Question

An industry has the market demand of: P= 6300−2Q. The market is served by a large collection of firms all with constant marginal costs: MC= 4200

a. what is initial price

b. if one firm was able to innovate and drive their MC=3200, what is price and quantity this firm would choose to set max profits as a monopolist if it had the market to itself?

c. suppose a one firm is able to drive their MC=3200. what is the price and quantity this firm would set? profits? is this innovation large or small?

d. there are a lot of firms in the market and a firm has reduced its costs. what is the output and profits of this innovative firm when practicing first degree price discrimination after MC=3200

Answer 1

a) Competitive price = 4200; quantity = 1050

Demand = 6300 - 2Q MC = 4200
Quanity: 6300 - 2Q = 4200 So, Q = 2100/ 2 = 1050: Price = 4200

b) Monopoly quantity = 775; Price = $4,750

With innovation, MC = 3200. Monopoly quantity and price:
MR = 6300 - 4Q (double slope of demand curve)
For monopoly, MR = MC
6300 - 4Q = 3200 So, Q = 3100/4 = 775; P = 6300 - 2*775 = 4,750

c) One firm quantity = 775; price = $4750

Profit =$1,201,250; Profit is large.

Profit = TR - TC (total revenue - total cost)
TR = price* quantity = 4750 * 775 = 3,681,250
TC = MC*quantity = 3200 * 775 = 2,480,000
So, profit = 3,681,250 - 2,480,000 = 1,201,250

This profit is 117.91% higher after innovation. So, the innovation is large enough to contribute a high percentage increase in profit.
(when MC = 4200, TR = 2,756,250; TC = 2,205,000; profit = 551,250
% Change in profit = (1,201,250 - 551,2520)/ 551,250) * 100 = 117.91%)

d) When the firm practices first degree price discrimination, quantity = 1550; the profit is: $2,402,500

Quantiy = 1550, which is a competitive quantity. The shaded area is the profit of perfectly price discriminating monopolist. It can be calculated as

½*(6300 - 3200) * 1550 = 2,402,500