5 föt the factors of production be labor and capital equipment. A competitive firm is facing the followinginput prices: the wage rate is wi = $8 per hour and the rental rate of capital is w2 = $16 per hour. Atthe current input mix the marginal product of labor is 24 and that of capital is 32. Should the firmchange its input mix? Why?

Cost is minimized where the right combination of labor and capital is used. following is the…

Answered: Let the factors of production be labor…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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12. A firm’s production is represented by the following function: Q = L0.4 K0.6 . The rental rate of capital (r) is $30 and the wage rate (w) is $5. For a given level of output, what should be the ratio of capital to labor in order to minimize costs? How much capital and labor should be used to produce 600 units of output? What is the total cost? What is the short run total cost if output is decreased to 300 units? What would be the optimal choice of capital and labor in the long run in order to produce 300 units of output? What is the long-run total cost? Does this production function exhibit increasing, decreasing, or constant returns to scale? Please answer based on the cost calculations in parts c and d.
A production function for a good Q uses inputs of labor (L) and capital (K) and takes the form Q=LK. The wage is equal to $20 and the rental rate of capital is equal to $80. The firm has to produce a target qo. What is the equation for the firm's long-run total cost curve?
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Marginal cost is the one more unit of a good and opportunity cost of producing increases as production O price that must be paid to consume; decreases as consumption O opportunity cost of producing: decreases as production O price that must be paid to consume; increases as consumption of the good increases.
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Economics A firm has the production function q = K0.25L0.25 , where K is capital, L is labor, and q is output. The price of capital is v = 4 and the price of labor is w = 4. [You may need this result: if Yα = Z. Then Y = Z1/α]. (i) Derive the firm’s short-run cost function if capital is fixed at K = 16. (ii) Derive the firm’s long-run cost function. (iii) Someone claims that the firm’s
14. The research department of Acme, Inc. has determined the marginal cost function for one particular item to be m(x) = 0.12e0.04x dollars per item, where x is the number of items produced. If Acme's fixed costs amount to $3,000, find the cost function, C(x), for the company.
4. Ikea Inc., a home remodeling business. The number of square feet they can remodel in a day is described by the Cobb-Douglas production function Q= F (L,K)= 4K5L0.5 where L is their number of workers and K is units of capital. The wage rate is $5 a day, and a unit of capital costs $20 a day. What is their minimum cost input combination for remodeling (Q=200) 200 square feet a day? What is the total minimum cost level? (15p)
Sugar Enterprises manufactures high speed personal computers as its main product line. Its short run production function is given by Q = 3600K - 4.5K² where Q is the number of computers produced in a week and K pertains to the number of units of capital. c.) Compute the marginal product of the 200th unit of capital. d.) How many computers can be produced by the firm in a week if there are 200 units of capital? e.) Compute the marginal product of the 300th unit of labor. f.) How many computers can be produced by the firm in a week if there are 300 units of labor?
Consider the "Cobb-Douglas" production function given by Y = AKº L¹-a where A> 0 and 0 < a < 1. Which of the following is FALSE? The marginal product of capital is positive The marginal product of labour is positive There is diminishing returns to capital O There is decreasing returns to scale

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Let the factors of production be labor and capital equipment. A competitive firm is facing the input prices: the wage rate is wi = $8 per hour and the rental rate of capital is w, = $16 per