17. Consider q is output level, K is capital input and L is labour input. In the short run, capital input is fixed at Ko. Labour input varies from 0 to 5. Production function is given by q = K LP. (a) Suppose a =B=0.5. Calculate the short-run outputs when labour input is 0, 1, 2, 3, 4, and 5 respectively. Calculate the total product and then use the total product values to calculate the marginal product and average product. Indicate whether or not marginal product is diminishing. (b) Suppose a = B = 0.5. Does this production function exhibit constant, increasing or decreasing returns to scale? Using the definition of returns to scale to explain. (c) Suppose a = ß= 1. Does this production function exhibit constant, increasing or decreasing returns to scale? Using the definition of returns to scale to explain. (d) Initially, L = K = 1. If the production function exhibits constant returns to scale, and a = 0.2, what is the value of ß?
17. Consider q is output level, K is capital input and L is labour input. In the short run, capital input is fixed at Ko. Labour input varies from 0 to 5. Production function is given by q = K LP. (a) Suppose a =B=0.5. Calculate the short-run outputs when labour input is 0, 1, 2, 3, 4, and 5 respectively. Calculate the total product and then use the total product values to calculate the marginal product and average product. Indicate whether or not marginal product is diminishing. (b) Suppose a = B = 0.5. Does this production function exhibit constant, increasing or decreasing returns to scale? Using the definition of returns to scale to explain. (c) Suppose a = ß= 1. Does this production function exhibit constant, increasing or decreasing returns to scale? Using the definition of returns to scale to explain. (d) Initially, L = K = 1. If the production function exhibits constant returns to scale, and a = 0.2, what is the value of ß?
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 5E
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Transcribed Image Text:17. Consider q is output level, K is capital input and L is labour input. In the short run,
capital input is fixed at Ko. Labour input varies from 0 to 5. Production function is
given by q = K LP.
(a) Suppose a =B=0.5. Calculate the short-run outputs when labour input is 0,
1, 2, 3, 4, and 5 respectively. Calculate the total product and then use the
total product values to calculate the marginal product and average product.
Indicate whether or not marginal product is diminishing.
(b) Suppose a = ß = 0.5. Does this production function exhibit constant,
increasing or decreasing returns to scale? Using the definition of returns to
scale to explain.
(c) Suppose α = ß = 1. Does this production function exhibit constant,
increasing or decreasing returns to scale? Using the definition of returns to
scale to explain.
(d) Initially, L = K = 1. If the production function exhibits constant returns to
scale, and a = 0.2, what is the value of ß?
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