Question

A typical firm in a monopolistically competitive industry faces the following demand and total cost equations for its product.

*Q***= 20 – ( P/ 3 )**

a. What is the firm’s short-run, profit-maximizing price and output level?

b. What is the firm’s economic profit?

Answer #1

Given information:

Demand function: Q = 20 - P/3

Total cost function: TC = 100 - 5Q +Q^{2}

---------

Q = 20-P/3

=> P = (20-Q) * 3

=> P = 60 - 3Q

TR = PQ

=> TR = (60-3Q)Q

=> TR = 60Q - 3Q^{2}

=> MR = dTR/dQ

=> MR = 60 -6Q

--------

TC = 100 - 5Q + Q^{2}

=> MC = dTC/dQ

=> MC = -5 + 2Q

A monopolistically competitive firm maximize profit at MR = MC

=> 60 - 6Q = -5 + 2Q

=> 60 + 5 = 2Q + 6Q

=> 65 = 8Q

=> Q = (65/8)

=> Q = 8.125

and, P = 60 - 3Q

=> P = 60 - 3(8.125)

=> P = 60 - 24.375

=> P= 35.625

**The firm's short-run profit-maximizing price is $35.625
per unit and output level is 8.125 units**

---------------------------------------

(b)

Economic profit = TR - TC

Economic profit = (P*Q) - (100 - 5Q + Q^{2}) =[35.625 *
8.125] - [100 -(5 * 8.125) + (8.125)^{2}]

Economic profit = 289.45 - 125.4

Economic profit = 164.05

**The economic profit is $164.05**

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