Question

Your firm's cost function is: C = 0.48Q3 - 4.7Q2 + 40Q + 1,383 Your firm faces the following demand: P = 126 - 0.23Q Find the price that maximizes the firm's profit if this firm operates in a monopolistically competitive market. Round your answer to two decimals. Show work plz :)

Answer 1

Answer

In order to maximize profit a monopolistic competitive firm produces that quantity at which MR = MC

where MR = Marginal revenue = d(TR)/dQ = d(PQ)/dQ = 126 - 0.23*2Q = 126 - 0.46Q

Note TR = Total revenue = PQ

MC = Marginal Cost = dC/dQ = 3*0.48Q² - 2*4.7Q + 40

=> MC = 1.44Q² - 9.4Q + 40

So, MR = MC

=> 126 - 0.46Q = 1.44Q² - 9.4Q + 40

=> 1.44Q² - 8.94Q - 86 = 0

Solving this equation we get Q = 11.43

Given that P = 126 - 0.23Q

=> P = 126 - 0.23*11.43 = 123.37

Hence,

he price that maximizes the firm's profit if this firm operates in a monopolistically competitive market is P = 123.37

Note whenever you have

aQ² - bQ - c = 0

then