Given production function=(k+2)(l+1),cost of capital=$4,wage=$6.money available to the firm =8130, how to find q*?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Given production function=(k+2)(l+1),cost of capital=$4,wage=$6.money available to the firm =8130, how to find q*?

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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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