Question

As the manager of We Do It Right Construction, you need to make a decision on how many home to build in a new residential area. The firm has some monopoly power in its local market. Its inverse demand curve is estimated to be P=300-3Q. Its cost function is 500+20Q+0.5Q^2. (Price and cost are in thousands, quantity is in units.)

a.) What is the revenue-maximizing price and quantity? Explain.

b.) What is the profit-maximizing price and quantity? How much profit can this firm make?

c.) Can you recommend any pricing strategy that would further improve profits for this firm beyond the profit-maximizing level you calculated in part (b)? If yes, explain the strategy and conditions necessary for its implementation.

d.) What market structure (perfect competition, monopolistic, oligopoly, etc.) is this market likely to have? What changes to price, quantity, and profits do you expect to happen in the long-run?

Answer 1

a)

P = 300 - 3Q

TR = P*Q

= 300Q - 3Q^2

MR = 300 - 6Q

TR is maximum where TR = 0

300 - 6Q = 0

300 = 6Q

Q = 300/6

= 50

P = 300 - 3(50)

= 300 - 150

= $ 150

Revenue Maximizing Quantity = 50

Revenue Maximizing Price = $ 150

B)

Profit maximization ; MR = MC

MR = 300 - 6Q .....(1)

TC =  500+20Q+0.5Q^2

MC = 20 + Q ...(2)

Equating (1) and (2)

300 - 6Q = 20 +Q

280 = 7Q

Q = 280/7

= 40

P = 300 - 3(40)

= 300 - 120

= 180

Profit Maximizing quantity = 40

Profit maximizing Price = $ 180

c)

Profit if firm behave like monopoly: TR - TC

= 180*40 - 500 -20(40) - 0.5(40)^2

=$ 5100

If firm behave like perfectly competitive: P = MC

300 - 3Q = 20+Q

280 = 4Q

Q = 280/4

= 70

P = 20 +70'

= 90

Profit = 70*90 - 50 - 20(70) - 0.5(70)^2

= 2400

Firm does not have any other strategy to maximize profit, since it is already maximizing profit by restricting its output level.

d)

This is monopolistic market structure since firm has little market power. There might be new entry of new firms in market. Thus, price and profit will witness fall,  while quantity shall rise.