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A small firm uses inputs L & K to produce output Q, and the production function...

A small firm uses inputs L & K to produce output Q, and the production function is Q = K + 4L. The firm needs to produce exactly Q* output. The price of K is $2 and the price of L is $1. What is the firm’s total cost function TC(Q*)?

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Answer #1

Q = K + 4L
MPL = 4, MPL= 1
MRS = 4/1= 4
PL/PK = 1/2= 0.5

Since MRS is greater than price ratio, only labor will be used.

L = Q*/4

Cost = PL*L = 1*Q*/4= Q*/4

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