Question

1.

Shooting Star Books is a small publishing company that specializes in science fiction books. Like most publishers, Shooting Star releases new books in hardcover form and later releases paperback versions of the books. The marginal cost of printing both types of books is $2 per book, and Shooting Star maximizes profits by practicing intertemporal price discrimination. The annual demand for recently released (hardcover) books is Q₁ = 400 - 10P₁ where quantity demanded is measured in thousands of books and price is measured in dollars per book. The annual demand for the paperback version of previously released books is Q₂ = 800 - 40P₂. What are the profit maximizing prices for hardcover and paperback books?

P1 =
P2 =

2.

The average daily demand for dinners at a restaurant is as follows:

Demand for dinners by senior citizens: Psc = 50 – 0.5Qsc

Demand for dinners by others:   Pother = 100 – Qother  

Marginal cost = 10 in both case

What is the profit-maximizing price for each group?

Psc =
Pother =

Answer 1

1) We would use the demand function to equate MR1 = MC and MR2 = MC

Inverse demand functions are

Q1 = 400 - 10P1 Q2 = 800 - 40P2

P1 = 400/10 - Q1/10 P2 = 800/40 - Q2/40

MR1 = 40 - 2Q1/10 MR2 = 20 - 2Q2/40

40 - Q1/5 = 2 20 - Q2/20 = 2

Q1 = (40 - 2)*5 = 190 ('000) Q2 = (20 - 2)*20 = 360 ('000)

P1 = 40 - 19 = $21 per book and

P2 = 20 - 9 = $11. per book

2) Use the same rule and process

Psc = 50 – 0.5Qsc Pother = 100 – Qother

MRsc = 50 - Qsc MRother = 100 - 2Qother

10 =  50 - Qsc 10 =  100 - 2Qother

Qsc = 40 and Qother = 45

Psc = 50 - 20 = $30

Pother = 100 - 45 = $55