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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must write your trade in the table below. Illustrate that trade in your Edgeworth box diagram. Sheila give Bruce 0.5 butter in return of 0.5 jelly and vice versa Sheila before trade utility 120 after trade 123.5 Bruce before trade utility 90 after trade 90.25 d) The utilitarian criterion would select the allocation that maximizes the product of the utilities of Bruce and Sheila. In this economy with this endowment and preferences the utilitarian criterion would select the equal split of (12,9) for each. Show that this allocation can NOT be achieved by mutually beneficial trade between Bruce and Sheila. To achieve equal split Shelia has to give 3 butter in return to 1 jelly and vice versa. Thus the term of trade will be 1/3 which is not in the range of mutually beneficial trade 2. Sheila is endowed with 8 pounds of coffee (x-good) and 16 quarts of milk (y-good) and Bruce is endowed with 4 pounds of coffee and 16 quarts of milk. We can represent Sheila’s and Bruce’s preferences over coffee (x) and milk (y) by the following utility functions: U S = x S y S and U B = x B y B 2 a) Draw an Edgeworth box diagram illustrating the feasible allocations for this 2 person, 2 good exchange economy. Include the endowment point in your diagram. Answer: b) Is the endowment a Pareto efficient allocation? Illustrate a pair of indifference curves (one for Sheila and one for Bruce) through the endowment point in your diagram in part (a). Answer: Sheila Bruce (8, 16) (4, 16) 32 quarts of milk 12 pounds of coffee
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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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