The graph below shows a firm's isoquant for output q=30. Initially the firm produces at point A, where it employs 20 units of physical capital ("machines") and 45 workers. 90 K 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 The firm must pay $6 for each unit of physical capital it uses, and it pays $24 for each unit of labor it employs. a. Draw the firm's isocost line through point A. b. Calculate the firm's total production cost and its average total cost at point A. Show your work. c. Given the costs of capital and labor, how can we tell that point A is not the long-run profit-maximizing input mix for the firm when it produces 30 units of output? Starting at point A, does the firm want to use more labor or more capital? Explain. d. What would be the firm's long-run optimal input mix, given that it produces 30 units of output? (You might not be able to identify the optimal mix exactly, but use the graph to estimate it as best you can.) Mark the optimal input mix as point B on your graph, and explain why you think your point B would be the firm's best long-run choice. e. Calculate the firm's total production cost and its average total cost at your point B. Show your work.

The graph below shows a firm's isoquant for output q=30. Initially the firm produces at point A, where it employs 20 units of physical capital ("machines") and 45 workers. 90 K 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 The firm must pay $6 for each unit of physical capital it uses, and it pays $24 for each unit of labor it employs. a. Draw the firm's isocost line through point A. b. Calculate the firm's total production cost and its average total cost at point A. Show your work. c. Given the costs of capital and labor, how can we tell that point A is not the long-run profit-maximizing input mix for the firm when it produces 30 units of output? Starting at point A, does the firm want to use more labor or more capital? Explain. d. What would be the firm's long-run optimal input mix, given that it produces 30 units of output? (You might not be able to identify the optimal mix exactly, but use the graph to estimate it as best you can.) Mark the optimal input mix as point B on your graph, and explain why you think your point B would be the firm's best long-run choice. e. Calculate the firm's total production cost and its average total cost at your point B. Show your work.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

In the isoquant/isocost diagram to the right, suppose that the firm is producing 1,000 units of output at point A using 100 units of labor and 200 units of capital. As an outside consultant, what actions would you suggest to management to improve profits? The firm can cut costs by hiring more and less Units of capital (K) 300- 250- A 200- 150- 100- 50- B q = 1,000 0 50 100 150 200 250 300 Units of labor (L) Q ☑
Suppose a firm has a Cobb Douglas production function and is initially producing 50 units of output using a long-run cost minimizing combination of inputs. The firm increases its output to 100 units. In the short run its level of capital remains fixed at the initial level (but the amount of labor used can be changed). In the long run, both inputs can change. On a graph, with amount of labor on one axis and amount of capital on the other, illustrate the expansion path in the long run and the short run. Draw an isocost line and an isoquant through each of the three solutions (i.e. before the increase in output, in the short run after the increase in output and in the long run after the increase in output. Note that both the second and third will be on the same isoquant). Your diagram does not need to be to scale, but should indicate the correct shapes and relative positions of the curves/lines.
1. Computing labor productivity and its relationship to the demand for labor Gopher Excavators produces shovels in a small factory and sells the shovels in a competitive market. The following table shows the company's production function: Labor Output (Number of workers) (Shovels) 1 90 175. 245 4 300 325 Use the blue points (circle symbol) to plot the production function for Gopher Excavators on the following graph. ?) 400 360 Production Function 320 280 240 200 160 120 80 1 3. 4 5. LABOR (Number of workers) Calculate marginal product of labor (MPL) of each worker, and then plot the MPL curve on the following graph using the blue points (circle symbol). Note: Remember to plot each point halfway between two integers. For example, when the number of workers increases from 0 to 1, the MPL of the first worker should be plotted with a horizontal coordinate of 0.5, the value halfway between 0 and 1. Line segments will automatically connect the points. OUTPUT (Shovels) 40
Consider a production process where flowers are grown (the output) using gardeners (labor) and greenhouses (capital). The quantity of flowers grown per day with various combinations of labor and capital are shown in the table below. Suppose that each gardener is paid $180 per day and the greenhouse is rented for $300 per day. Fill in total cost in the table below. (Enter your responses as integers.) Etext pages Get more help Labor Capital Output Total Cost 0 1 0 1 1 120 2 360 480 4 5 540 570 80 a 0 1 F2 F3 F4 F5 F6 & Clear all Check answer A DII 4 F7 F8 F9 F10 F11 F12 * delete
4. Ikea Inc., a home remodeling business. The number of square feet they can remodel in a day is described by the Cobb-Douglas production function Q= F (L,K)= 4K5L0.5 where L is their number of workers and K is units of capital. The wage rate is $5 a day, and a unit of capital costs $20 a day. What is their minimum cost input combination for remodeling (Q=200) 200 square feet a day? What is the total minimum cost level? (15p)
3. The Chipper Cookie Company's output is given by the Cobb-Douglas Production function P = 120L0.7 K0.3, where P is the number of units produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 600 and K = 600? b. Find the marginal productivities. c. Evaluate the marginal productivities with L= 600 and K = 600. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $1200 then there is a constraint L+ K = 1200. Use Lagrange multipliers (^) to find the values of L and K that will maximize production and find the maximum production f. Find and interpret 2 for this problem. only need part e and f!
Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use two gumball presses and one worker to produce 1,000 gumballs per hour. a. Explain why the cost per hour of producing 1,000 gumballs is 2v + w (where v is the hourly rent for gumball presses and w is the hourly wage). b. Assume Acme can produce any number of gumballs they want using this technology. Explain why the cost function in this case would be TC = q(2v +w), where q is output of gumballs per hour, measured in thousands of gumballs. c. What is the average and marginal cost of gumball production (again, measure output in thousands of gumballs)? (show the complete formula) Draw the graph for the average and marginal cost curves for gumballs assuming v=3, w-5 (show working) Now draw the graph for these curves for v=6, w=5.( show working) Explain why these curves have shifted.
The following is a production function. 50,000- 45,000- 40,000- Draw a graph of marginal product as a function of labor. 35,000- 30,000- 25,000- Total output (Q) 20,000- 15,000- 10,000 ng 5,000- 0+ 0 200 100 300 Units of labor (L) 400 L Q 1.) Using the line drawing tool, graph the marginal product curve from 0 to 100 units of labor. Label this line 'MP Segment 1" 2.) Using the line drawing tool, graph the marginal product curve from 100 to 300 units of labor. Label this line 'MPS Note: Carefully follow the instructions above and only draw the required objects. Does this graph exhibit diminishing returns? Explain your answer. ○ A. Yes, it does exhibit diminishing returns, because the marginal product of labor decreases. B. No, it does not exhibit diminishing returns, because the marginal product of labor is zero. ○ C. No, it does not exhibit diminishing returns, because the marginal product of labor is increasing. ○ D. Yes, it does exhibit diminishing returns, because the marginal…
Sandra and Trey operate a small company that produces souvenir footballs. Their fixed cost is $2,000 per month. Each worker costs $1,000 per month. Their monthly production function for footballs is as given in the accompanying table. Quantity of labor (workers) 2. a. 0 2 3 Quantity of footballs 5 0 300 800 1,200 1,400 1,500 :) For each quantity of labor, calculate average variable cost (AVC), average fixed cost (AFC), average total cost (ATC), and marginal cost (MC). b.) On one diagram, draw the AVC, ATC, and MC curves.
Suppose you are considering hiring another worker. Also assume that you are at a firm that is operating at a point where the marginal product of labor is 5 and the price of each unit of labor is $2, and the marginal product of capital is 20 and the price of each unit of capital is $10. Should you hire another worker? If you hire another worker, what will happen to the marginal product of labor and why?
Consider the production function of the firm below. Which of the following is NOT true? The marginal product of labor at B is 70 units. The total product is increasing as inputs to production increase. The marginal product of capital at point D is 50. The marginal products of both labor and capital are always increasing.
. In the short run, labor is a hat-making firm’s only variable input. Wage rate is $5.00/hour. The firm currently employs a certain amount of labor H (hours), such that the marginal product of labor is 10 hats per worker-hour, and average product is 15 hats per worker-hour. MPL(H) = 10; APL(H) = 15. (Note: marginal and average products of labor for this firm are not constant. 10 and 15 are their values at a particular point, H, not everywhere.) What is the marginal cost of a hat for that firm?