3. Consider a firm that produces a single output Q using two inputs, q1 and 92. The production technology is the Cobb-Douglas: Let pi be the price of q₁, and p2 be the price of 92. Assume that the price of the output Q is 1. Given: Implicit function theorem Implicit function theorem. - Consider an equation F(x₁... Xm. y) = 0. If an implicit function y = f (x₁..... Xm) exists, then the desired derivatives can be found by

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter2: Mathematics For Microeconomics
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Problem 2.8P
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3. Consider a firm that produces a single output Q using two inputs, q1 and 92. The
production technology is the Cobb-Douglas:
Q = atat.
Let pi be the price of q₁, and p2₂ be the price of 92. Assume that the price of the output
Q is 1.
Given:
Implicit function theorem
• Implicit function theorem. - Consider an equation
F(x₁,..., Xm. y) = 0. If an implicit function y = f (x₁..... Xm) exists,
then the desired derivatives can be found by
Question:
ay
axi
ƏF/axi
ƏF/ay
(a)
Find the effect of an input price p2 change on the optimal quantity, qi, of
the input good 1 using the implicit function theorem.
Transcribed Image Text:3. Consider a firm that produces a single output Q using two inputs, q1 and 92. The production technology is the Cobb-Douglas: Q = atat. Let pi be the price of q₁, and p2₂ be the price of 92. Assume that the price of the output Q is 1. Given: Implicit function theorem • Implicit function theorem. - Consider an equation F(x₁,..., Xm. y) = 0. If an implicit function y = f (x₁..... Xm) exists, then the desired derivatives can be found by Question: ay axi ƏF/axi ƏF/ay (a) Find the effect of an input price p2 change on the optimal quantity, qi, of the input good 1 using the implicit function theorem.
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