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- Suppose that the production function takes the form X = min(10L, 5K) and that a competitive firm faces a wage rate of £60 per week and a weekly capital rental of £32. (a) How much must the firm spend to produce 100 units of output, and what is the average cost of production when X = 100? (b) What is the incremental cost of producing the 101st unit of output? (c) What happens to the cost of producing 100 units of output if the wage rate and the rental cost of capital rise by 25 per cent each? What happens to the average and marginal cost? (d) What happens to the cost of producing 100 units of output if the wage rate increases by £1, or if the cost of capital increases by £1?A small rural hospital’s management assesses the following production and input price situation with respect to two types of labor (e.g., RNs with and without bachelor’s degrees) which can be imperfectly substituted for one another: MPL1 = 10; PL1 =5; MPL2 =4; PL2 = 4. The hospital is operating in the second stage of the production function with respect to each type of labor. If the firm wishes to minimize cost for the current output, it should: A. Make no change. B. Increase L2 and decrease L1. C. Increase L1 and decrease L2. D. Increase both inputs. E. Decrease both inputs.A firm produces output according to a production function: Q = F(K,L) = min {4K,8L}. a. How much output is produced when K = 2 and L = 3? 192 Numeric ResponseEdit Unavailable. 192 incorrect.unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: 80 Numeric ResponseEdit Unavailable. 80 incorrect. Labor: 480 Numeric ResponseEdit Unavailable. 480 incorrect. c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour? multiple choice Capital and labor increase. It does not change. Capital increases and labor decreases. Incorrect Capital decreases and labor increases.
- A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with qThe production function for a firm is: q=-0.6L3+18L2K+10L where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. b For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. Hint: you will not be able to solve the total product curve for L as a function of output. So, instead construct a table, See the headings. Use this definition ΔTC/Δq…Assume labor (L) is the only variable input used in the production process, a firm’s production function is given by Q=7L+10L2-L3 where Q represents total product. Classify the production function in to the three stages of production.
- Assume that housing output is a function of the quantities of capital (k) and land (l) employed by adeveloper, y = h(l, k), where h( ) is the housing production function. Also, assume that the developer’slong-run cost function is c = rl + ik, where r = price for a unit of land and i = price for a unit of capital.(a) Draw an arbitrary cost-minimizing scenario for this developer using isoquants and iso-costlines. Identify the cost-minimizing bundle as (l*, k*). Be sure to plot k along the y-axis. Pleaselabel your graphs. 5pt(b) Within a city, the price of capital, i, does not typically vary with a development’s distance fromthe city center. However, the price of land traditionally declines as distance from the centerrises. Using the cost-minimizing framework set up above, show how homes’ capital-to-landratios likely change as distance to the city center rises, holding housing output fixed. 5pt(c) Does your answer from above do anything to explain the differences in the types of homes…You are a manager for a company that manufactures office furniture. To estimate the production function for a particular line of office chairs, you hired an economist to work with engineering and operations experts. The report from these experts indicates that the relevant production function is ? = 2?½?½ where K represents capital equipment and L is labour.Workers at the firm are paid a competitive wage of 120 cedis per day and chairs can be sold for 400 cedis each. a. Your company has already spent a total of 8,000 cedis on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. i. Is this firm operating in the short-run or in the long-run? Explain your choice. ii. what is your profit-maximizing level of output and labour usage? iii. What is your maximum profit?Qno1.You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Required. a). Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?
- (a) Show that the production function Q = (Kα + Lα)β, where Q is output, K is capital input, L islabour input and α > 0 and β > 0 exhibits diminishing returns when α < 1 and increasing returns to scale when αβ > 1.(b) Specify a translog cost function for two inputs and show that the input shares depend on inputprices.A firm produces output according to the production function:Q = F(K, L) = 4K + 8L.a. How much output is produced when K = 2 and L = 3? unit(s)b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output?Capital: Labor: c. If the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour, what is the cost-minimizing input mix for producing 32 units of output?Capital: Labor:A firm produces output according to the following production function:Q = F (K, L) = 4K + 8L(a) How much output is produced when K = 2 and L = 3?(b) If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the costminimizing input mix for producing 24 units of output?(c) If the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour,what is the cost minimizing input mix for producing 24 units of output?
