Suppose we interpret capital to include human capital as well knowledge as capital. Hence, production function can be simplified as Y = AK. The term for capital K already includes labor as human capital as well as knowledge as capital. Show that this production function does not exhibit diminishing MPK. Give arguments why capital which includes knowledge may not exhibit diminishing returns in this setting?
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- 6. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q = K'2 L12 where K is capital (for example nest boxes, cages the like) and L is parrot food. The price of K is $8 and the price of L is $2. and d. Does capital obey the "law of diminishing returns?" Explain. e. Suppose that Duane wants 144 parrot chicks, how much K and L should be employed to minimize costs, and what is the cost of producing 144 parrot chicks? f. Suppose that Duane is faced with the same problem as in (f) except that he has a fixed amount of K. In fact, K = 16. How much L should be employed to minimize costs, and what is the total cost?Consider the production function Y = K1/2 N12 a. Compute output when K = 49 and N = 81 %3D b. If both capital and labor double, what happens to output? c. Is this production function characterized by constant returns to scale? Explain. d. Write this production function as a relation between output per worker and capital per worker. e. Let K/N = 4. What is Y/N? Now double K/N to 8. Does Y/N double as a result? f. Does the relation between output per worker and capital per worker exhibit constant returns to scale? g. Is your answer to f. the same as your answer to c.? Why or why not?Consider the production function Y=K1/2 N1/2 a. Compute output when K=37 and N=80 b. If both capital and labour double, what happens to output? c. Is this production function characterized by constant returns to scale? Explain. d. Are there decreasing returns to capital? Explain. e. Are there decreasing returns to labour? Explain. f. Write this production function as a relationship between output per worker and capital per worker. Show all your work. g. Let capital per worker be 6. What is output per worker? Now, double capital per worker to 12. Does output per worker more or less than double? h. Does the relation between output per worker and capital per worker exhibit constant returns to scale? Explain/show your work
- If capital and labour are perfect complements then the marginal products of capital and labour are undefined A True Faise Question 16 A firm uses 10 units of labour and 20 units of capital to produce 10 units of output. The marginal product of labour is 0.5. If there are constant returns to scale the marginal product of labour must be 0.25 True B False Question 17 Afirm uses 10 units of labour and 30 units of capital to produce 10 units of output. The marginal product of labour is 05. If there are constant returns to scale the marginal product of labout must be 0.25 A True FalseConsider the following diagram of the per-worker production function (output per worker as a function of capital per worker) Production function Capital equipment per worker (S thousands) Which 2 of the following statements are correct? Select one or more: O a. The higher capital per worker is, the higher the marginal product of capital is. O b. The diagram is consistent with the diminishing marginal product of capital. Oc. 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 (S thousands)Question 7 According to the production model, what happens if there is an increase in total factor productivity and simultaneously a decrease in population? capital per worker does not change output per person decreases O capital per worker decreases output per person increases D Question 8 In the production model, an increase in the exogenous supply of labor, from L to L'.L'> L) causes which of the following in the labor market: O An shift to the left of the supply of labor curve and an upward movement along the demand for labor curve, so wages increase. A shift to the right in the demand for labor curve and an upward movement along the supply of labor curve, so wages increase. O Ashift to the right of the supply of labor curve and a downward movement along the demand for labor curve, so wages fall O Ashift to the left in the demand for labor curve for labor and a downward mavement along the supply of labor curve, so wages fall,
- Labor productivity tends to fall as the capital to labor ratio rises. O a. True O b. False1. Consider the production functions for good X and good Y: X = K? +L ; Y= 20VKL A. Show and discuss which production function(s) exhibit(s) diminishing marginal productivity of labor and capital. B. Show and discuss which production function(s) exhibit(s) diminishing MRTSLK. C. Suppose capital and labor are doubled, solve for the returns to scale of each production function, and interpret your results.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)
- Units of Units of Labor, L Capital, K 1 2 3 4 1 50.0 66.7 75.5 80.0 2 66.7 100.0 120.0 133.3 3 75.0 120.0 150.0 171.4 4 80.0 133.3 171.4 200.0 This table illustrates a production function because capital and labor long-run; are used in equal increments short-run; can both be varied O long-run; can both be varied short-run; are used in equal incrementsSuppose the production function is given by O = 5K - 2L What is the marginal product of the 6th capital when 5 units of capital and 10 units of labor are employed? A.5 b. 4 C. 11 d. 45Suppose that the production function is What is the average product of labor AP₁, holding capital fixed at Â? O A. APL =q/L. B. AP₁ = L-0.50 0.50 APL = 0.50L-0.500.50 D. Both a and b. E. All of the above. q=L0.50 0.50