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11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and...
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...
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.
. 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 a firm with production function f(K,L) = K +L. (a) Suppose that capital level is...
Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r=1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal to 10...
12. Consider a firm with production function f(K,L) = K+L. (a) Suppose that capital level is currently fixed at K =...
12. Consider a firm with production function f(K,L) = K+L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r = 1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal...
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...
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...
(c) Consider a competitive producer with a production function of l0.4k0.1 , labor price of w...
(c) Consider a competitive producer with a production function of l0.4k0.1 , labor price of w and capital price of 1(not v, the number one), and an output price of p. Suppose capital in the short run is fixed at k. Given: Short Run Cost Function (C): C = k + w(q2.5/k0.25) Profit Maximizing Quantity (q): q = (w /4k0.25p)1/0.75 Question: Find the firm’s unconditional demand for labor?
Consider a production function Q=Q(K,L)=6K^(1/2)L^(1/3) with K as capital and L as labor input. Let the...
Consider a production function Q=Q(K,L)=6K^(1/2)L^(1/3) with K as capital and L as labor input. Let the price per unit of output be P=$0.50, the cost or rental rate per unit of capital be r=$0.10 and let the price (wage rate) of labor be w=$1. a) find the profit max level of K and L and check with second order condition (my answer was L=3.375 and K=1.5) b) Find max profit (I got profit=1.986)
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...
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)=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.
. 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 a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r=1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal to 10...
12. Consider a firm with production function f(K,L) = K+L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for producing outputs greater than or equal to 10 units when w = 1 and r = 1. (b) Suppose wage goes up to w' = 2 while the price of capital remains same at r = 1. Find the new short-run cost function for producing output greater than or equal...
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...
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...
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...
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