Suppose the production function for widgets is given by:Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2(a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve.(b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point?(c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0?(d) Does this production function exhibit constant, increasing or decreasing returns to scale?

Answered: Suppose the production function for…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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Suppose the production function for widgets is given by:

Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2

(a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve.
(b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point?
(c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0?
(d) Does this production function exhibit constant, increasing or decreasing returns to scale?

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