3. Consider a firm that produces a single output Q using two inputs, q₁ andproduction technology is the Cobb-Douglas:Q = 9tq².2 -Let pi be the price of q1, and p2 be the price of q2. Assume that the price of the outputQ is 1.(b)Find the effect of an input price p2 change on the optimal quantity, q2, ofthe input good 2 using the implicit function theorem.

Answered: 3. Consider a firm that produces a…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Consider a firm that produces a single output Q using two inputs, q₁ and
production technology is the Cobb-Douglas:
Q = 9tq².
2 -
Let pi be the price of q1, and p2 be the price of q2. Assume that the price of the output
Q is 1.
(b)
Find the effect of an input price p2 change on the optimal quantity, q2, of
the input good 2 using the implicit function theorem.

Expert Solution

Implicit function theorem

When we have a function like:

$f (x, y) = d; w h e r e x a n d y e x p r e s e s s i o n s a r e u n s e p a r a b l e (w h i c h m a k e s i t a n i m p l i c i t f u n c t i o n) t h e n t o f i g u r e o u t t h e s l o p e o f t h e f u n c t i o n, w e h a v e : = > \frac{d y}{d x} = - \frac{\partial f / \partial x}{\partial f / \partial y}$

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