Exercise 2 A firm has the single-input production function q(L) = 12L² - 21³. a) What is the average product of labor, APL. 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 to labor is zero, = 0] dAPL dL c) What is the marginal product of labor, MPL.
Exercise 2 A firm has the single-input production function q(L) = 12L² - 21³. a) What is the average product of labor, APL. 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 to labor is zero, = 0] dAPL dL c) What is the marginal product of labor, MPL.
Chapter1: Making Economics Decisions
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f0128e8-6553-498c-afa0-dd14e88e258d%2F8cfc1a29-917d-4a25-b12b-dbb62e919319%2F824g9xil_processed.jpeg&w=3840&q=75)
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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