Suppose that your production process is characterized by the production function x = f(e) = 100 In (€ + 1). For purposes of this problem, assume w> 1 and p > 0.01. a. Set up your profit-maximization problem. b. Derive the labor demand function. C. The labor demand curve is the inverse of the labor demand function with p held fixed. Can you demonstrate what happens to this labor demand curve when p changes?

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Chapter1: Making Economics Decisions
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B. Suppose that your production process is characterized by the production function
x = f(e) = 100 In ( + 1). For purposes of this problem, assume w > 1 and p > 0.01.
a.
Set up your profit-maximization problem.
b.
Derive the labor demand function.
C.
The labor demand curve is the inverse of the labor demand function with p held fixed. Can you
demonstrate what happens to this labor demand curve when p changes?
d. Derive the output supply function.
e.
The supply curve is the inverse of the supply function with w held fixed. What happens to this
supply curve as w changes? (Hint: Recall that In x = y implies e' = x, where e ≈ 2.7183 is
the base of the natural log.)
f.
Suppose p = 2 and w
profit will you make?
=
10. What is your profit-maximizing production plan, and how much
Transcribed Image Text:B. Suppose that your production process is characterized by the production function x = f(e) = 100 In ( + 1). For purposes of this problem, assume w > 1 and p > 0.01. a. Set up your profit-maximization problem. b. Derive the labor demand function. C. The labor demand curve is the inverse of the labor demand function with p held fixed. Can you demonstrate what happens to this labor demand curve when p changes? d. Derive the output supply function. e. The supply curve is the inverse of the supply function with w held fixed. What happens to this supply curve as w changes? (Hint: Recall that In x = y implies e' = x, where e ≈ 2.7183 is the base of the natural log.) f. Suppose p = 2 and w profit will you make? = 10. What is your profit-maximizing production plan, and how much
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