apital equipment per worker ($ thousands) g statements are correct? e function is the marginal product of capital. vs that higher capital per worker increases output per worker. vs that each extra $ of capital per worker raises output per worker by an equal ar "convex" (i.e., it has a slope which increases as capital per worker rises)

apital equipment per worker ($ thousands) g statements are correct? e function is the marginal product of capital. vs that higher capital per worker increases output per worker. vs that each extra $ of capital per worker raises output per worker by an equal ar "convex" (i.e., it has a slope which increases as capital per worker rises)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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Production function Capital equipment per worker ($ thousands) Which 2 of the following statements are correct? Select one or more: Ja. The figure shows that higher capital per worker increases output per worker. b. The figure shows that each extra $ of capital per worker raises output per worker by an equal amount. O c. The function is "convex" (i.e., it has a slope which increases as capital per worker rises) d. The slope of the function is the marginal product of capital. Output per worker ($ thousands)
Production function Capital equipment per worker ($ thousands) Which 2 of the following statements are correct? Select one or more: O a. The figure shows that higher capital per worker increases output per worker. O b. The figure shows that each extra $ of capital per worker raises output per worker by an equal amount. O. The function is "convex" (i.e., it has a slope which increases as capital per worker rises) O d. The slope of the function is the marginal product of capital. Output per worker ($ thousands)
Suppose that production function of certain devices is determined by: q = k * L - 0.8 k2 - 0.2 L2 Where q represents annual quantity of devices produced, k represents annual quantity of capital factor, and L represents annual quantity of labor factor. (a) Suppose k = 10; draw a graph with average and total labor productivity. What is level of labor (L) factor at which average productivity reaches a maximum? How many devices are produced at that point? (b) Assuming again that k = 10, plot Marginal Product (MP) curve. At what level do we have that labor (L) factor is MP = 0? (c) Suppose capital (k) factor were to increase to k = 20. How would your previous answers change?
3. Imagine we live in a classical world. Suppose that the production function is Y = L²K², 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. 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? C.
1. Assume the following Cobb-Douglas production function: Y = 0.5K°.2 10 .8 If L=100, a. What is the marginal product of capital?e b. With your answer in (a), can you prove diminishing marginal product of capital?- c. Estimate real capital incomee
3. What are the 2 variables that the Production Function is analyzing/graphing? Why does the production function diminish over time?
4) Suppose you are a hard-working software engineer that works 2000 hours a year, which you allocate between meetings (m), learning activities (I) and working effort (e) doing actual coding tasks (m + 1 + e = 2000). a. Write down your personal production function f (m, 1, e). Briefly describe how your output depends on the three activities. b. Does your production function exhibit increasing, decreasing or constant returns to scale (at all or some output levels)? Explain. c. Suppose a new technology doubles the productivity of your coding hours but requires you to spend X hours to adopt the technology (reducing your available work hours to 2000-X). What is the maximum X that makes adopting the technology worthwhile in the first year?
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?
Consider the following diagram of the per-worker production function (output per worker as a function of capital per worker) A. Production function Capital equipment per worker ($ thousands) Which 2 of the following statements are correct? Select one or more: а. The higher capital per worker is, the higher the marginal product of capital is. b. The diagram is consistent with the diminishing marginal product of capital. O c. When workers have less capital, an increase in capital per worker has much more impact than when they already have a lot. O d. The slope of a tangent to the curve shows the marginal product of labour Output per worker ($ thousands)
. Determine the average products of capital (K) and labour (L)
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.
1. We have assumed that the production function simultaneously has constant returns to scale and diminishing marginal products. What do each of these terms mean? Is it a contradiction for a production function to feature constant returns to scale and diminishing marginal products? Why or why not?