Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Given production function=(k+2)(l+1),cost of capital=$4,wage=$6.money available to the firm =8130, how to find q*?
Expert Solution
Step 1
Production function : q=(k+2)(l+1)
q=kl+k+2l+2
Cost function: wage*labor+cost of capital*capital=Money available
C:6l+4k=8130
The firm would like to maximize the production that is the value of q with respect to its cost function:
We will use the lagrangian function:
Max q subject to C
L=kl+k+2l+2-λ(6l+4k-8130)
Differentiating L wrt k, l, and λ
dL/dl=k+2-6λ=0
k+2=6λ....(1)
dL/dk=l+1-4λ=0
l+1=4λ....(2)
dL/dλ=6l+4k-8130=0
6l+4k=8130....(3)
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