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Problem 3 - Profit Maximization Consider the case of a firm that produces output x (sold...
Consider the case of a firm that produces output x (sold at price p) using a...
Consider the case of a firm that produces output x (sold at price p) using a production function x = A*/*klaße, where / is labor, kis capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization problem for the firm. d)...
Consider the case of a firm that produces output x (sold at price p) using a...
Consider the case of a firm that produces output x (sold at price p) using a production function x = A*l^(α)*k^(1‐α‐β)*e^β, where l is labor, k is capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization problem for the firm....
Problem 3 - Profit Maximization Consider the case of a firm that produces output x (sold...
Problem 3 - Profit Maximization Consider the case of a firm that produces output x (sold at price p) using a production function x = A*1941-a-Beß, where lis labor, k is capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization...
Consider the case of a firm that produces output x (sold at price p) using a...
Consider the case of a firm that produces output x (sold at price p) using a production function x = A*lαk1‐α‐βeβ, where l is labor, k is capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization problem for the firm....
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...
1. Consider the profit maximization problem for the firm. Say the pro- duction function f(k, n)...
1. Consider the profit maximization problem for the firm. Say the pro- duction function f(k, n) is strictly concave jointly in all arguments and once continuously differentiable (C), where k (resp, n) denotes the input of capital (resp, labor) (a) Assume a maximum exists for the firms profit maximization problem. What are the first order conditions (FOCs) to characterize all optimal solutions for factor demands for capital and labor in the general problem? (b) Say f(k, n) = (ak" +...
Consider a textile manufacturing firm that uses labor and capital inputs and has the production technology...
Consider a textile manufacturing firm that uses labor and capital inputs and has the production technology given by the equation Q = 8K0.25L 0.5 , where Q is output, K is capital and L is labor. Each unit of capital costs 10 TL while each unit of labor costs 5 TL. a) Does this firm have increasing, decreasing or constant returns to scale? (1) b) Define the cost minimization problem faced by firm. What is the objective function, what is...
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 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...
Consider the case of a firm that produces output x (sold at price p) using a production function x = A*/*klaße, where / is labor, kis capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization problem for the firm. d)...
Problem 3 - Profit Maximization Consider the case of a firm that produces output x (sold at price p) using a production function x = A*1941-a-Beß, where lis labor, k is capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up 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 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...
1. Consider the profit maximization problem for the firm. Say the pro- duction function f(k, n) is strictly concave jointly in all arguments and once continuously differentiable (C), where k (resp, n) denotes the input of capital (resp, labor) (a) Assume a maximum exists for the firms profit maximization problem. What are the first order conditions (FOCs) to characterize all optimal solutions for factor demands for capital and labor in the general problem? (b) Say f(k, n) = (ak" +...
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