1. A firm's production technology is Y = A * K^0.25 * L^0.75, where the technology level A=8. For such a production function the marginal product of capital is MPK = 0.25 * 8 * K^-0.75 * L^0.75 The firm is stuck with K=81 but is flexible on workers. If the price of the firm's output is P=20 and the cost of a unit of capital is R=8.33, how many workers should the firm have? Round your answer to the whole worker. The answer is 10. I just need to know how to solve it

1. A firm's production technology is Y = A * K^0.25 * L^0.75, where the technology level A=8. For such a production function the marginal product of capital is MPK = 0.25 * 8 * K^-0.75 * L^0.75 The firm is stuck with K=81 but is flexible on workers. If the price of the firm's output is P=20 and the cost of a unit of capital is R=8.33, how many workers should the firm have? Round your answer to the whole worker. The answer is 10. I just need to know how to solve it

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter7: Proudction Costs

Section: Chapter Questions

Problem 3SQP

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1. A firm's production technology is Y = A * K^0.25 * L^0.75, where the technology level A=8. For such a production function the marginal product of capital is MPK = 0.25 * 8 * K^-0.75 / L^0.75 The firm is stuck with K=81 but is flexible on workers. If the price of the firm's output is P=20 and the cost of a unit of capital is R=8.33, how many workers should the firm have? Round your answer to the whole worker.
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1. Assume that a firm has the following production function: q = L0.5K0.6 a. Calculate output when L = 64 K = 32. b. What returns to scale does this production function exhibit? c. Calculate output if technology utilized by the firm increases by 25%. d. Determine, both, the marginal product of labour and capital functions (ignore c.). e. Calculate, both, the marginal product of labour and capital when L = 64, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 64, K = 32 and interpret your answer.
Question 1. Suppose a small firm employs Capital (K) and labour (L) at its production of output. The production function of the firm is: q = -56³ + 10L²K + 100LK0.5. Assume that K-25 in the short run. a. What is its short-run production function? b. What are the firm's marginal product of labour and average product of labour in the short run? c. In the short run, when marginal output is maximized, what is the value of L? d. Calculate the short-run elasticity of output with respect to labour when L=10 and K-25 (Hint: the firm's elasticity of output with respect to labour in the short run is a function of marginal product of labour and average product of labour)
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A firm’s production function is given by q = min{M, L1/2}, where M is the number of machines and L is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit. a. Is this technology decreasing return to scale? Show your argument. b. Is it true the statement that if average production cost is increasing, a firm’s technology exhibits the decreasing return to scale. (If yes, show the proof. If not, show a counter example) c. Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)
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