2. A seller's production function is q = f(k,1) = (kl), w = v = 1, and the competitive output price is P. For all parts going forward, assume we are in the long run and all inputs are variable. e. Find the profit-maximizing q. f. Find unconditional demand for labor. g. Find the profit function.
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- 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 aboveSuppose the firm is hiring labor and capital and that the ratio of marginal products of the two inputs equals the ratio of input prices. Does this imply that the firm is maximizing profits? Why or why not?7. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What are the demand functions for labor 1(v,w.p) and capital k(v,w,p)? [Show your work] 8. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What is the supply function q(v,w,p)? [Show your work]
- 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=.......... Group of answer choices a. 1/w b. 100/w c. 10/w d. 50/w e, None of the aboveA firm uses labor (L) and capital (K) to produce rocking chairs (Q) with the following production function Q=LK. The wage (w) is $10 and the rate of capital (r) is $20. The target number of rocking chairs to produce is 800. It is the short run and the amount of K is fixed at 5. What the optimal values for L* and K* in the short run? Enter the number for the the optimal amount of L in the short run? Enter the number for the the "optimal" amount of K in the short run?Consider the following shortrun production function: (Q=100L- L*L), where Q is the output level and L is labour input If the price of output in the market is K.sh 50 and labour costs K.sh 1200 per hour, how many hours would the firm use to maximize profits. What is the profit maximizing level of output?
- A competitive firm produces its output, y according to the production function: y = F(K, L), where K and L are capital and labour inputs. Let the prices of output K and L be given by p, w, and s, respectively. Assume that K is fixed in the short run. In addition, assume that the production function exhibits constant returns to scale in K and L. Show that the firm’s short-run supply function is linear in L.Why is the long run labor demand curve more elastic than the demand for labor in the short run? Group of answer choices a. In the long run, firms are better able to substitute capital for labor than in the short run. b. Firms are more likely to shut down in the long run c. Firms face diseconomies of scale in the short run, but economies of scale in the long run d. The demand for labor is perfectly inelastic in the short run, but perfectly elastic in the long runSuppose that John is a shrubber. As a master shrubber, he hires apprentices, L, at wage w and purchases capital, K, (electric shrubbery trimmers, for example) to create his high-end shrubberies. Capital is expensive, so he generally borrows money to purchase the equipment. The cost of capital is r. John can produce shrubberies according to the production function q = 10 · K^1/4 L^1/4. We can assume John is a price taker. If wages are $10/hour, the cost of capital is $40/hour, and shrubberies sell for p = $160, how many shrubberies will John produce and sell? How much labor and capital will he purchase to produce that output? What are his profits?
- 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=24Widget factory Inc. in Wisconsin has the following production function: F(L,K)=2L L represents the number of labours hours. Workers at this factory are paid an hourly wage of $30 and they rent capital at$25/ hour.since this is a competitive market, the factory output is $50 per unit. Let's pretend the firm operates in the short run with capital fixed at 900, how many workers would widget factory Inc employ? What is their profit rate?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.