Homework_10_sol

# Homework_10_sol - Homework 10_solution 1. Sheila is endowed...

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Homework 10_solution 1. Sheila is endowed with 15 jars of peanut butter (x) and 8 jars of jelly (y) and Bruce is endowed with 9 jars of peanut butter and 10 jars of jelly. Sheila's utility function is U S (x,y) = x S y S and Bruce's is U B (x,y) = x B y B . a) What are Bruce and Sheila’s marginal rates of substitution at the endowment point? In the Edgeworth box diagram on the next page illustrate the endowment point and draw a sample set of indifference curves through the endowment point. Is the endowment Pareto efficient? Why or why not? Since MRS is both y/x for Bruce and Sheila Bruce’s MRS=10/9 Shelia’s MRS=8/15 Since Bruce MRS and Shelia’s MRS doesn’t coincide the initial endowment is not Pareto efficient. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? What will be the range of the terms of trade that are associated with mutually beneficial trade? Since Shelia value y more than Bruce at the initial endowment the pattern of mutually beneficial trade will be Shelia gives Bruce x good Shelia gets y in return The range of the terms of trade will be between the two initial MRS that is smaller than 10/9 and bigger than 8/15 c) Provide an example of one trade that would make both Sheila and Bruce strictly better off. You

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2 S S S y MRS x = = at (8, 16), 2 2 22 BB B B yy MRS xy x = = at (4, 16) Since the MRS of Sheila and Bruce are the same at the endowment bundle, it is a Pareto efficient allocation.

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## This note was uploaded on 02/10/2010 for the course IEOR 3600 taught by Professor Chudnovsky during the Winter '09 term at Columbia.

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Homework_10_sol - Homework 10_solution 1. Sheila is endowed...

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