Question

You own the only video store in town that specializes in foreign classic movies. you have estimated that your average customer's demand per year is Q=20-2P, and you know that the marginal cost of each rental is $1. how much should you charge for an annual membership in order to extract the entire consumer surplus via an optimal two part pricing strategy?

Answer 1

OPTIMAL TWO PART PRICING STRATEGY:

In order to maximize profit under two part pricing, a Firm should charge price equal to Marginal cost and then Charge the consumer Surplus that consumers receive as an Annual Membership fee(Fixed Fee)

Price = Marginal cost => P = MC => (1/2)(20 - Q) = 1 => Q = 20 - 2 = 18

Thus P = MC = 1 and Q = 18.

Consumer surplus is the benefit consumer receives by paying a price lesser than what they are willing to pay.

Mathematically Consumer surplus is the area above price line(P = 1) and Below demand curve.

When Q = 0 , P = 10 (Vertical intercept of demand).

Thus Consumer Surplus = (1/2)(10 - 1)*18 = 81

=> Annual Membership Fee = $81

Annual membership that should be charged in order to extract the entire consumer surplus via an optimal two part pricing strategy is $81.