Answer to Question #311109 in Microeconomics for Thato

Question #311109

If the pre-tax cost function for John’s Shoe Repair is C(q) = 100 + 10q - q2 + 1/3

q3, and it faces a specific tax of t = 10, what is its profit-maximizing condition if the 

market price is p? Can you solve for a single, profit-maximizing q in terms of p? 

(Hint: See Exercise 3.3 and Solved Problem 8.2.)



1
Expert's answer
2022-03-14T13:27:15-0400

If the cost function function before tax is

C(q)=100+10q-"q^2" +"\\frac{1}{3}q^3"

then

Marginal Cost (MC)="\\frac{dc}{dq}" =10-2q+"q^2"

at profit max. condition:

P=MC (but is affected by tax) therefore

P+10=10-2q+"q^2"

P="q^2" -2q

By factorizing P=q(q-2)

divide by q-2

(this profit maximixing quantiy)

q="\\frac{p}{q-2}"


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