Question

A local golf club estimates its average customer's inverse demand per year is P = 351 - 25 Q, and it knows the marginal cost of each round is $ 22.
How much should the golf club charge for an annual membership in order to extract the entire consumer surplus via an optimal two-part pricing strategy?

Round all calculations to 2 decimals

Answer 1

When a monopoly extract entire consumer surplus then it is said to be undertaking first degree price discrimination.

In such scenario, it produce a level of output corresponding to which price equals MC.

P = 351 - 25Q

MC = 22

P = MC

351 - 25Q = 22

25Q = 329

Q = 329/25 = 13.16

Price when the Q is zero.

P = 351 - 25Q = 351 - (25*0) = 351

Calculate Consumer surplus -

CS = 1/2 * (Price when Q is zero - MC) * Q

CS = 1/2 * (351 - 22) * 13.16

CS = 2,164.82

As entire consumer surplus will be extracted,

The golf club should charge $2,164.82 as the annual membership.