3. Answer all parts (a)-(e) of this question.Consider the following production function: Q = 3K&L, with marginal products given byL3MPL = Kand MPKDefine the unit prices of L and K as w and r, respectively.Finally, assume that the firm takes the price of its product, p, as given and maximizes profits.L3K3(a)Imagine capital is fixed at Ko = 1 in the short run. What is the short-run costfunction of the firm? Explain briefly.(b)(c)(d)(e)when rw = 1?What is the long-run cost function of the firm?What is the long-run supply function of the firm?What is the profit function of the firm?Now suppose that set-up costs are £1. What is the shut down rule of the firm

MPL(Marginal product of labor) is the extra/additional output that the firm receives from employing…

3. Answer all parts (a)-(e) of this question. Consider the following production function: Q = 3K3 L3, with marginal products given by MPL = Ka and MPK = Define the unit prices of L and K as w and r, respectively. Kś Finally, assume that the firm takes the price of its product, p, as given and maximizes profits. L3 (a) Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost function of the firm? Explain briefly. What is the long-run cost function of the firm? What is the long-run supply function of the firm? What is the profit function of the firm? (b) (c) (d) Now suppose that set-up costs are £1. What is the shut down rule of the firm (e) when r = w = 1?

3. Answer all parts (a)-(e) of this question. Consider the following production function: Q = 3K3 L3, with marginal products given by MPL = Ka and MPK = Define the unit prices of L and K as w and r, respectively. Kś Finally, assume that the firm takes the price of its product, p, as given and maximizes profits. L3 (a) Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost function of the firm? Explain briefly. What is the long-run cost function of the firm? What is the long-run supply function of the firm? What is the profit function of the firm? (b) (c) (d) Now suppose that set-up costs are £1. What is the shut down rule of the firm (e) when r = w = 1?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.3P

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A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm’s production function is:X=-0.2L3 + 18L2 + 1620L.Where X is the number of units of the product per week, and L is the number of persons employed.A. A t what weekly output is marginal cost equal to average variable cost?B. if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?
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