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) = F 1/3 C 2/3 . Roy has the utility function V (F, C) = F 2/3 C 1/3 . 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 efcient allocation of F and C between the two con sumers? Explain briefy. (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? (d) What is the allocation of F and C between the two consumers 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) = F 1/3 C 2/3 . Roy has the utility function V (F, C) = F 2/3 C 1/3 . 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 efcient allocation of F and C between the two con sumers? Explain briefy. (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? (d) What is the allocation of F and C between the two consumers in a competitive equilibrium?
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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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) = F 1/3 C 2/3 . Roy has the utility function V (F, C) = F 2/3 C 1/3 . 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 efcient allocation of F and C between the two con sumers? Explain briefy. (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? (d) What is the allocation of F and C between the two consumers in a competitive equilibrium?
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