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Marginal Rates of Substitution Apples Sally Bananas Bananas More on The Edgeworth Box Apples Sally When they are on the contract curve, MRSSAB = MRSHAB Harry Harry Lectures in Microeconomics-Charles W. Upton Marginal Rates of Substitution Apples Sally Two Qualifications • Consumer Sovereignty Bananas When they are on If not, trading is the contract curve, possible. MRSSAB = MRSHAB Suppose MRSSAB = 4 MRSHAB= 3 More on the Edgeworth Box Then trade Harry More on the Edgeworth Box Two Qualifications • Consumer Sovereignty – Are we comfortable with welfare checks being spend on drugs and alcohol? – Do we think children know what is best for them? More on the Edgeworth Box More on the Edgeworth Box Two Qualifications • Consumer Sovereignty • Do we have anything to say about the right point on the contract curve? More on the Edgeworth Box 1 The Utility Possibility Frontier The Utility Possibility Frontier Harry’s Utility Harry’s Utility We construct the Utility Possibility Frontier by reading off the different levels of utility from the Contract Curve Sally’s Utility More on the Edgeworth Box Simply another way of stating the We construct the contract curve Utility Possibility Frontier by reading off the different levels of utility from the Contract Curve Sally’s Utility More on the Edgeworth Box The Utility Possibility Frontier The Utility Possibility Frontier Harry’s Utility Harry’s Utility Simply another way If we had social of stating the We construct the indifference curves for contract curve Utility Possibility the various Frontier by combinations of utility, reading off the we coulddifferent find thelevels best of point along the the utility from Contract contract curveCurve Sally’s Utility More on the Edgeworth Box Sally’s Utility More on the Edgeworth Box The Core and Markets The Core and Markets • The yellow area is the core. Apples Sally More on the Edgeworth Box Apples Sally Bananas Bananas Harry • The yellow area is the core. • If only Harry and Sally are involved, they will sit down and simply haggle with each other. Harry More on the Edgeworth Box 2 The Core Apples Sally More on the Edgeworth Box The Core Apples Sally More on the Edgeworth Box The Core Apples Sally Bananas We tell Harry that he can buy and sell apples and bananas at prices (1,pb). The only constraint is that (aXH- aH) + pb(bXH- bH) = 0 Harry More on the Edgeworth Box More on the Edgeworth Box Apples Sally The normal laws of supply and demand will work and will tell us exactly where we will end up Suppose that Harry and Sally start out with (aXH,bXH) and (aXS,bXS). Harry More on the Edgeworth Box Bananas Harry Sally The Core Bananas The normal laws of supply and demand will work and will tell us exactly where we will end up Apples Suppose there are hundreds of Harry's and If only Harry Sallies? and Sally are involved, they will sit down and simply haggle with each other. Harry Bananas Bananas If only Harry and Sally are involved, they will sit down and simply haggle with each other. Harry The Core Markets (aXH- aH) + pb(bXH- bH) = 0 Revenue from Apples Purchases of Bananas More on the Edgeworth Box 3 The Core Apples Harry Z Bananas If Harry’s budget line is the dotted line, he will want to move to Z Sally More on the Edgeworth Box Markets • If Sally is told that she can buy and sell apples and bananas subject to a budget constraint (aXS- aS) + pb(bXS- bS) = 0 she will be willing to buy and sell. • However the price that persuaded Harry to move to Z, might or might not move her to Z. More on the Edgeworth Box The Fundamental Theorem For any starting point there is a price pb which will lead both Harry and Sally to move to That is,the theresame is a price that on the point equates supply and demand. It contract puts Harry and Sally oncurve. the Markets • If Sally is told that she can buy and sell apples and bananas subject to a budget constraint (aXS- aS) + pb(bXS- bS) = 0 she will be willing to buy and sell. More on the Edgeworth Box The Fundamental Theorem For any starting point there is a price pb which will lead both Harry and Sally to move to the same point on the contract curve. More on the Edgeworth Box Summary •Normal trading gets Pareto Optimality in distribution. MRS(Harry ) = MRS(Sally) •More to Come contract curve More on the Edgeworth Box More on the Edgeworth Box 4 End ©2006 Charles W. Upton More on the Edgeworth Box 5
