Question

2. Individual Problems 14-2

German brothels recently began offering a monthly subscription service for multiple purchasers. If you thought that the brothels' encouragement of prostitution was immoral to begin with, would you consider this pricing plan to be even more immoral?

Suppose a particular patron at a German brothel has the following willingness-to-pay schedule for services at the brothel, per session.

Session	Willingness to Pay
1st	$70
2nd	$60
3rd	$50
4th	$40
5th	$30
6th	$20

Suppose this consumer would not demand any more sessions, even for free. Also assume that the marginal cost to the brothel, per session, is constant at $10.

At a price of $55.00 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 brothel 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 $202.50 and can have up to 6 sessions total.

Using this subscription pricing model, this consumer would demand(2 or, 3, or 4, or 4 or 6) 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.)

PLEASE ANSWER ALL THE QUESTIONS FOR THOSE WITH PARANTHESIS .THANK YOU.

Answer 1

1. At a price of $55.00 per session, the number of sessions demanded by this consumer would be 2. At this price and quantity, consumer surplus is 20 and producer surplus is 90.

reason: When price = $55, consumer will buy 2 sessions as for the 3rd session, his willingness to pay is lower than the price.
His consumer surplus = $15 form the first session (70 - 55 = 15) + $5 from the second session (60 - 55 = 5).
So, is total consumer surplus = 15 + 5 = 20
Producer surplus = (price - cost) * quantity = (55 - 10)*2 = 45*2 = 90

2. Using this subscription pricing model, this consumer would demand 6 sessions. Under this scenario, consumer surplus is 67.50 and producer surplus is 142.50.

reason: When the consumer has to pay a subscription (a flat fee), he will consume as much as he can (or would like to). In the case of this consumer, it is 6 sessions. So, he will demand 6 sessions (he has to pay $202.50 no matter how many sessions he would demand. So as a rational consumer, he would demand 6 sessions).
Consumer surplus = Total willingness to pay - subscription fee = 270 -202.50 = 67.50
Producer surplus = Subscription amount - (cost * number of sessions: 10*6) = 202.50 - 60 = 142.50