Answer to Question #282326 in Microeconomics for ketty

Question

In a monopoly market, there are 2 consumers, their demand functions are: Q = 5 – p and Q = 10 - 2p. the monopolist ‘s cost function is C = 0.5q, and he decide to implement the two-part tariff strategy, i.e. each consumer pays a fixed/entry fee (a) and a price (p) for each unit consumed: T(q) = a + pq.

1. At a given price “p”, what is the fixed fee “a”?
2. What is the optimal fixed fee “a” and price “p”?

Answer 1

1. At a given price “p”, the fixed fee “a” is:

a = pq/T.

2. The optimal fixed fee “a” is a = MC = 0.5. And price “p” is optimal, when output is produced at MC = MR.

Total quantity demanded is:

Qd = 15 - 3p,

p = 5 - q/3.

$MR = TR'(q) = 5 - 2/3 q.$

5 - 2/3q = 0.5,

q = 6.75,

$p = 5 - 6.75/3 = 2.75.$