1. Consider the following static model. The consumer has preferences such that he always sets his consumption equal to è, where è is exogenously fixed. The consumer has h units of time that he can allocate between working hours (N*) and leisure (I). The wage per hour is w. The representative firm has a technology for producing consumption goods, given by y = 2Nd where z is the total factor productivity and Nd is the labor input. Denote the profit of the firm as . The firm belongs to the representative consumer. The government imposes proportional tax 7 (set exogenously) on the labor income of the representative consumer. The government spends the tax revenue to give lump-sum subsidy B to the representative consumer. 1). Write down the consumer's budget constraint. 2). Solve consumer's optimization problem. 3). Write down the firm's optimization problem and find and w. 4). Write down market clearing condition for the labor market and for the goods market. 5). Write down the government budget constraint. 6). Find the subsidy B in equilibrium (i.e., using your solution to the firm's and consumer's problem). 7). Using your results above, solve for the competitive equilibrium consump- tion and leisure.

1. Consider the following static model. The consumer has preferences such that he always sets his consumption equal to è, where è is exogenously fixed. The consumer has h units of time that he can allocate between working hours (N*) and leisure (I). The wage per hour is w. The representative firm has a technology for producing consumption goods, given by y = 2Nd where z is the total factor productivity and Nd is the labor input. Denote the profit of the firm as . The firm belongs to the representative consumer. The government imposes proportional tax 7 (set exogenously) on the labor income of the representative consumer. The government spends the tax revenue to give lump-sum subsidy B to the representative consumer. 1). Write down the consumer's budget constraint. 2). Solve consumer's optimization problem. 3). Write down the firm's optimization problem and find and w. 4). Write down market clearing condition for the labor market and for the goods market. 5). Write down the government budget constraint. 6). Find the subsidy B in equilibrium (i.e., using your solution to the firm's and consumer's problem). 7). Using your results above, solve for the competitive equilibrium consump- tion and leisure.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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