3. (14 points) Let the production function be Q(K,L)=2K L. The cost of one unit of laboris w, the cost of one unit of capital is r, and the quanitity to produce is y.(a) (4 points) Set up the firm's cost-minimization problem, and clearly write down the con-Page 6straint the firm faces.The cost minimization problem of the firm is min(KL) WL+rK. The constraint:y=2K!L!.anscribed Text(b) (5 points) What are two conditions that the optimal bundle L and K need to satisfy?Write down their expressions.Tangency: -=-; production: y = 2(K)! (L)!.(c) (5 points) Solve for the optimal bundle of L. and K that minimizes the firm's cost aty=144 by finding L and K", assuming that w $16 and r $81.By solving the system of two conditions in Part (b), it should be not that hard to getL = 162 and K* = 32.

The objective of the question is to understand the cost-minimization problem of a firm given a…

Answered: 3. (14 points) Let the production…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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