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Assume the production function is q = f(h, k) = 2n12 a) (4 marks) What is...
4) Labor Demand (33 marks) Assume the production function is a) (4 marks) What is the marginal product of labor (M P)?...
4) Labor Demand (33 marks) Assume the production function is a) (4 marks) What is the marginal product of labor (M P)? b) (4 marks) What is the marginal product of capital (MPk)? c) (8 marks) Assume p 2, W1/2, andr3. Calculate the profit maximizing level of labor demand (h') d) (6 marks) If w increases to w3 (and p and r stay at p 2 and r 3), what is the new profit maximizing level of labor demand? e)...
3. Consider the production function y= . Assume r 1. (a) Show that the production function...
3. Consider the production function y= . Assume r 1. (a) Show that the production function y(x) is concave. (b) Show that the inverse production function r(y) is convex (c) The price of y is p 10. Find the firm's total product TP(x), marginal product MP(a) and average product AP(a) (d) Find the firm's value of marginal product VMP(a), and value of average product VAP(r) (e) Assume w < marVAP (x) Find the firm's input demand curve r*(w) (f) Suppose...
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...
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...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital,...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,r,q) and labor L*(w,r,q), and the long run minimized cost C* (w,r,q). (Hint: reduce the cost function for the next part. (b) Setup and solve the profit maximization problem over quantity using the cost function you solved for in the previous part. Solve for the profit maximizing quantity q *(p,w,r), cost...
. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote...
. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w, r, and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p.
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital,...
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function.
3. Consider the production function y=. Assume r > 1. (a) Show that the production function...
3. Consider the production function y=. Assume r > 1. (a) Show that the production function y(«) is concave. (b) Show that the inverse production function z(y) is convex. (e) The price of y is p= 10. Find the firm's total product TP(x), marginal product MP) and average product AP (a). (d) Find the firm's value of marginal product VMP), and value of average product V AP(x). (e) Assume w<marV AP(x) Find the firm's input demand curve r*(w). (1) Suppose...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,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 10. Consider the production function: f(K,L)=KLI. Let w...
4) Labor Demand (33 marks) Assume the production function is a) (4 marks) What is the marginal product of labor (M P)? b) (4 marks) What is the marginal product of capital (MPk)? c) (8 marks) Assume p 2, W1/2, andr3. Calculate the profit maximizing level of labor demand (h') d) (6 marks) If w increases to w3 (and p and r stay at p 2 and r 3), what is the new profit maximizing level of labor demand? e)...
3. Consider the production function y= . Assume r 1. (a) Show that the production function y(x) is concave. (b) Show that the inverse production function r(y) is convex (c) The price of y is p 10. Find the firm's total product TP(x), marginal product MP(a) and average product AP(a) (d) Find the firm's value of marginal product VMP(a), and value of average product VAP(r) (e) Assume w < marVAP (x) Find the firm's input demand curve r*(w) (f) Suppose...
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...
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...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w, r, and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p.
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function.
3. Consider the production function y=. Assume r > 1. (a) Show that the production function y(«) is concave. (b) Show that the inverse production function z(y) is convex. (e) The price of y is p= 10. Find the firm's total product TP(x), marginal product MP) and average product AP (a). (d) Find the firm's value of marginal product VMP), and value of average product V AP(x). (e) Assume w<marV AP(x) Find the firm's input demand curve r*(w). (1) Suppose...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,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 10. Consider the production function: f(K,L)=KLI. Let w...
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