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10 POINTS. Consider the two-period firm optimization problem. Suppose that the only factor of production is...
1. (45 points) Consider the closed-economy one-period macroeconomic model developed in class. The...
1. (45 points) Consider the closed-economy one-period macroeconomic model developed in class. The consumer is endowed with h units of time, and chooses consumption C and leisure ` to maximize U = log(C) + θlog(`), subject to the budget constraint C = wNs + π. Production is described by Y = zNd . Government spending G is financed with a proportional revenue tax (tax rate τ ) on the firm. (a) (10) Find the firm’s optimal demand for labor Nd...
From now on, let the production function of the firm be Y = 2K*N1-a, where a...
From now on, let the production function of the firm be Y = 2K*N1-a, where a is a parameter between 0 and 1. 4. Verify that this production function has constant return to scale. 5. Derive the marginal product of labor MPx and marginal product of capital MPK. How does MPN change with N and K? 6. Solve the firm's optimization problem analytically. That is, to derive the firm's opti- mal choice as a function of exogenous variables (i.e., in...
Consider an unincorporated firm with a two period (1 and 2) time horizon. At the beginning...
Consider an unincorporated firm with a two period (1 and 2) time horizon. At the beginning of period 1, the firm has a predetermined capital stock, K. Důring period 1, gross investment expenditure, I, financed out of retained earnings, are incurred with the purpose of both maintaining and increasing the capital stock in period 2. In each of the two periods, the capital stock depreciates at a rate 6, so at the beginning of period 2, the firm's capital stock...
Problem 2. The firm expects that its production function in the next period will be given...
Problem 2. The firm expects that its production function in the next period will be given by Fe(K, L)-10 v KL. The firm employs 25 workers. The real interest rate equals 5% and the depreciation rate equals 20%. The price for the firm's products is 1 EUR while the price of capital goods is 10 EUR a) Find the user cost of capital. Find net investments, assuming that initially the firm has a capital stock of 88. Modify your answer...
Competitive Equilibrium (10 pts) Consider an economy with a representative consumer, a representative firm, and a...
Competitive Equilibrium (10 pts) Consider an economy with a representative consumer, a representative firm, and a government. • The consumer can work up to h hours at an hourly rate of w. She only gets utility from consumption and does not care about how much she works. Their preferences are represented by the utility function U(C, l) = ln(C). The consumer also owns an exogenously given K units of capital, which they can rent to the firms at a price...
Problem 2. The firm expects that its production function in the next period will be given...
Problem 2. The firm expects that its production function in the next period will be given by Fe (KL) 10VKL. The firm employs 25 workers. The real interest rate equals 5% and the depreciation rate equals 20%. The price for the firm's products is 1 EUR while the price of capital goods is 1O EUR Find the user cost of capital. Find net investments, assuming that initially the firm has a capital stock of 88. Modify your answer to part...
Consider an unincorporated firm with a two period (1 and 2) time horizon. At the beginning...
Consider an unincorporated firm with a two period (1 and 2) time horizon. At the beginning of period 1, the firm has a predetermined capital stock, K1 . During period 1, gross investment expenditure, I, financed out of retained earnings, are incurred with the purpose of both maintaining and increasing the capital stock in period 2. In each of the two periods, the capital stock depreciates at a rate δ, so at the beginning of period 2, the firm's capital...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form,...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form, Y = Ka (LE)1-a, where 0 < α < 1. The savings rate s s, the depreciation rate isỗ, and the growth rate of E is g and the growth rate of L is n. Denote y E and LE 1. The economy is at the steady state. Report the steady-state growth rates of y, k, Y, K, L' K' ?, an 2. Assume...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
1. Consider a risk-neutral firm that operates for two periods with a production function that depends...
1. Consider a risk-neutral firm that operates for two periods with a production function that depends only on the amount of labor hired: f(L) = 100L 1/2 . Assume that the interest rate (r) is equal to 5%. The wage in the first period is equal to $10 per hour, but the second period’s wage is either $10 (with probability 0.4) or $20 (with probability 0.6). The current price for the firm’s output is P 0 =$20. In the second...
From now on, let the production function of the firm be Y = 2K*N1-a, where a is a parameter between 0 and 1. 4. Verify that this production function has constant return to scale. 5. Derive the marginal product of labor MPx and marginal product of capital MPK. How does MPN change with N and K? 6. Solve the firm's optimization problem analytically. That is, to derive the firm's opti- mal choice as a function of exogenous variables (i.e., in...
Consider an unincorporated firm with a two period (1 and 2) time horizon. At the beginning of period 1, the firm has a predetermined capital stock, K. Důring period 1, gross investment expenditure, I, financed out of retained earnings, are incurred with the purpose of both maintaining and increasing the capital stock in period 2. In each of the two periods, the capital stock depreciates at a rate 6, so at the beginning of period 2, the firm's capital stock...
Problem 2. The firm expects that its production function in the next period will be given by Fe(K, L)-10 v KL. The firm employs 25 workers. The real interest rate equals 5% and the depreciation rate equals 20%. The price for the firm's products is 1 EUR while the price of capital goods is 10 EUR a) Find the user cost of capital. Find net investments, assuming that initially the firm has a capital stock of 88. Modify your answer...
Problem 2. The firm expects that its production function in the next period will be given by Fe (KL) 10VKL. The firm employs 25 workers. The real interest rate equals 5% and the depreciation rate equals 20%. The price for the firm's products is 1 EUR while the price of capital goods is 1O EUR Find the user cost of capital. Find net investments, assuming that initially the firm has a capital stock of 88. Modify your answer to part...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form, Y = Ka (LE)1-a, where 0 < α < 1. The savings rate s s, the depreciation rate isỗ, and the growth rate of E is g and the growth rate of L is n. Denote y E and LE 1. The economy is at the steady state. Report the steady-state growth rates of y, k, Y, K, L' K' ?, an 2. Assume...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
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