Consider the market for a product with 2 types of potential users: group a and g
ID: 3313365 • Letter: C
Question
Consider the market for a product with 2 types of potential users: group a and group b. Let's assume that the population is normalize to 1 and there are 0.5 individuals of group a and 0.5 individuals of group b. Their corresponding demand curves are as follows. Pa=5-0.5 *Qa; and Pb=10-Qb. Monopolist face a constant MC of MC=2.
a. What is the optimal (profit-maximizing) 2-part tariff that induces both types of consumers to buy?
b. What is the optimal 2-part tariff when only high demand consumers purchase the good?
c. Re-do a-b-c and determine which pricing scheme yields to a higher total profit is there are 0.75 individuals of group a and 0.25 individuals of group b.
Explanation / Answer
Solution:
(a) What is the optimal (profit-maximizing) two-part tariff that induces both types of consumers to buy?
Demand is smaller/more elastic for A, so the fixed part of tariff = consumer surplus of A
CS for A= ½ * 2*6= 6
And per unit fee is found by maximizing TR = = 2*6 + ( P-2) ( Qa+Qb) = 12+(P-2) (10-P+10-2P)
= 12 +(p-2) ( 20-3P)
= -28 +26P -3P2
Maximise this ;
-6P +26=0
P=26/6 = 4.33
(b) what is the optimal two part tariff when only high demand consumers purchase the good?
B is high demand , so the fixed part= entry fee= consumer surplus at P= 2
CS= ½ *2*8 = 8
And per unit fee = MC= 2
c) Re-do a-b-c and determine which pricing scheme yields to a higher total profit is there are 0.75 individuals of group a and 0.25 individuals of group b
Both consumers:
Demand is smaller/more elastic for A, so the fixed part of tariff = consumer surplus of A