Question

Suppose that Mahesh is a typical Buffalo Bills fan, and his demand curve
for Bills football games is: P = 120 – 10G where G is the number of games
the fan attends.
Suppose that there are 30,000 Bills fans with demand equivalent to
Mahesh’s. Suppose that the Bills are able to charge
a two-part price including a fixed fee for entry and a price per game. If
the marginal cost of attendance is $0, what is the optimal fixed fee per
fan (again assuming that all have the same demand curve)?

Answer 1

Individual demnd function: P = 120 - 10G

10G = 120 - P

G = 12 - 0.1P

Since there are 30,000 fans, aggregate number of games (Q) = 30,000 x G

G = Q / 30,000

Q / 30,000 = 12 - 0.1P

Q = 360,000 - 3,000P

3,000P = 360,000 - Q

P = (360,000 - Q) / 3,000

In the two-part pricing scheme, unit price equals Marginal cost and Fixed fee equals entire consumer surplus.

Equating P with MC,

(360,000 - Q) / 3,000 = 0

360,000 - Q = 0

Q = 360,000

P = MC = 0

From demand function, when Q = 0, P = 360,000 / 3,000 = $120 (Reservation price)

Aggregate Consumer surplus (CS) = Area between demand curve and market price = (1/2) x $(120 - 0) x 360,000

= 180,000 x $120 = $21,600,000

Fixed fee per fan = Aggregate Consumer surplus / Number of fans = $21,600,000 / 30,000 = $720