18. A firm operating on the production function of ? = ? ?? ? pays w...
18. A firm operating on the production function of ? = ? ?? ? pays w and r for the labor and capital respectively in a competitive market. Write the profit maximizing first order condition for optimal level of K and L (you don’t need to solve it !). Check whether the sufficient condition for a maximization hold. Assume that; ? = ? ??? 0 < ? < 0.5 .
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18. A firm operating on the production function of ? = ? ?? ?
pays w...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
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...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this form with both the two step and 1 step methods and provine that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K'(..) and labor L'(w. ), and the long run minimized cost C"(w.ne). (Hint: reduce...
Problem 5. This problem asks you to find the supply function of a firm that only...
Problem 5. This problem asks you to find the supply function of a firm that only uses one input (z) to produce one output (q). In addition, it highlights how the choices we make to represent an economic situation can influence the conclusions we arrive at. Suppose there is a firm operating in a competitive environment. The firm has a technology given by f(z)Az, where z 20 is the amount of labor the firm hires at a wage of w...
Competitive Firms - Optimal Labor and Capital 1. A competitive firm has production technology q A...
Competitive Firms - Optimal Labor and Capital
1. A competitive firm has production technology q A K La. lt can sell output at price P and hire capital and labor at competitive factor prices r and w. Write down the firm's profit maximization problem. What are the firm's first- order necessary conditions for a maximum. a. w Suppose now that α-,P-1 and -1. b. What is the firm's optimum capital labor-intensity? Why can't the optimum scale of production q be...
Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two...
Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two inputs of production; each unit of labor is paid the market wage (w), and each unit of capital is rented at the rental price of capital (r). Output (Y) is therefore a function of labor and capital, or Y = f (K, L), and is sold at the market price (P). The goal of this firm is to maximize profit given the price of...
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the outpu...
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the output good is p > 0. The prices of the inputs Labour and Capital are w> 0 and r>0 respectively. The firm chooses L and K in order to maximize profits, (L.K). (a) How does the short-run production function differ from the long-run production function? (b) Write out the profit function for the firm, (L,K). (c) Derive the first order...
9. A firm uses capital and labor to produce a single output good. The production function...
9. A firm uses capital and labor to produce a single output good. The production function is given by F(K,L)=K^0.5L, where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, respectively r=$5 and w=$6. Based on this information, characterize the optimal (output maximizing) allocation of inputs given that the firm decided to limit its total cost to $12,000. Illustrate your solution graphically:...
[Short-Run Production] Suppose that a firm is producing in the short run with output given by:...
[Short-Run Production] Suppose that a firm is producing in the short run with output given by: Q = 200.5L – 2.5L2, The firm hires labor at a wage of $25 per hour and sells the good in a competitive market at P = $50 per unit. Find the firm’s optimal use of labor and associated level of output. (For extra practice, what is the firm’s associated profit?) I have already finished and went to check my work on Chegg and...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this form with both the two step and 1 step methods and provine that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K'(..) and labor L'(w. ), and the long run minimized cost C"(w.ne). (Hint: reduce...
Problem 5. This problem asks you to find the supply function of a firm that only uses one input (z) to produce one output (q). In addition, it highlights how the choices we make to represent an economic situation can influence the conclusions we arrive at. Suppose there is a firm operating in a competitive environment. The firm has a technology given by f(z)Az, where z 20 is the amount of labor the firm hires at a wage of w...
Competitive Firms - Optimal Labor and Capital
1. A competitive firm has production technology q A K La. lt can sell output at price P and hire capital and labor at competitive factor prices r and w. Write down the firm's profit maximization problem. What are the firm's first- order necessary conditions for a maximum. a. w Suppose now that α-,P-1 and -1. b. What is the firm's optimum capital labor-intensity? Why can't the optimum scale of production q be...
Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two inputs of production; each unit of labor is paid the market wage (w), and each unit of capital is rented at the rental price of capital (r). Output (Y) is therefore a function of labor and capital, or Y = f (K, L), and is sold at the market price (P). The goal of this firm is to maximize profit given the price of...
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the output good is p > 0. The prices of the inputs Labour and Capital are w> 0 and r>0 respectively. The firm chooses L and K in order to maximize profits, (L.K). (a) How does the short-run production function differ from the long-run production function? (b) Write out the profit function for the firm, (L,K). (c) Derive the first order...
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