A firm's production function is Q = 5 + 25L - .5L2 + 30K – K2, and its demand function is PQ = MRQ = d = $30. The prices of L and K are PL = $6 and PK = $12. Use Excel Solver to find the profit-maximizing and cost minimizing amounts of L and K to employ. The profit- maximizing and cost minimizing amount of L is:
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- Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of $1,500. a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in the long run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph as part a, graphically show the impact of the minimum wage on the optimal level of employment in the long run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price of capital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts the optimal levels of employment and capital in the long run. Clearly identify the resulting scale and substitution effects caused by the lower cost of capital.A firm's production function is: q= 10L1/2K1/4 where q is the firm's daily total product, L is the quantity of labor employed in hours, and K is the quantity of capital employed in units. Assume that the quantity of capital employed is fixed at 256 units. The labor market is perfectly competitive, and the current wage is $12 per hour. The firm sells its product in a perfectly competitive market and the price is $6 per unit. a. What is the firm's value of marginal product for labor? b. What is the firm's profit maximizing quantity of labor?A firm's production function is: q = 16L1/2K1/3 where q is the firm's hourly total product, L is the quantity of labor employed, and K is the quantity of capital employed. Assume that the quantity of capital employed is fixed at 125 units per hour. The labor market is perfectly competitive, and the current wage, w, is $10 per hour. The firm sells its product in a perfectly competitive market and the price is $5 per unit. a. What is the firm's value of marginal product of labor? b. What is the firm's profit maximizing quantity of labor?
- Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L − L2/(23*100), where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $5 per hour (wage plus fringe benefits). The firm faces the fixed selling price, P = $40. How much labor should the firm employ? (Round your answer to the nearest whole number.)Suppose the hourly wage rate is $17, the rental price of capital is $2 and the price of output is constant at $45 per unit. Firm's production technology is q = 4K0.25E0.75, the marginal product of employment is MPE =3K0.25E-0.25 and the marginal product of capital is MPK = K-0.75E0.75. What is firm's optimal demand of labor if firm plans to produce q=26 units of outputs in the long-run? (please keep 1 decimal place in your answer)Suppose that the production function is Yt = AtKt^(1/2) Lt^(1/2) where Yt is output, Kt is the stock of capital and Lt is amount of labor firms hire. Assume that Kt = 100, At = 2. (a) Firms in this economy maximize their profits, given by revenue net of labor costs: Yt −WtLt . Derive the firm’s labor demand curve. (b) Workers in this economy maximize their utility, given by U(Ct , Nt) = log(Ct) − Nt , where Ct is consumption and Nt is the amount of labor workers supply. Their budget constraint is Ct = WtNt . Derive the workers’ labor supply curve. (c) Calculate the equilibrium wage rate and employment in this economy using the expressions for labor demand and supply you derived above. Also calculate the total amount of output the economy produces. (d) Suppose that capital doubles, to Kt = 200. Calculate what happens to the wage rate, employment and output. Illustrate the effects of this increase in capital graphically, using a labor demand/supply diagram.
- Goleta Brewing Company hires only two types of labor, managers and brewing assistants (denoted M and B, respectively). GBC has the following Cobb-Douglas production function F(M,B) = M.5 B.5 and wants to produce 10 barrels of pale ale this week. If the wage of managers is $50 per hour and the wage of brewing assistants is $10 per hour, how many managers and brewing assistants should the firm hire (round to nearest whole number)? How does your answer change when the wage of managers decreases to $30 per hour and the wage of brewing assistants remains constant. Is this result consistent with your intuition?Suppose, the demand and supply curve in a US manufacturing firm are provided as follows: ES = 20 + 2w ED = 70 − 3w where E is the level of employment and w is the hourly wage. Let’s assume this firm shows the representative wage of the manufacturing industry. Suppose the price of each unit of capital used in this industry is $25. The price of output is constant at $50 per unit. The production function is f(E,K) = E½K ½ , so that the marginal product of labor is MPE = (½)(K/E) ½ If the current capital stock is fixed at 1,600 units, how much labor should the industry employ in the short run? How much profit will the industry earn?Given the Production function for Mwaba & Mutale Enterprises as follows: Q = f (k,l) = 300k 2l2 - k 3l3, Assuming the value of K is 5, Determine the value of L, for which APL is maximum Prove that at the point where MPL is equal to APL , APL is maximum. The value of labor input L, for which output is maximum Total output at this value of labour
- Assume in a given company the marginal productivity can be characterized by the following function MPL = 100 - L, where L denotes the number of higher workers.If the price of the good purchased by the company is 10 gel, and the workers wage is set at 600 gel. How many workers should a company hire to achieve the maximum profit? Select one a - 40 b - None c- 99 d- 60The price of factor A is GHC20 per units and the price of factor B is GHC300.00 per unit. The marginal product of factor A is 40 units and the marginal product of factor B is 60 units. Should the firm increase employment of factor A and decrease employment of factor B to minimise the total long run cost of producing existing output? ExplainConsider a firm for which production depends on two normal inputs, labor and capital, with prices w and r,respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of$1,500.a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in thelong run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph aspart a, graphically show the impact of the minimum wage on the optimal level of employment in thelong run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price ofcapital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts theoptimal levels of employment and capital in the long run. Clearly identify the resulting scale andsubstitution effects caused by the lower cost of capital. Could you please answer this question using the graphs please.
