Consider the following production function: q=100L0.80.4 Currently the wage rate (w) is $4.00 and the price of capital (r) is $2.00. If the firm is using 20 units of capital in production, how much labor should be employed t Labor input = units. (Enter a numeric response using a real number rounded to t

Consider the following production function: q=100L0.80.4 Currently the wage rate (w) is $4.00 and the price of capital (r) is $2.00. If the firm is using 20 units of capital in production, how much labor should be employed t Labor input = units. (Enter a numeric response using a real number rounded to t

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 7E

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Given the linear production function: Log (Q) = 1.5 + 0.76 Log (L) + 0.24 Log (K) Where Q is the level of output, L is the units of labor and K is the units of capital employed. a. If one worker's wages are $30 per day, how many workers should the firm employ per unit of output? b. What is the percentage of the firm's revenue spent on labor?
Suppose the long-run production function for a competitive firm is f(L,K)= L 1/3 K 1/4 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. Fixed costs are zero. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the L-y and K-y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost and marginal cost functions, as functions of y.
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell?
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell? What will be the price of a zamboni? If the market for zambonis were competitive, how many zambonis would be produced? If the market for…
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. If the market for zambonis were competitive, how many zambonis would be produced? If the market for zambonis were competitive, how many assembly workers would be hired? If the market for zambonis were competitive, at what price would zambonis be sold?
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 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)?
The production function for a product is given by q = 10 K1/2L1/2 where K is capital, and L is labor and q is output. a) Find the marginal product of labor and the marginal product of capital. b) Find the marginal rate of technical substitution between labor and capital. c) Denote the wage of labor by w and the rental of capital by What is the cost minimization condition for a firm? Show it diagrammatically. d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d. However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?
A widget manufacturer has an infinitely substitutable production function of the form q= 2K+L a. Draw the isoquant maps on a graph for q=20, q=40, and q=60. What is the RTS along these isoquants show formula and working? b. If the wage rate (w) is $1 and the rental rate on capital (v) is $1, what cost-minimizing combination of K and L will the manufacturer employ for the three different production levels in part a? What is the manufacturer’s expansion path, draw the line on the graph? (show all working for this) c. If (v) rose to $3 with (w) remaining at $1, what cost-minimizing combination of K and L will the manufacturer employ for the three different production levels in part a? What is the manufacturer’s expansion path, draw the line on the graph? (show all working for this)
Suppose 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?
Assume a Cobb-Douglas production function in which the share of capital is a = 0.25 and the share of labor is b = 0.75. If the rental cost of capital is rc = 10%, what will the desired capital stock of a cost-minimizing firm be?
A widget manufacturer has an infinitely substitutable production function of the form q= 2K+L a. Graph the isoquant maps for q=20, q=40, and q=60. What is the RTS along these isoquants? b. If the wage rate (w) is $1 and the rental rate on capital (v) is $1, what cost-minimizing combination of K and L will the manufacturer employ for the three different production levels in part a? What is the manufacturer’s expansion path? c. How would your answer to part b change if (v) rose to $3 with (w) remaining at $1?