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1. Consider a firm's production function is given by, F(K,L) al bK, where a and b...
Consider 2 firms with the following 2 different production functions (i.) y(L,K) = aL + bK...
Consider 2 firms with the following 2 different production functions (i.) y(L,K) = aL + bK (ii.) y(L,K) = L^0.5K^0.5 where y denotes the quantity produced and L and K are the amount of labor and capital, respectively. a. Assume K is fixed at 100. Do these production functions exhibit decreasing marginal products of labor? b. Assume K can be freely chosen. Do these production functions exhibit constant returns to scale? c. For each of the production functions, draw the...
1. [30 POINTS] Consider the production function y=f(L,K) = 4/1/2K1/4 where L is labor and K...
1. [30 POINTS] Consider the production function y=f(L,K) = 4/1/2K1/4 where L is labor and K is capital. Price per unit of the labor is w, price per unit of the capital is r, and the price per unit of the output is p. (a) (10 POINTS] In long-run, if the firm's objective is to maximize its profit, what are the factor demand functions of labor and capital? (b) (10 Points) What is the optimal output level y and the...
Consider a firm that has the following CES production function: Q = f(L,K) = [aL^ρ + bK^ρ]^1/ρ where ρ ≤ 1. Please...
Consider a firm that has the following CES production function: Q = f(L,K) = [aL^ρ + bK^ρ]^1/ρ where ρ ≤ 1. Please clearly show each STEP and make sure your handwriting is LEGABLE. Thank you Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) What are the returns to scale for this production function? Show...
1. A firm's production function is f(K, L) = (K-1 + L-1)-1 = 1 a. Solve...
1. A firm's production function is f(K, L) = (K-1 + L-1)-1 = 1 a. Solve for the firm's long-run conditional factor demands, K(r,w,9) and L(r, w,9). b. The plant manager tells you “At our current output level, a $1 increase in the wage rate would raise our total costs by $280." Use Shephard's Lemma and the CES tangency condition to infer (approximately) what current output is.
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
Consider the standard continuous-time Solow model where the production function is given by F (K,...
Consider the standard continuous-time Solow model where the production function is given by F (K,AL)- BK AL (a) Is this a neoclassical production function? Explain. (b) Derive the fundamental dynamic equation in terms of per capita capital kK/I (c) Can we have sustained growth? Explain (d) Characterize the dynamics in a phase diagram of (k,k
Consider the standard continuous-time Solow model where the production function is given by F (K,AL)- BK AL (a) Is this a neoclassical production function? Explain....
6. A firm's production function is given by q 20(EV2 +K2), where q is output and...
6. A firm's production function is given by q 20(EV2 +K2), where q is output and E and K are amounts of labour and capital, respectively. If the wage rate is w $15 per hour and the price of capital is r $60 per hour, what is the firm's profit maximizing capital/labour ratio? A. K/E 20 D. K/E 4 E. K/E = 16 B. K/E 200 C. K/E 1/2
The firm's production function is given as f(L,K) = 4L0.5K0.5 and input prices are w =...
The firm's production function is given as f(L,K) = 4L0.5K0.5 and input prices are w = 4 and r = 16. In the short-run, the level of capital is fixed at K = 2. What is the firm's short-run average cost function? Wählen Sie eine Antwort: O a. 0.125q 32/q b. 0.25q 16/q О с. 0.125q O d, 4 + 32/q
Suppose the firm's production function is given by f(K,L) = min {K",L"} (a) For what values...
Suppose the firm's production function is given by f(K,L) = min {K",L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive
Gainesville airline's production function is given by a Cobb-Douglas form: Y = AL"K,a.B>0 where: Y =number...
Gainesville airline's production function is given by a Cobb-Douglas form: Y = AL"K,a.B>0 where: Y =number of passengers carried per year A coefficient L number of pilots (labor) K number of aircraft (capital) Suppose that the annual wage for each pilot is p, and the "price" of each aircraft (amortized annual cost) is p 1. Derive the output cost function for the Gainesville airline 2. Calculate the average and marginal cost functions, and discuss the condition when economies of scale...
1. [30 POINTS] Consider the production function y=f(L,K) = 4/1/2K1/4 where L is labor and K is capital. Price per unit of the labor is w, price per unit of the capital is r, and the price per unit of the output is p. (a) (10 POINTS] In long-run, if the firm's objective is to maximize its profit, what are the factor demand functions of labor and capital? (b) (10 Points) What is the optimal output level y and the...
1. A firm's production function is f(K, L) = (K-1 + L-1)-1 = 1 a. Solve for the firm's long-run conditional factor demands, K(r,w,9) and L(r, w,9). b. The plant manager tells you “At our current output level, a $1 increase in the wage rate would raise our total costs by $280." Use Shephard's Lemma and the CES tangency condition to infer (approximately) what current output is.
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
Consider the standard continuous-time Solow model where the production function is given by F (K,AL)- BK AL (a) Is this a neoclassical production function? Explain. (b) Derive the fundamental dynamic equation in terms of per capita capital kK/I (c) Can we have sustained growth? Explain (d) Characterize the dynamics in a phase diagram of (k,k
Consider the standard continuous-time Solow model where the production function is given by F (K,AL)- BK AL (a) Is this a neoclassical production function? Explain....
6. A firm's production function is given by q 20(EV2 +K2), where q is output and E and K are amounts of labour and capital, respectively. If the wage rate is w $15 per hour and the price of capital is r $60 per hour, what is the firm's profit maximizing capital/labour ratio? A. K/E 20 D. K/E 4 E. K/E = 16 B. K/E 200 C. K/E 1/2
The firm's production function is given as f(L,K) = 4L0.5K0.5 and input prices are w = 4 and r = 16. In the short-run, the level of capital is fixed at K = 2. What is the firm's short-run average cost function? Wählen Sie eine Antwort: O a. 0.125q 32/q b. 0.25q 16/q О с. 0.125q O d, 4 + 32/q
Suppose the firm's production function is given by f(K,L) = min {K",L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive
Gainesville airline's production function is given by a Cobb-Douglas form: Y = AL"K,a.B>0 where: Y =number of passengers carried per year A coefficient L number of pilots (labor) K number of aircraft (capital) Suppose that the annual wage for each pilot is p, and the "price" of each aircraft (amortized annual cost) is p 1. Derive the output cost function for the Gainesville airline 2. Calculate the average and marginal cost functions, and discuss the condition when economies of scale...
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