently?– It depends on production technology and preferences– 1stWelfare Theorem• Can distributional equity and economic efficiency issues be separated?– The answer again, depends on technology and preferences– 2ndWelfare TheoremA simple exchange economy• Imagine an economy with two consumers, Elizabeth and Geoffrey• They consume two goods, apples and raspberries• Suppose that total quantities of raspberries and apples are fixed in the economy• Each one of the consumers has an endowment of apples an raspberries.• Let Elizabeth and Geoffrey trade. Will the resulting allocation be Pareto Efficient?The Edgeworth Box2Conditions determining Pareto Efficient Allocation• Assume that Elizabeth’s and Geoffrey’s preferences are (strictly) monotonic and convex• Then in a Pareto optimal allocation the marginal rates of substitution between the two goods (apples and raspberries) of Elizabeth and Geoffrey 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 optimalContact Curve• Contract Curve is a set of all Pareto efficient allocations• It also describes all allocations that may result from a voluntary contracts between rational informed economic agents.100;100;;Example=+=+==BEBEBBBEEERRAAARMRSARMRSDescribe the contract curveUtility-Improving TradesThe Contract Curve and the CoreA core is the set of allocations that can not be improved upon by any agent acting alone or by any group of agents acting together.Competitive Equilibrium Allocation• Consider a Walrasian Auctioneer who announces prices for apples and raspberries in the economy.• Both agents behave as price-takers.• Once the prices are announced, Elizabeth and Geoffrey announce their supply (amount they will sell) and demand (amount they will buy) of apples and raspberries.• The procedure continues till the markets for apples and raspberries clear (supply for each good equals to the demand)Competitive Behavior: Geoffrey3Competitive Behavior: ElizabethElizabeth and Geoffrey’s Market Game• Assume that Elizabeth’s and Geoffrey’s MRS between apples and raspberries are as follows• Assume that Elizabeth initially holds 50 units of raspberries and 80 units of apples• Geoffrey’s endowment is 50 units of raspberries and 20 units of apples• What are the market clearing prices that will be announced by the auctioneer?;;BBBEEEARMRSARMRS ==What did we learn?• Only the ratio of prices matter– if prices are doubled or tripled, the markets still clear, as the budget constraints of neither Geoffrey nor Elizabeth will change• The resulting allocation lies on the Contract curve.– This means it is Pareto efficient.– Is it a coincidence?First Welfare Theorem• If – consumers act as price takers;– there is a market for every commodity;– all the commodities are rival and excludable;– consumers’ preferences are “well-behaved”• Then a market allocation is Pareto Efficient• Next three slides contain a sketch of a proof.Efficiency Condition for the Exchange Economy• Marginal Rate of Substitution between the Goods of Elizabeth should equal to that of Geoffrey()( )GEGEGEGEGGGAAERRAARRRRAAAAURAUtsRAUGEGE0000,,,,..,max+=++=+=Market Equilibrium AllocationSatisfies the Efficiency CriterionMarginal rate of transformation of agent i(Elizabeth or Geoffrey) is equal to the ratio of prices()iriairiaiiiFCRpApRpAptsRAUii00,..,max+=+4Exchange Economy is Efficient• Marginal rate of substitution of Elizabeth is equal to the ratio of prices• The same is true for the marginal rate of substitution of Geoffrey• Thus, the marginal rates of substitution of Elizabeth and Geoffrey are equal to each other, which means that the equilibrium allocation is