Given the production function: y=Alα, where l=labor and 0<α<1, price and wage are equal to P...
Given the production function: y=Alα, where l=labor and 0<α<1, price and wage are equal to P and W, respectively.
a) Find the profit-maximizing level of labor.
b) Show that the SOC is satisfied.
c) Show that demand for labor is inversely related to W and directly related to P. No need to take derivatives.
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Given the production function:
y=Alα, where l=labor and 0<α<1, price and wage are
equal to P...
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...
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...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and...
11. 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. 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...
1. [30 POINTS] Consider the production function y=f(L,K) = 4/1/2K1/4 where L is labor and K...
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A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
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. 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.
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Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y The input prices are w and w2 respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) 1/3 1/3 (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w, and output price...
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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)...
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...
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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...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
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Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y The input prices are w and w2 respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) 1/3 1/3 (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w, and output price...
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)...
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