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![(a) Consider the production function Y = [(ALL)P +(AH H)P]/P, where
Y is output, L is low-skilled labour, H is high-skilled labour, and
AL and AH measure the productivity of the two types of labour.
Assuming that labour markets are perfectly competitive, derive the
wage for high-skilled labour, and discuss how it varies with L and H.
How is this related to Q-complementarity between L and H?
(b) Derive the ratio of high-skilled wages to low-skilled wagesw = WH/WL.
How does an increase in AH affect w? Does it matter if L and H
are gross complements or substitutes? What do Katz and Murphy
(1992) conclude about this issue empirically, and how?
(c) Explain what Tinbergen's "Race Between Education and Technol-
ogy" is, and how it is related to your previous answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7686321c-dfa2-4dd5-977c-dd58c3cfde24%2Fa14e270e-c551-43e9-8180-37c84f40c98d%2Fqqcghsk_processed.jpeg&w=3840&q=75)
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- Production Function. Consider the Cobb-Douglas production function discussed in class:F(K, L) = AK1/3 L2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. D) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-ment on how and why these numbers changed relative to (c) and why they did so.a) ChrisNaan Company produces fruit smoothies for students at the University of Ghana. Suppose its production function is given by y = LK/10, where L and K are labour and capital, respectively. Suppose the factor prices are w = 10, and r = 100, where w and r are wages and rental cost, respectively. i. Find the marginai product of labour and capital. ii. What is the marginal rate of technical substitution? iii. Now suppose that under a new scheme introduced by the Government of Ghana to ehcourage fruit intake by students, ChrisNaan Company is provided with an amount of C2,000,000 as cost for the programme. Determine the maximum quantity of fruit smoothies that can be produced by ChrisNaan Company. %3DAnimoSpace Support ? Question 4 Given the isocosts and isoquants of various quantities of labor and capital in the ficure below, which of the ff. is correct? Сapital TC4 TC3 TC2 MP IP = M TC K* R° ISO3 ISO? ISOI Labour L* Quantity that can be produced at ISO3 is less than the quantity that can be produced at ISO2 sr O Ris the combination of L&K that minimizes cost O At least 2 of the choices O None of the Choices O TC3>TC1 a No new data to save. Last checked at 7:59pm o search PrtSc Del F6 F7 F8 F9 F10 Fl1 F12 F2 F3 F4 F5 A+ Pause Scr Lk SysRq Ins #
- Production Function. Consider the Cobb-Douglas production function discussed in class:F(K, L) = AK^1/3 L^2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. d) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-ment on how and why these numbers changed relative to (c) and why they did so. E) Suppose that the quantity of capital K doubles as well. (So now both K and L aretwice their previous value). Calculate Y, w, r, Y/L, and K/L. Comment on how thesenumbers changed relative to both their initial values, and their values in (d).Consider a firm that produces output using a typical production function as discussed in the course, and that hires workers in a competitive labor market. 1. Explain what determines the firm's choice of its labor input. Use a suitable figure. Discuss how changes in the capital stock and in the wage affect the firm's choice of its labor input. Suppose that the firm uses a Cobb-Douglas production function Y = K"N-«. In this case, the marginal product of labor is given by (1 – a)K“N-«. The parameter a is 2/3, and the firm uses one unit of capital. 2. Calculate (show your steps) how the firm's labor input changes if the wage increases by 1%. 3. Calculate how the firm's labor input changes if the wage is unchanged, but the firm decides to double its capital stock.A firm has the production function, Q=15L^1/3 K^2/3 where ? is output, ? is labour units and ? is capital units. Calculate and interpret the degree of homogeneity. If labour and capital units increase by 5%, what is the percentage change in output?
- Consider the following production function: q = 9LK + 6L² – Assuming capital is measured on the vertical axis and labor is measured on the horizontal axis, determine the value of the marginal rate of technical substitution when K= 30 and L= 10. MRTS = -. (Enter a numeric response using a real number rounded to two decimal places.) 20 tv MacBook Air F6 FB 10 F3 23 2$ & з 4 6 7 8 { [ E Y U P D F G J K > C V N M command option - .. .- B8. In the constant elasticity of substitution (CES) production function q = A[SKP +(1-8)LP]/P, find the degree of homogeneity of the marginal product of capital MPk and the marginal product of labour MP,. Show also that Euler's Theorem applies. 9. Find the global maximum and minimum values of2. Consider the production function given by Y= altbK. The prices of labor and capital are wLand wK, respectively. a. Find the conditional input demand for L and K b. Find the cost function C. How will an increase in wk affect the labor demand in a? Show graphically d. If K is fixed at 10, find the conditional labor demand
- 5 Supposing that a single consumer works for a firm, the quantity of labor input for the firm, N, is identical to the quantity of hours worked by the consumer, h - l. Graph the relationship between output produced, Y on the vertical axis and leisure hours of the consumer, l, on the horizontal axis, which is implied by the production function of the firm. (In Chapter 5, we refer to this relationship as the production possibilities frontier.) What is the slope of the curve you have graphed? PLEASE DO NOT COPY OTHER PEOPLE'S WORK AND GRAPHSuppose that a firm has production function f(K, L) = K2a + Lª where a > 1. Assume that PK = PL where pk is the price of capital per unit and på is the price of labour per unit. If the firm is producing at an optimal point then which of the following can we conclude? The firm will use equal quantities of capital and labour. The firm will use twice as much capital as labour. O The marginal rate of technical substitution will equal the price ratio. O The firm will only use capital in production. O More than one of the above.Suppose the production function is given by Q=K1/2L1/2, and that Q=30 and K = 36. How much labor isemployed by the firm?A. 49 B.6 C.36 D.25
