Quiz 6 Practice Problems Question 1: The production function is given by Y = 2 Sqrt(L) + 2 Sqrt (K) where L denotes labor and K denotes capital. MPL = 1/Sqrt(L) and MPK = 1/Sqrt(K). The firm has a fixed amount of capital, K = 4, and can expand production by hiring more workers only. The output is p, the price of labor is wL and the price of capital is wk. a. Graph the production function for 1 = 0 to 100

Quiz 6 Practice Problems Question 1: The production function is given by Y = 2 Sqrt(L) + 2 Sqrt (K) where L denotes labor and K denotes capital. MPL = 1/Sqrt(L) and MPK = 1/Sqrt(K). The firm has a fixed amount of capital, K = 4, and can expand production by hiring more workers only. The output is p, the price of labor is wL and the price of capital is wk. a. Graph the production function for 1 = 0 to 100

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.3P

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3. If MPL = 5L¹/³ is a firm's marginal-product function, where L is the single input labor and output is zero when L = 0, find the production function for the firm.
In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L,K), q = 6LK + 7L2 – where g is output, Lis workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MP, =. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.) For example, if L = 5 and K= 23, then the marginal product of labor equals MP, =. (Enter a numeric response using an integer.) If L=9 and K= 23, then the marginal product of labor equals MP, =. (Enter a numeric response using an integer.) 20 tv MacBook Air S0 F2 F3 F4 % & 4 6 { E R Y P F G J K > C V M command option レ .. .- V * C B *3
In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L,K), - ²³. q=6LK +4L² where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL = (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.)
3. a. b. C. d. Don Corneo's firm has a Cobb-Douglas production function given as: Y = AK 0.5 N 0.5 Show that the production function exhibits Diminishing returns with respect to Capital, K. Show that the production function can exhibit Constant returns to scale Estimate the output per worker, N. Calculate the elasticity of substitution, o.