In the mathematical formulation of the short-run production function: O the quantity of output is usually assumed to be fixed. the quantity of capital employed is usually assumed to be fixed. O the quantity of both labor and capital must be allowed to vary so that output can vary in the short run. the quantity of both labor and capital employed are usually assumed to be fixed.

In the mathematical formulation of the short-run production function: O the quantity of output is usually assumed to be fixed. the quantity of capital employed is usually assumed to be fixed. O the quantity of both labor and capital must be allowed to vary so that output can vary in the short run. the quantity of both labor and capital employed are usually assumed to be fixed.

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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The production function is the relationship between the maximum amount of output that can be produced and the inputs required to make that output. Comment.
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Question 3: Consider the following production function: Q = ALa K¹. Assume A > 0. Further assume 0 < a < 1, and 0 < b < 1. 1. What is the Marginal Product of Labor (MPL)? Is it diminishing as L increases? What is the Marginal Product of Capital (MPK)? Is it diminishing as K increases? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (APK)? 3. What is the TRSL,K? Is the absolute value of TRSL,K diminishing in K? Is it diminishing in L? 4. Are there constant, decreasing, or increasing returns to scale? How does this depend on the parameters?
Include correctly labeled diagrams, if useful or required, in explaining your answers. A correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. If the question prompts you to “Calculate,” you must show how you arrived at your final answer. A firm’s short-run production function shows the relationship between the firm’s input and output. Assume the firm uses one variable input, labor, and one fixed input, capital. The following table shows short-run production function for a firm that produces widgets. Quantity of Labor Total Product 0 0 1 6 2 14 3 24 4 32 5 39 6 42 (a) Calculate the marginal product of the sixth worker. Show your work. (b) Does the production function exhibit diminishing returns to labor? Explain. (c) When marginal product is falling, what happens to marginal cost?
Include correctly labeled diagrams, if useful or required, in explaining your answers. A correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. If the question prompts you to “Calculate,” you must show how you arrived at your final answer. A firm’s short-run production function shows the relationship between the firm’s input and output. Assume the firm uses one variable input, labor, and one fixed input, capital. The following table shows short-run production function for a firm that produces widgets. Quantity of Labor Total Product 0 0 1 6 2 14 3 24 4 32 5 39 6 42 (a) Calculate the marginal product of the sixth worker. Show your work. (b) Does the production function exhibit diminishing returns to labor? Explain. (c) When marginal product is falling, what happens to marginal cost? (e) on a single correctly labeled graph, draw the firms short run average total cost curve (ATC), average variable cost…