ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Consider an industry in which firms produce undifferentiated commodity for which
where Y is the level of output and a is some constant from (0, 1), K is the amount of capital employed, and L is the amount of labor employed. The
(a) Suppose precisely six firms are in this industry, all of which maximize profits taking prices as given. What is the equilibrium in this case?
(b) Suppose there is free entry into this industry, with all of the firms having the production function given above. What is the equilibrium in this case?
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- Suppose a firm’s production function is q= 2L+ 5K, the wage is w= 4, and the rental rate of capital is r= 8. What is the firm’s cost function C(q)?arrow_forwardA competitive firm's production function is given by y = f(K, L) = 8K 1/2 + L 1/4 Assume that the price of the good produced is p = $100, the price of capital is r = $4, and the price of labor is w = $5. Find the profit- maximizing levels of capital and labor (K * and L * ). Find the profit-maximizing level of output (y * ). What is the maximum profit of the firm (π * )?arrow_forwardSuppose the production of Scooby Snacks at x units of labor and y units of capital is given by the Cobb-Douglas production function P(x, y) = kx"y" where m, n, k are known positive constants and m+ n = 1. The company can spend only p dollars for the production of Scooby Snacks. The cost of one unit of labor is b dollars, while the cost of one unit of capital is c dollars. Using Lagrange multipliers, find an expression for x and y where maximum production will occur?arrow_forward
- Consider a firm with production function in the Cobb-Douglas form q = K^.5L^.5 Suppose that one unit of capital costs r=12.5, whereas one unit of labor costs w=8. Determine the optimal input mix that leads to an output of q = 2. Determine the firm’s cost function, that is, the minimum cost required to produce output q.arrow_forward1/3 1/3 Bridget's Widgets produces widgets with the production function, y = x1 x2, where 1 is the quantity of labor input, x2 is the quantity of capital input, and y is the quantity of output. The per-unit price of labor input is w₁ = 20 and the per-unit price of capital input is w₂ = 80. What is Bridget's long run total cost function, C(y), given that both inputs can be varied in the long run? C(y) 20/2 C(y)-80y/ C(y)-80y = ⚫ C(y)=20y³arrow_forwardSuppose a firm uses a single input to produce a single output according to a production function f(x) = 10√x where x is the number of units of input. The output initially sells for £120 per unit. The input costs £20 per unit. A change in the market causes the product price to increase from £120 per unit to £200 per unit, all else equal. How does this change in product price affect the firm's profit maximizing level of profits? a. Profits increase by £16,000 Ob. Profits do not change Profits increase by £8,000 d. None of the other answers is correct Profits increase by £9,000 f. Profits increase by £18,000 g. Profits increase by £50,000 h. Profits increase by £32,000 C. e.arrow_forward
- A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. The production function is given by: Q=60L-2L^2+180K-3K^2, where Q is total output. Determine the firm's optimal combination of capital (K) and labor (L)?arrow_forwardSuppose w= 1 and r= 3. Solve the cost minimization problem to find L*(q) and K*(q). Then find the cost function C(q).arrow_forwardConsider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for production. The price of product is $p. The production function is Q (K; L) = 4L^1/4 K^1/4 . Assume that the hourly wage of workers is fixed at $w and the price per machine is $r Write out the optimal inputs quantities, L and K, as a function of parameters, p, w, and rarrow_forward
- To minimize costs in the short run, a firm should operate where which of the following optimizing conditions is true? Marginal productivity of labor is at a maximum Marginal product relative to own price of every input is equal Marginal revenue product of the variable input equals its marginal costarrow_forwardConsider a price-taking firm whose production function is given by q = 3 L1/5 K1/9 where L and K denote respectively the amount of labour and capital the firm uses to produce q units of output. Suppose the price of labour is w = 16, the price of capital is 24 and the price of the firm's output is p=225 . Find the firm's cost function. Then enter below the value of the firm's marginal cost at the point where q = 100.arrow_forwardA profit-maximizing, perfectly competitive firm produces a single output from two inputs. The logarithm of the maximized profit function is given by: Int (p,r,w) = a, + a, In w+ a, ln r + a, In p where w, r, and p denote the price of labor, the price of capital, and the price of the firm's output, respectively. a) Derive the supply function and the demand functions for capital and labor. b) What restrictions can you place on the parameters a1, a2, and a3?arrow_forward
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