d) How much should the firm to produce to maximize marginal product of labor? [Hint: MP₁ curve is maximized when its slope is zero. That is, when derivative of MP, with respect to dMPL dL labor is zero, = 0] e) At what level of labor do the marginal product and average product curves cross? [Hint: The AP and MP, cross at the point at which AP, reaches its maximum - Two curves cross at the point they are equal] f) How much should the firm produce to maximize total product? [Hint: Total product curve is maximized when its slope is zero. That is, when the derivative of q (L) with respect to labor is zero, dq (L) dL = 0]

Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter7: Production And Cost In The Firm
Section7.A: Appendix: A Closer Look At Production And Cost
Problem 1AQ
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Show full answers to part d), e) & f)
Exercise 2
A firm has the single-input production function q(L) = 12L² - - 21³.
a) What is the average product of labor, AP₁.
b) How much should the firm produce to maximized average product of labor? [Hint: AP₁
curve is maximized when its slope is zero. That is, when the derivative of AP, with respect
dAPL
to labor is zero,
0]
dL
c) What is the marginal product of labor, MPL.
=
1
d) How much should the firm to produce to maximize marginal product of labor? [Hint: MP₁
curve is maximized when its slope is zero. That is, when derivative of MP, with respect to
labor is zero, dMPL = 0]
dL
e) At what level of labor do the marginal product and average product curves cross? [Hint:
The AP, and MP, cross at the point at which AP, reaches its maximum - Two curves cross
at the point they are equal]
f) How much should the firm produce to maximize total product? [Hint: Total product curve
is maximized when its slope is zero. That is, when the derivative of q(L) with respect to
0]
labor is zero,
dq (L)
dL
Transcribed Image Text:Exercise 2 A firm has the single-input production function q(L) = 12L² - - 21³. a) What is the average product of labor, AP₁. b) How much should the firm produce to maximized average product of labor? [Hint: AP₁ curve is maximized when its slope is zero. That is, when the derivative of AP, with respect dAPL to labor is zero, 0] dL c) What is the marginal product of labor, MPL. = 1 d) How much should the firm to produce to maximize marginal product of labor? [Hint: MP₁ curve is maximized when its slope is zero. That is, when derivative of MP, with respect to labor is zero, dMPL = 0] dL e) At what level of labor do the marginal product and average product curves cross? [Hint: The AP, and MP, cross at the point at which AP, reaches its maximum - Two curves cross at the point they are equal] f) How much should the firm produce to maximize total product? [Hint: Total product curve is maximized when its slope is zero. That is, when the derivative of q(L) with respect to 0] labor is zero, dq (L) dL
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