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- Consider a price-taking firm whose production function is given by q = 3 (L-9)1/5 (K-5)1/9 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 . Enter below the value of the firm's fixed cost.A firm produces output that can be sold at a price of $10. The production function is given by Q = F(K, L) = K1/2 L1/2 If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2?If q = 4 lnL and the good is sold for $10 then if the wage rate is $5 the number of units of labor used would be............... and the wage bill (variable cost) will be ___________. a. 8, 40 b. 40, 8 c. 8, 8 d. 5, 50 e. none of the above. If the short run production function is given by q=(1/10)lnL and the price at which the good is sold is 100 then the demand for labor L is Group of answer choices a. 1/w b. 100/w c. 10/w d. unit elastic e. both c and d. f. None of the above
- 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)?A firm has the production function q=L2K The wage rate is w=55 and the rental rate is r=44. In the long run, what is the optimal quantity of labor to produce q=1,618? Round your answer to the nearest whole numberA firm produces output y using two factors of production (Inputs), Labour L and capital K. The firm's production function is f(L,K) = 1/2 In(L) + 1/2 In(K) . The wage rate w=4 and the rental price of capital r=4 are taken as parameters (fixed) by the firm. Solve the firm''s long run cost minimization problem (minimize costs subject to the output constraint ) to derive the firm's demand function for labour L = L(y) and for capital K =K(y) , and the firm's long run total cost function C=C(y).
- Suppose that at a quantity of q=20, A firms cost are as follows: MC=20, AVC=12, ATC=30. If the firm employees 12 units of capital and 10 units of labor, then the wage is a) w=30 b)w=20 c)w=18 d)w=24Only typed answer A firm has the production function Q = K^0.8L^0.2. The wage is W and the rental rate on capital is R. Derive the long-run demand functions for capital and labor. Using Lagrangian is optional.Why would a profit-maximizing firm expand the use of each input until its marginal revenue product equals the price of the input?
- Suppose a firm’s conditional factor demand functions (the inputs needed to produce q at minimum cost with prices w and q) for labor and capital are given by L(w, q, r) = 4rq and K(w, q, r) = 4wq . What is its total cost function?Suppose a firm uses two inputs: capital, K, and labour, L. The profit function is π(K, L, p, w, r) = pf(K, L) − wL − rK where p is the output price and w and r are the wage rate and rental rate respectively. (a) Evaluate the rate of change in the maximum profit function from a change in p. (b) Evaluate the rate of change in the maximum profit function from a change in w.(c) Evaluate the rate of change in the maximum profit function from a change in r.Suppose that a firm has a short-run cost function C(q) = q2 +1. Part a Find the short-run supply function of this firm. Part b Given this production function, at what output is average cost (AC) minimized?
