Problem 3:Write each production function given below in terms of output per person y =Y/L and capital per person k = K/L. Plot these per person versions in a graphwith y on the vertical axis and k on the horizontal axis. (You can assume Ã isa constant positive number).(a) Y=AK 1/3 L2/3 and Y = AK3/4L1/4 (plot them on the same graph).(b) Y = K.(c) Y = KL(d) YK-AL

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Answered: Problem 3: Write each production…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 8E

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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?
Please give exact answer to every part step by step and take a like
A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?
5. Determine the degree of homogeneity of each of the following production function and determine the returns to scale. (HINT: The degree of homogeneity tells us a lot about returns to scale) (a) Q= a + 6xy +7y2 (b) Q = r - xy² +3y+?y (c) Q= (d) Q = 0.9K0.2 L0.6 %3D
Assume the following production function for maize: Q=3K^1.2 L^0.5, where Q is the number of bags of maize produced, K is the units of capital used and L the units of the labour employed. (a) Derive the MRTS of K and L. (b) Estimate the factor intensity of the production function and interpret results. (c) Is the above production function characterized by decreasing returns of scale? Explain
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Problem 7 This homework is about returns to scale. Labor, L, and capital, K, are the only inputs in each of the following production functions: 91 = (L+ K')² a 92 = (VI + VR)* b (20 + VT + vR)* 93 = For each production function, use a spreadsheet to find the joutput associated with the following output combinations: L 2, K = 2; L=4, K = 4; and L= 8, K = 8. Determine whether each production unction exhibits increasing returns to scale, decreasing returns to scale, constant returns to scale, or variable returns to scale of this range.
*0.65 0.35 where x is the amount of labor and y is the amount of capital. The productivity of a country is given by f(x,y) = 100x (a) Compute the marginal productivities of labor and capital when x = 300 and y = 500. (b) Use part (a) to determine the approximate effect on productivity of increasing capital from 500 to 502 units, while keeping labor fixed at 300 units. (c) What would be the approximate effect of decreasing labor from 300 to 298.5 units while keeping capital fixed at 500 units? (a) The marginal productivity of labor is (Do not round until the final answer. Then round to two decimal places as needed.) The marginal productivity of capital is (Do not round until the final answer. Then round to two decimal places as needed.) (b) When capital is increased from 500 to 502 units, the approximate change in productivity is (Do not round until the final answer. Then round to two decimal places as needed.) (c) When labor is decreased from 300 to 298.5 units, the approximate change…
Computing levels: Suppose xt grows at 2% per year and yt grows at 5% peryear, with x0 = 2 and y0 = 1. Calculate the numerical values of zt for t = 0,t = 1, t = 2, t = 10, t = 17, and t = 35 for the following cases:(a) z = x(b) z = y(c) z = x3/4y 1/4
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Returns to scale in production: Do the following production functions exhibitincreasing, constant, or decreasing returns to scale in K and L? (Assume Ais some fxed positive number.)(a) Y = K1/2L1/2(b) Y = K2/3L2/3(c) Y = K1/3L1/2(d) Y = K + L(e) Y = K + K1/3L1/3 (f ) Y = K 1/3L2/3 + A (g) Y = K 1/3L2/3 − A

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