A firm estimates its long-run production function to be Q = -0.0050 K³L³ + 15 K²L² Suppose the firm employs 10 units of capital. At product of labor begins to diminish. A) 150 B) 66.67 C) 1000 D) 100 E) 200 units of labor, marginal

1. For each of the following production functions, (a) F(L, K) = LK³ (b) F(L, K) = L+3K (c) F(L, K) = (min{L, K})³ i. Sketch a representative isoquant. ii. Calculate the marginal product for each input, and indicate whether each marginal product is diminishing, constant, or increasing. iii. Calculate the marginal rate of technical substitution for each function. iv. Also indicate whether the function exhibits constant, increasing, or diminishing returns to scale.

Suppose a chair manufacturer maintains the existing plant and equipment. The manufacturer has observed the following levels of production corresponding to different numbers of workers: Number of Workers Number of Chairs 1 10 2 18 3 24 4 28 5 30 28 7 25 a. Calculate the average and marginal product of labor for this production function. APL MPL - 1. 10 2 18 3 24 4 28 5 30 6 28 7 25 b. Does this production function exhibit diminishing returns to labor? Explain. c. Explain intuitively what might cause the marginal product of labor to become negative.

For a production function that exhibits diminishing marginal product:
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a. Marginal product is typically below average product b. Average product is typically below marginal product c. Average product is typically equal to marginal product d. Both marginal and average product must be zero

Suppose that a firm's production function is: 112 q= 10L05K0.5 98 Its marginal product functions are: 84 MP =5KL05 = 0.5q/L and 70 MP 5L05K5 =0.5g/K. The cost of a unit of labor, w, is $20 and the cost of a unit of capital, r, is $80 Isoquants for output of 140 and 280 are illustrated in the figure to the right 42 20 Initially, the firm is producing 140 units of output and has dotermined that the cost-minimizing quantities of labor and capital are 28 and 7, respectively. 14+ Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? 9. 14 25 42 04 LUnits of labor The firm will now require units of labor. (Enter your response rounded to two decimal places. ) K Unts of capta

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a) Determine whether the following production functions exhibit increasing, constant, or decreasing returns to scale. • F(K, L) = 4 K0.$L0.6 • F(K, L) = AK0³L04 b) Calculate the marginal product of labor (MPL) for the production function of the following form: Q = 10L0.75K©25

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Suppose that a firm's production function is: q=10L0.50.5 Its marginal product functions are: and MPL = 5K0.5/0.5 = 0.5q/L MPK-5L0.50.5 =0.5q/K. The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require 56.00 units of labor. (Enter your response rounded to two decimal places.) K If the marginal rate of technical substitution is find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is ☐ units. (Enter your responses as integers.) K, Units of capital 112 98- 84-…

When Marginal Product of Labor intersects the Average product of labor, minimum average product of labor obtains at the intersection. True False