Let the production by the representative firm be represented by the production function Y = ZN...

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Let the production by the representative firm be represented by the production function Y = ZN d Where Y is the aggregate output, z is the total factor productivity or level of technology parameter, and Nd is the labor input. The firm hires labor units at the market determined wage rate, w up to the point of profit maximization. Labor is the only input used in the production process hence z represents labor productivity. There is a representative consumer who wishes to maximize utility represented by utility function U(c.1) where c is consumption, 1 is leisure. The consumer has h amount of maximum hours during the day. Suppose the utility function of the consumer is as follows: U(c. ) = c 2/3 & 1/3 Suppose that there is a government which collects taxes on consumption expenditures of the consumer, such as a value added tax on consumption, at rate 0 <T 0< 1. The government uses the proceeds of these taxes to finance government purchases, G. The government is assumed to run a balanced budget. There are no lump-sum taxes collected. a) (5 points) Define a competitive equilibrium for this economy, where the representative consumer maximizes utility subject to budget constraint and time constraint, representative firm maximizes profits subject to production technology, all markets clear, government budget is balanced. b) (5 points) Given the production technology, write down the firm's profit maximization problem. What is the firm's maximum profits under this production technology? c) (12 points) Write down the consumer's budget constraint and time constraint. Then, given the consumer's budget constraint and time constraint, write down the consumer's utility maximization problem. Then, set up the Lagrangean and write down the first order necessary conditions for a maximum, finally solve for the consumer's equilibrium choices of consumption and leisure, (c*. *) as functions of the given values of z, h, t. Finally, depict this solution on the appropriate graph for the consumer's utility maximization problem. d) (8 points) What is the total supply of output, Y? What is the total amount of tax collected, and hence what is the government spending that satisfies government's budget balance? Finally, prove that the national income identity (or the resource constraint) holds. e) (10 points) Now suppose that the government spending increases from GO to G1. To accommodate for the increase in the government spending, the government also increases the value added tax rate, T'> T0. How does the consumer's equilibrium change in response to the increase in value added tax rate? Show your analysis on an appropriate diagram for the consumer's utility maximization under two different tax rates. f) (10 points) Show the two general equilibrium points on an appropriate diagram (with 7 0 and with r'), before and after the government spending increase. Also, show the social planner's choices under the two cases. Do you think this increase in government spending has been favorable to social welfare? Comment. Let the production by the representative firm be represented by the production function Y = ZN d Where Y is the aggregate output, z is the total factor productivity or level of technology parameter, and Nd is the labor input. The firm hires labor units at the market determined wage rate, w up to the point of profit maximization. Labor is the only input used in the production process hence z represents labor productivity. There is a representative consumer who wishes to maximize utility represented by utility function U(c.1) where c is consumption, 1 is leisure. The consumer has h amount of maximum hours during the day. Suppose the utility function of the consumer is as follows: U(c. ) = c 2/3 & 1/3 Suppose that there is a government which collects taxes on consumption expenditures of the consumer, such as a value added tax on consumption, at rate 0 <T 0< 1. The government uses the proceeds of these taxes to finance government purchases, G. The government is assumed to run a balanced budget. There are no lump-sum taxes collected. a) (5 points) Define a competitive equilibrium for this economy, where the representative consumer maximizes utility subject to budget constraint and time constraint, representative firm maximizes profits subject to production technology, all markets clear, government budget is balanced. b) (5 points) Given the production technology, write down the firm's profit maximization problem. What is the firm's maximum profits under this production technology? c) (12 points) Write down the consumer's budget constraint and time constraint. Then, given the consumer's budget constraint and time constraint, write down the consumer's utility maximization problem. Then, set up the Lagrangean and write down the first order necessary conditions for a maximum, finally solve for the consumer's equilibrium choices of consumption and leisure, (c*. *) as functions of the given values of z, h, t. Finally, depict this solution on the appropriate graph for the consumer's utility maximization problem. d) (8 points) What is the total supply of output, Y? What is the total amount of tax collected, and hence what is the government spending that satisfies government's budget balance? Finally, prove that the national income identity (or the resource constraint) holds. e) (10 points) Now suppose that the government spending increases from GO to G1. To accommodate for the increase in the government spending, the government also increases the value added tax rate, T'> T0. How does the consumer's equilibrium change in response to the increase in value added tax rate? Show your analysis on an appropriate diagram for the consumer's utility maximization under two different tax rates. f) (10 points) Show the two general equilibrium points on an appropriate diagram (with 7 0 and with r'), before and after the government spending increase. Also, show the social planner's choices under the two cases. Do you think this increase in government spending has been favorable to social welfare? Comment.

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The representative consumer supplies labor and demands consumption goods The representative firm demands labor and supplies consumption goods The Representative Firm assume a representative firm which ... View the full answer