Consider an economy with a single consumer whose preferences are given by U = log(x) - , where x is consumption and labor supply. Assume that the consumption good is produced using labor alone with a constant-returns-to-scale technology. Units of measurement are chosen so that the producer prices of both the consumption good and the wage rate are equal to 1. a. Let the consumer’s budget constraint be qx = , where the consumer price is q = 1 + t, and t is the commodity tax. By maximizing utility, find the demand function and the labor supply function. b. Assume the revenue requirement of the government is 1 10 of a unit of labor. Draw the production possibilities for the economy and the consumer’s offer curve. c. By using the offer curve and the production possibilities, show that the optimal allocation with commodity taxation has x = 9/10 and = 1. d. Calculate the optimal commodity tax. e. By deriving the first-best allocation, show that the commodity tax optimum is second-best.
Consider an economy with a single consumer whose preferences are given by U = log(x) - , where x is consumption and labor supply. Assume that the consumption good is produced using labor alone with a constant-returns-to-scale technology. Units of measurement are chosen so that the producer prices of both the consumption good and the wage rate are equal to 1. a. Let the consumer’s budget constraint be qx = , where the consumer price is q = 1 + t, and t is the commodity tax. By maximizing utility, find the demand function and the labor supply function. b. Assume the revenue requirement of the government is 1 10 of a unit of labor. Draw the production possibilities for the economy and the consumer’s offer curve. c. By using the offer curve and the production possibilities, show that the optimal allocation with commodity taxation has x = 9/10 and = 1. d. Calculate the optimal commodity tax. e. By deriving the first-best allocation, show that the commodity tax optimum is second-best.
Chapter1: Making Economics Decisions
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Consider an economy with a single consumer whose preferences are given by U = log(x) -
, where x is consumption and labor supply. Assume that the consumption good is produced using labor alone with a constant-returns-to-scale technology. Units of measurement are chosen so that the producer prices of both the consumption good and the wage rate are equal to 1.
a. Let the consumer’s budget constraint be qx = , where the consumer price is q = 1 + t, and t is the commodity tax. By maximizing utility, find the demand function and the labor supply function.
b. Assume the revenue requirement of the government is 1 10 of a unit of labor. Draw the production possibilities for the economy and the consumer’s offer curve.
c. By using the offer curve and the production possibilities, show that the optimal allocation with commodity = 1.
d. Calculate the optimal commodity tax.
e. By deriving the first-best allocation, show that the commodity tax optimum is second-best.
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