Question

Assume a firm faces two customers in the market. Customer 1 has an inverse demand of p = 110-q1, and Customer 2 has an inverse demand of p= 140-q2. Marginal cost per unit is constant and equal to $40. Determine the profit -maximizing price and identical lump-sum fee charged to these two customers. For the following questions, assume the firm will always sell to both customers. The profit -maximizing price is $ The lump-sum fee is $ . (Enter a numeric response rounded to the nearest penny.)

Answer 1

two part tariff scheme :

MC= 40

Profit maximization price = MC = $ 40

now lump sum fixed fees equals the Consumer surplus of each group

now at P = 40, Q1 = 110-40 = 70

Q2 = 140-40 = 100

So CS1 = .5*(110-40)*70

= .5*70*70

= 2450

CS2 = .5*(140-40)*100

= .5*100*100

= 5,000

so fixed fee, from group 1 = $ 2,450

from group 2, = $ 5,000

Q2) now if firm sells to both types

Then again profit maximization price = $ 40

Now charge fixed fees equals the lower CS

so that both type of people will participate

So fixed fee = $ 2,450