Answer to Question #164388 in Economics of Enterprise for Mudrika

Question

2 Price Discrimination

A monopolist produces a good with constant marginal cost equal to c with c < 1. Assume for now that all consumers have the demand Q(p) = 1 − p. The population is of size 1.

(a) Suppose that the monopolist cannot discriminate in any way among the consumers and has to charge a uniform price, pU . Calculate the price that maximizes profits and the profits that correspond to this price. (10 marks)

(b) Suppose now that the monopolist can charge a two-part tariff (m, p) where m is the fixed fee and p is the price per unit. Expenditure for each con- sumers then is m + p · q. Calculate the two-part tariff that maximizes profits and the profits that correspond to this tariff. (10 marks)

(c) Compare pU and p and comment briefly. Calculate and then compare the situation with a uniform price and a two-part tariff in terms of social welfare. (10 marks)

(d) Assume now instead that there are two types of consumers. The consumers of type 1 have the demand Q1(p) = 1 − p, and the consumers of type 2 have the demand Q2(p) = 1 − p/2. The population is of size 1 and there are equally many consumers of the two types. Calculate the two-part tariff that maximizes the profits of the monopolist. (10 marks)

(e) Compare the two-part tariffs found in questions (b) and (d) and comment briefly. Calculate and compare the two situations in term of social welfare. (10 marks) 

Answer 1

$(a)q=1-p$

$P=1-Q$

$Mr=1-2q$

$Mc=1$

$Mr=mc$

$1-2Q=1$

$Q=0$

$Pu=1$

$Profit=0$

(B) $1-q=1$

$Q=0$

$P=1$

$M=2$

(C) price increases when a fixed fee is charged.

$(D)p=1-q ,p=1-q/2 ,mc=1$

$1-q=1 ,q=0$

$1-q/2=1 ,q=0$

Low income will pay $2$

High income will pay $3$

(E) All consumers will pay $2$ when there is no price discrimination .high income will pay $3$ when there is price discrimination.