Question

You are the manager of a monopolistically competitive firm. The inverse demand for your product is given by P = 180 – 10Q and your marginal cost is MC = 6 + Q.
a. What is the profit-maximizing level of output?
b. What is the profit-maximizing price?

c. What are the maximum profits? Note that C(Q)=5Q + (Q^2)/2 + FC.
d. What do you expect to happen to the demand for your product in the long run? Explain.

Answer 1

Part a

To find out profit maximization level of output we firstofall have to find out the marginal revenue( MR) which is the derivative of total revenue function(TR)

TR= average revenue (AR)×quantity (Q)

For any linear demand function AR =price demand function which is P=180-10Q

SoTR =(180-10Q)×Q

TR=180Q-10Q^2

MR=derivative of TR=180-20Q

For a monopolistic firm the maximum profit is achieved when marginal revenue (MR)=marginal cost(MC)

MC=6+Q

So MR=MC

180-20Q=6+Q

Q=8.28 or 8 rounded off to nearest whole number since product units can't be in decimals

Part b

The profit maximum price is the price at maximum profit output level i.e. P=180-10×8=100

Partc

Maximum profit = total revenue at maximum output level(TRm) - Total cost at maximum output level(TCm)

TRm= maximum output price ×maximum output quantity

=100×8=800

Our total cost function is given by

C(Q)=5Q +(Q^2)/2+FC

Therefore TRm = 5x8+(8^2)/2 +FC =72 +FC

Maximum profit = 800-(72+FC)

=728 -FC

Where FC means fixed cost which is not given in the question

Part d

In monopolistic competition there is no barrier on entry or exits so if the current firm are making super normal profits in monopolistic markets new firms would get attracted to these market and they will enter into the markets which will increase the supply and resultingly the demand curve will shift to the left with every unit increase in supply demand curve will keep on shifting to the left and settling at lower price then before which will bring the prices down to a certain and all the firms in monopolistic markets will endup earning normal profits in long run just like perfect competition markets.