dont copy from chegg please Consider a firm that produces output using a typical production function as discussed in thecourse, and that hires workers in a competitive labor market.1. Explain what determines the firm's choice of its labor input. Use a suitable figure.Discuss how changes in the capital stock and in the wage affect the firm's choice of itslabor input.Suppose that the firm uses a Cobb-Douglas production function Y = K"N1-a.In this case, the marginal product of labor is given by (1– a)K"N-".The parameter a is 2/3, and the firm uses one unit of capital.2. Calculate (show your steps) how the firm's labor input changes if the wage increases by1%.3. Calculate how the firm's labor input changes if the wage is unchanged, but the firmdecides to double its capital stock.

A firms optimal level of input choices are achieved at the point where the value of marginal product…

Answered: onsider a firm that produces output…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.5P

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What is the difference between a fixed input and a variable input?
Consider a firm that produces output using a typical production function as discussed in the course, and that hires workers in a competitive labor market. 1. Explain what determines the firm's choice of its labor input. Use a suitable figure. Discuss how changes in the capital stock and in the wage affect the firm's choice of its labor input. Suppose that the firm uses a Cobb-Douglas production function Y = K"N-«. In this case, the marginal product of labor is given by (1 – a)K“N-«. The parameter a is 2/3, and the firm uses one unit of capital. 2. Calculate (show your steps) how the firm's labor input changes if the wage increases by 1%. 3. Calculate how the firm's labor input changes if the wage is unchanged, but the firm decides to double its capital stock.
Short Answer Q1 A firm's production function is estimated as Q = 400K + 80L -0.2K 2-0.4L? where K is capital and Lis labor. If the firm is using 200 units of K and 50 units of L, solve for: The marginal product of capital MPK The marginal product of labor MPL Don't just give your answers for MPK and MPL, show your computations If the price of Kis $70 per unit and the price of L is $14 per unit, is this an optimal production choice for the firm? Explain why it is or is not.
A firm's production function is: q = 20L1/2K1/2 where q is the firm's total product, L is the quantity of labor employed, and K is the quantity of capital employed. The price of labor is $25 per unit and the price of capital is $100 per unit. a. What is the equation for the marginal product of labor? b. What is the equation for the marginal product of capital? c. Given the price of labor is $25 per unit and the price of capital is $100 per unit, what is the cost-minimizing combination of capital and labor that can produce 800 units of output?
2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function Y = K2/6 L3/6 H1/6 a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is found by differentiating the production function (Y) with respect to labor (L)) b) Derive an expression for the marginal product of capital. How does an increase in the amount of human capital affect the marginal product of capital? (Hint: The marginal product of capital MPK is found by differentiating the production function (Y) with respect to capital (K)).
1. What is the optimal level of Labor that maximize marginal production if the production function is given as: Q = 10 L2 0.3 L Enter your answer
A firm can manufacture a product according to the production function Q = 2(K)1/4 (L)3/4 where K represents capital equipment and L is labor. The company has already spent $10,000 on the 4 units capital. a. Please show the expression for the average product of labor, APL and the marginal product of labor, MPL. If workers at the firm are paid a competitive wage of $100 and the product is sold for $200 each, what is optimal level of labor usage and what is the maximum profit?
X 15:01 EC5011 - Seminar 2.do... II. Problems and Exercises .ıl 4 1. Consider the following production function: . Does this production function exhibit constant returns to scale? (Hint: Replace K and L by 2K and 2L, respectively, and check if F(2K, 2L) = 2F(K, L).) 2. Consider the following production function: . a. Calculate the marginal product of labour. b. Calculate the marginal product of capital. c. Does this production function exhibit diminish MPL and MPK? d. Does this function exhibit constant returns to scale? 3. Suppose represents the production function of both Mexico and Spain. Use the following information to answer the next questions. L = Population K = Capital Y = Output Country (millions) (trillion) (trillion) Mexico 105 0.18 1.0 Spain 45 0.74 1.7 a. Calculate total factor productivity for both countries using the PF in question 2. b. Calculate per capita income for both countries. c. Explain the difference in per capita income. 4. A snack food factory in the Tuas…

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