Geometrically this implies that the two indifference

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Unformatted text preview: XB OB ICB ICA OA YB XA Now, there are a set of points in the CORE that give rise to a final Pareto Optimal allocation. The core is the set of Pareto Optimal points between the original indifference curve positionings. We may eventually arrive at a Pareto Optimal allocation where the indifference curves are tangent to one another... YA XB Price Ratio OB Pareto Optimal solution ICB OA ICA YB XA 160 All right, but how do we get this tangency condition in terms of the slopes of the indifference curves? The tangency condition of the two indifference curves implies that they must have the same slopes, and hence, the same marginal rates of substitution. Indifference Curve of is tangent to Consumer A Consumer B Indifference Curve of Slope of Indifference Curve = of Consumer A Slope of Indifference Curve of Consumer B Simply means that: MRSA = MRSB Now, we can finally rephrase our allocation problem in terms of the basic concept of marginal rates of substitution as follows: To find a point in the Edgeworth Box such that MRSA = MRSB Is this going to give us a unique allocation? In other words, is there only one Pareto Optimal allocation? Not necessarily! There may be more than one Pareto Optimal allocation in the Edgeworth Box. That is, it is possible (indeed, likely) that there are several pairs of indifference curves tangent to each other at various points. In this case, the curve that connects all of these Pareto Optimal points is called a contract curve. 161 YA XB ICB1 Price Ratio Pareto Optimal solution OB Pareto Optimal solution ICA1 Price Ratio ICA2 ICB2 OA Y B XA So the curve connecting the origins and all points of tangency between the two families of indifference curves is the Contract Curve. CONTRACT CURVE How do we derive the contract curve? Let's suppose that consumer A and consumer B have utility functions that are both Cobb-Douglas form as follows: UA = XAYA1- MRSA = __YA__ (1-) XA UB = XBYB1- MRSB = __YB__ (1-) XB And we know that the Pareto Optimal allocations must sa...
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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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