= L2K2, 3. Imagine we live in a classical world. Suppose that the production function is Y where L is the amount of labor and K is the amount of capital. The economy has 100 units of labor and 100 units of capital. a. Does the production function show Constant Returns to Scale? Why? b. Derive an expression for the marginal product of labor. Is the marginal product of labor diminishing? How does an increase in the amount of capital affect the marginal product of labor? Explain. c. What are the real wage and rental price of capital? d. What is the income share paid to labor? What is the income share paid to capital?

= L2K2, 3. Imagine we live in a classical world. Suppose that the production function is Y where L is the amount of labor and K is the amount of capital. The economy has 100 units of labor and 100 units of capital. a. Does the production function show Constant Returns to Scale? Why? b. Derive an expression for the marginal product of labor. Is the marginal product of labor diminishing? How does an increase in the amount of capital affect the marginal product of labor? Explain. c. What are the real wage and rental price of capital? d. What is the income share paid to labor? What is the income share paid to capital?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.8P

See similar textbooks

Similar questions

What is a production function?
What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?
What is the difference between a fixed input and a variable input?
Consider the production function: Q = L1/4 K 3/4 Does this production show increasing, decreasing, or constant returns to scale? Show your work. I. II. Derive an expression for the marginal product of labor. Ш. Show mathematically whether the marginal product of labor is increasing, decreasing, or constant, as the labor input is increased. IV. Derive the average product of labor. Explain whether the average product of labor is increasing, decreasing, or constant, as the labor input is increased.
An economy has the following Cobb-Douglas production function: ?=100?^(1/3)?^(2/3) . The economy has 125 units of capital and 64 units of labor. d. Calculate the marginal product of capital MPK. e. Calculate the marginal product of labor (MPL).
1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.
How does the slope of the production function illustrate diminishing returns? The slope of the production function becomes steep as the quantity of increases because of diminishing returns. O A. more; capital OB. more; labor O C. less; labor O D. less; capital Click to select your answer.
Use the Cobb-Douglas production function to show that when the number of units of labor and the number of units of capital are doubled, the production level is also doubled.
1. Is it possible to have diminishing returns to a single factor of production and constant returns to scale at the same time? Discuss. 2. Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you about the nature of the production function? What does each of these shapes tell you about the MRTS?
Suppose the production function is given by q = 3k - 41. what is the average product of capital when 10 units of capital and 10 units of labor are employed? A. 3 B. 4 C. 7 D. 45
1. Suppose the production function is Q = 8L + 15K where Q is the quantity of output, L is the quantity of labor used in production, and K is the quantity of capital used in production. What can be said about this production function? It has Decreasing Returns to Scale It has Constant Returns to Scale It has Increasing Returns to Scale There isn’t enough information to determine the Returns to Scale for this production function 2. You’re dreaming of what to do during a nice summer day. You could mow the lawn which you would pay someone $15 to do for you. You could go for a walk which you value at $11. You could also take a nap and ignore everyone and everything else which you would pay $29 to do. If you to take a nap, what is your opportunity cost? Group of answer choices $29 $26 $15 $11
10. Consider the following isoquant - isocost diagram (i.e., graph). K a. C. MPL b. = W a MPL Z W O a Ob Od С MPK r MPK d. The slope of the isocost is not e. MPL must be greater than MPK. d MPK r e 31> 90 W L