191hw6-09

# 191hw6-09 - Econ 191 Spring 2009 Francis Lui Problem Set 6...

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1 Econ 191 Spring 2009 Francis Lui Problem Set 6 Due Date: Tuesday, May 12, 2009, 12:01 pm. (This is a challenging homework.) 1) (Second Fundamental Theorem of Welfare Economics.) Let there be two persons, A and B, in a pure exchange economy. A is endowed with 60 units of good X and 0 units of good Y. B is endowed with 60 units of good X and 80 units of good Y. The utility function of A is U(A) = xy, where x is A’s consumption of good X, and y is his consumption of good Y. B’s consumption of good X and good Y must be 120 – x and 80 – y, respectively. Person B’s utility function is U(B) = x*y*, where x* is B’s consumption of good X and y* is his consumption of good Y. Note that x*y* = ln(120-x) + ln(80-y). (a) Draw an Edgeworth Box for this economy. Locate the endowment point in the Edgeworth Box. (b) Find an expression for the slope of the indifference curves of A, i.e., dy/dx when dU(A) = 0. (c) Find an expression for the slope of the indifference curves of B, i.e., dy*/dx* when dU(B) = 0. (d) Find an expression for the Contract Curve, i.e., the relationship between x and

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## This note was uploaded on 10/11/2009 for the course ECON 191 taught by Professor Chen during the Spring '08 term at HKUST.

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191hw6-09 - Econ 191 Spring 2009 Francis Lui Problem Set 6...

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