1. Consider a pure exchange economy with two goods and two consumers. Let F denote food and C denote clothing. Lacy has the utility function U(F, C) = F¹/³C2/3. Roy has the utility function V(F, C) = F2/3¹/3. Each consumer has an initial endowment consisting of 9 units of F and 9 units of C. Normalize the price of F to one. Let P denote the price of C. (a) Is the initial endowment a Pareto efficient allocation of F and C between the two con- sumers? Explain briefly. (b) What is each consumer's demand for F and C as a function of P? [Hint: the wealth of each consumer is 9 + 9P.] (c) What is the price of C in a competitive equilibrium?

1. Consider a pure exchange economy with two goods and two consumers. Let F denote food and C denote clothing. Lacy has the utility function U(F, C) = F¹/³C2/3. Roy has the utility function V(F, C) = F2/3¹/3. Each consumer has an initial endowment consisting of 9 units of F and 9 units of C. Normalize the price of F to one. Let P denote the price of C. (a) Is the initial endowment a Pareto efficient allocation of F and C between the two con- sumers? Explain briefly. (b) What is each consumer's demand for F and C as a function of P? [Hint: the wealth of each consumer is 9 + 9P.] (c) What is the price of C in a competitive equilibrium?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.5P

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