Question

Let’s return to Fredonia Brewery, the monopoly beer producer in Nacogdoches. Suppose again that the pandemic, followed by a plague, followed by a zombie apocalypse has left Nacogdoches completely isolated from the rest of the world. Demand for beer faced by Fredonia is P = 15 − 0.33Q, and the marginal and average cost of brewing and bottling beer is $1 per bottle.

(a) Find the profit maximizing price and quantity of beer; also find the consumer surplus and the deadweight loss.

(b) The city residents decide to regulate Fredonia so that it has to set price of a bottle of beer equal to marginal cost. However, the city will also compensate the brewery so that it is as well off with this regulation as it was before. How much of a subsidy will the city have to give Fredonia brewery? (Hint: find the brewery’s profit before regulation). Is this a good deal for the city residents?

Answer 1

(a) Fredonial Brewery as monopoly:

P = 15 - 0.33Q; So, MR = 15 - 0.66Q (double slope) ; MC = AC = 1

He will produce quanity where MR = MC

15 - 0.66Q = 1. So, Q = 21; Plugging in the value of Q in demand function to find P:

15 - 0.33*21 = 8; P = 8

Therefore his profits = TR - TC = (8*21) - (1*21) = 168 - 21 = 147 Profit = 147

Total revenue (TR) = price * quantity; Total cost (TC) = AC * quantity

(b) Fredonial Brewery at competitive price:

15 - 0.33Q = 1 So,Q = 42; P = 1 (= MC)

Profit = (42*1) - (42*1) = 0 (economic profit = 0)

So subsidy = 147 - 0 =147 Subsidy = $147

City will compensate the brewery with $ 147

Yes, it is a good deal for the city residents as they are getting more quantity at reduced price compared to pre-regulation monopolistic deal.