optimal two-part pricing

[Atika Gupta]

Ques: A local video store estimates their average customer's demand per year is q=7-2p, and knows the marginal cost of each rental is 0.5Rs. What is the annual profit that the video store expects to make on an average customer if it engages in optimal two-part pricing?

I am getting following answer: optimal tariff pricing is 9+0.5q where 0.5 is the price charged per unit and profits are = 9.
Please confirm if my answer is correct.

[RajEco]

Is the question right ? there is only 1 market demand function.
Normally in 2 part pricing we have 2 markets.

Please confirm.

[Homer Simpson]

The question seems fine. This is second-degree discrimination case. We usually have 2 demand curves for the third degree price discrimination case as elasticity in the markets are different.

[The Villain]

I'm getting profit as 16.5.What is the ans?

[RajEco]

I am getting the same answer as atika

profit =9
price = .5

I am still confused.

Please correct my reasoning, if wrong.
profit = a + (p-MC)q
where a= (p-3.5)q
 profit = .5 (3.5- p)q +(p-.5) q
substituting q and solving for FOC wrt p.

[RajEco]

whats the answer finally ?

[SoniaKapoor]

What is the answer Atika?

[Ashima]

Yeah, even I got profits as 9 and price as 0.5!

The approach is absolutely correct! :)