we know that consumer a and consumer b have utility

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Unformatted text preview: hape of the contract curve. How do we do that? We compare the ______ and the ______ terms. (1 ) (1 ) 173 We know that ___1/2___ > ___1/4___ thus the indifference curve for A is 1/2 3/4 steeper than the indifference curve for B on the main diagonal, this leads to the slopes being equal below the main diagonal. In the reverse case, the opposite is true. YA XB OB ICA ICB OA Y B XA So now we can add the contract curve to our Edgeworth Box diagram that represents the Pareto Optimal competitive equilibrium solution to our example... 174 Y=1 ICA 2/7 OB Now we can see that from the main A diagonal, IC is steeper as it crosses the main diagonal than ICB is. This means that the Pareto Optimal set (contract curve) is bowed down from the main diagonal and connects the origins of the consumers. Very nice! Now we know that our solution is in the right range of the box to be on the contract curve (MRSA = B MRS ). This completes our Edgeworth Box representation of this example. Slope = -7/11 5/11 6/11 ICB OA 5/7 X=1 Now, what if there is a quasi-linear consumer? They don't have any wealth effects so wouldn't the Contract Curve look different if we had a quasi-linear agent? I'm very glad that someone asked me that!!!! PARETO OPTIMAL THEORY PURE EXCHANGE ECONOMY EXAMPLE: QUASI-LINEAR PREFERENCES Consider a simple pure exchange economy with two consumers, A and B, and two goods, X and Y. Consumer A has a Perfect Substitutes utility function defined by U(X,Y) = 5X +2Y while Consumer B has Quasi-linear preferences defined by U(X,Y) = 2X + 4Y1/2 . Each good is allocated between the two consumers according to the following endowment distribution: Consumer A Consumer B Total GOOD X XA = 12 XB = 3 X = 15 175 GOOD Y YA = 1 YB = 14 Y = 15 We want to solve for the general equilibrium price ratio, and report the equilibrium quantities of both goods demanded for each consumer. We also wish to draw the final Edgeworth Box diagram for this economy. UA = 5X + 2Y A = (XA , YA) = (12,1) We can figure out cons...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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