Bonus Question 1 (6 pts) The manager of a national retailing outlet recently hired an economist to estimate the firm's production function. Based on the economist's report, the manager now knows that the firm's production function is given by Q=K0.5L0.5 and that capital is fixed at 4 units. a. Calculate the average product of labor when 9 units of labor are utilized. b. Calculate the marginal product of labor when 9 units of labor are utilized. c. Suppose the firm can hire labor at a wage of $10 per hour and output can be sold at a price of $100 per unit. Determine the profit-maximizing levels of labor and output. d. What is the maximum price of capital at which the firm will still make nonnegative profits?

Bonus Question 1 (6 pts) The manager of a national retailing outlet recently hired an economist to estimate the firm's production function. Based on the economist's report, the manager now knows that the firm's production function is given by Q=K0.5L0.5 and that capital is fixed at 4 units. a. Calculate the average product of labor when 9 units of labor are utilized. b. Calculate the marginal product of labor when 9 units of labor are utilized. c. Suppose the firm can hire labor at a wage of $10 per hour and output can be sold at a price of $100 per unit. Determine the profit-maximizing levels of labor and output. d. What is the maximum price of capital at which the firm will still make nonnegative profits?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Given the production function: q = 2KL, (a) Fill in the table below which has information on the short-run production function, the marginal product of labor (MPL), and the average product of labor (APL) if capital is held fixed at 3 units in the short-run. Labor Quantity of Output (MPL) (APL) 0 1 4 9 16 25 (b) Plot the short-run production function. (c) Plot the marginal and average products of labor on a new graph. (d) Does the law of diminishing marginal returns apply? If so, at what level of labor do diminishing marginal returns set in? (e) What is the relationship between the marginal product of labor (MPL) and the average product of labor (APL)? (f) If the amount of capital increased to 6 units, what would happen to your graphs in part C)?
Subpart 1-3
Lesson 7- Production Question 8
University level intermediate microeconomics, theory of production
Suppose the representative firm of the economy has a production function of the form F(K, N) = AKO.5N 0.5 The marginal product of labor is then given by MP N = 0.5AK0.5N –0.5 . The current capital 3. stock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some important features of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w)= 10. What is the equilibrium wage w, employment level N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w, employment level N, and full employment output Y ? (e) Depict this change graphically. Denote the original labor supply and demand curves by NS and ND respectively. Denote the new labor demand curve after the productivity shock by ND' . (Does not need to be to scale).
Problem 2 (a) Find an example of a production technology that is such that two inputs must be used in fixed proportions (hopefully a different one from the examples discussed in class). Explain why you chose this example. Draw a typical isoquant of the example you found. (b) Find an example of a production technology that is such that two inputs are completely inter- changeable. Explain why you chose this example. Draw a typical isoquant of the example you found. (c) Find an example of convexity of production technology. Explain why you chose this example. Draw a typical isoquant of the example you found.
Consider a firm that produces a good using capital and labor. We denote by L the quantity of labor and by K the quantity of capital. In the short term, the firm has a fixed amount of capital K. The short-run production function of the firm is given by f (K; L). Graphically, we measure the amount of work on the abscissa and the output on the ordinate. The average product of labor is (a) the slope of the production function. (b) the area that is below the production function. (c) Both of the above answers are correct. (d) None of the above is correct.
Problem 1: Your firm has employed an economist to estimate your firm's production function. After gathering the appropriate data, the economist estimates that your is of the form shown below. You also know that capital is fixed at 8 units in the short run. 12 Q=K³L²³ a. Calculate the average product of labor when 27 units of labor are utilized and interpret your result. b. Calculate the marginal product of labor when 27 units of labor are utilized and interpret your result. c. Suppose the firm can hire labor at a wage of $5 per hour and output can be sold at a price of $15 per unit. Determine the profit-maximizing levels of labor and output. d. What is the maximum price of capital at which the firm will still make nonnegative profits?
1. Suppose the production function is Q = 8L + 15K where Q is the quantity of output, L is the quantity of labor used in production, and K is the quantity of capital used in production. What can be said about this production function? It has Decreasing Returns to Scale It has Constant Returns to Scale It has Increasing Returns to Scale There isn’t enough information to determine the Returns to Scale for this production function 2. You’re dreaming of what to do during a nice summer day. You could mow the lawn which you would pay someone $15 to do for you. You could go for a walk which you value at $11. You could also take a nap and ignore everyone and everything else which you would pay $29 to do. If you to take a nap, what is your opportunity cost? Group of answer choices $29 $26 $15 $11
The law of diminishing marginal returns states: Select one: a. As a firm uses more of a variable factor of production, total product (TP) eventually decreases. b. As the size of a plant increases, marginal product (MP) eventually decreases. c. As a firm uses more of a variable factor of production, its average cost (AC) eventually decreases. d. As a firm uses more of a variable factor of production, with a given quantity of the fixed factor of production, the MP of the variable factor eventually decreases.
The Production Function for Wilson Company Economists at the Wilson Company are interested in developing a production function for fertilizer plants. They collected data on 15 different plants that produce fertilizer PLANT OUTPUT (TONS) CAPITAL ($) LABOUR (HOURS) 1 605.3 18,891 700.2 2 566.1 19,201 651.8 3 647.1 20,655 822.9 4 523.7 15,082 650.3 5 712.3 20,300 859.0 6 487.5 16,079 613.0 7…
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 = 10L^2 – 0.5L^3 where L is variable input labor, Q is output of Cars assembled a. Find the ranges of the three stages of production. b. Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above. c. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L^.30K^.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant.…