4. Given the equation for the Cobb-Douglas production functionY = AK" L-where 0 < a < 1, A > 0, K 2 0, and L 2 0:(a) Derive the equation for the marginal product of capital. Show your work.(b) Can the marginal product of capital be negative in an economy described by theCobb-Douglas production function? Briefly explain.

Cobb Douglas Production function: Y = AKα L1-α. Where Y is output; A is total factor productivity; K…

Answered: 4. Given the equation for the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 2: Consider the following production function that depends only on labor:Q = 2L+6L² - 3L³ 1. Compute the APL (average product of labor). 2. Compute the MPL (marginal product of labor). 3. What is the value of L* at which APL is the highest? 4. For L > L*, which one is bigger, APL or MPL? How about when I < L* and L = L* ? 5. Draw APL and MPL on the y-axis as a function of L on the x-axis. Label the point of the intersection of APL and MPL.
4. Assume that the production function is Q = 2√KL. Label the isoquants in the diagram below to reflect this production function. Capital (K) 4 0 4 9 Labor (L) 2
Company Z has the following data corresponding to the production function. Where (L) is the amount of the labor factor and (K) capital. Q=K0.4 L 0.6 a) Calculate the amount of production, applying the production function for each of the respective values of K and L. K L Q 10 80 30 160 50 320 70 640 90 1200 a) Graph the amount of production obtained on the Y axis, and with the labor input on the Х аxis b) Draw isoquant lines for each level of production, placing capital on the Y axis and labor on the X axis, to better appreciate the displacement.
3. The Chipper Cookie Company's output is given by the Cobb-Douglas Production function P = 120L0.7 K0.3, where P is the number of units produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 600 and K = 600? b. Find the marginal productivities. c. Evaluate the marginal productivities with L= 600 and K = 600. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $1200 then there is a constraint L+ K = 1200. Use Lagrange multipliers (^) to find the values of L and K that will maximize production and find the maximum production f. Find and interpret 2 for this problem. only need part e and f!
1. What should the firm do if the marginal product obtained from the last dollar spent on capital is smaller than the marginal product derived from the last dollar spent on labor and why? Graphically illustrate.
5. A company that produces auto parts has a production function of Q = 300 L-75 K-5. %3D If L= 250 and K= 25, what is the output of auto parts? If L increases to 350, what is the output of auto parts? What does the change in output show regarding labor as a factor of production?
Refer to the graph shown. Within which section(s) of the production function is marginal product decreasing? A B C Number of workers O Band C O A O B O A and B Output
You have been doing research for a firm andhave discovered that the firmâ€™s averageproduct of capital is decreasing. If capital is the onlyvariable input, what does this imply about the firmsmarginal product of capital?
Pls explain in simplest way how the marginal product of labor and the average product of labor change as the quantity of labor employed increases (a) initially and (b) eventually
4. At Alan's landscaping firm, labor is fixed in the short run. Increasing his use of capital always leads to additional output and his production function exhibits both increasing and diminishing marginal returns to capital at different points. Using a two-panel diagram, sketch the marginal, average, and total product of canital at Alan's firm. Your diagram does not need to be to scale, but must be internally consistent and consistent with both the information given and economic theory. Explain your diagram and the relationship between the different curves.
The Cobb-Douglas production function with output Q and capital and labor inputs K and L, respectively, is given by: Q = f(K,L) = K«LB where 0 < a <1 and 0
4

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