$2.$ Individual Problems $14-2$

A local Pilates studio recently began offering a monthly subscription service for its patrons.

Suppose a particular patron at this studio has the following willingness$-$to$-$pay schedule, per session.

Session

Willingness to Pay

$1$st$$1052$nd$$903$rd$$754$th$$605$th$$456$th$$30$

Suppose this consumer would not demand any more sessions, even for free. Also assume that the marginal cost to the studio, per session, is constant at $$15.$

At a price of $$82\mathrm{.}50$ per session, the number of sessions demanded by this consumer would be

$.$ At this price and quantity, consumer surplus is

$$and producer surplus is

$.$

Suppose the studio has devised a new pricing scheme for consumers who demand more than $1$ session. This pricing scheme is a subscription service, whereby consumers can pay a flat fee of $$303\mathrm{.}75$ and can have up to $6$ sessions total.

Using this subscription pricing model, this consumer would demand$$sessions$.$ Under this scenario, consumer surplus is

and producer surplus is

$.($Hint: For consumer surplus, consider how much total value the consumer places on all sessions, versus the total price paid.$)$