Question

Sheep Books, a profit-maximizing business, is the only book supplier in a small farming village with the following consumers.

Price ($/book)	Customers
36	1
32	2
28	3
24	4
20	5
16	6
12	7
8	8
4	9

Assuming that the marginal & average total cost for each book is $12, the store's single profit maximizing price is:

Assuming that the marginal & average total cost for each book is $12. If the store offers an $8 coupon only to those customers unwilling to pay the profit maximizing price, then its combined profit from all its customers is:

Assuming that the marginal & average total cost for each book is $12. If the store owner was able to do Perfect Price discrimination, then its combined profit from all its customers is:

Answer 1

Customers	Price	Total Revenue	Marginal Revenue
1	36	36	36
2	32	64	28
3	28	84	20
4	24	96	12
5	20	100	4
6	16	96	-4
7	12	84	-12
8	8	64	-20
9	4	36	-36

1. Single profit maximizing price for a monopolist is to produce where MR=MC. Since MC= $12 and MR=12 when number of customers is 4, this is his optimal point. Corresponding to 4 customers, the price charged should be $24.

2. If the store offers $8 coupon to those unwilling to pay, the lowest price offered is 24-8 = $16. Corresponding to P=$16, number of customers is 6. That is, store will have to offer the coupon to 2 customers.

Profit from 4 customers= Total Revenue - Total Cost = $24x4 - $12x4= $48

Profit from 2 customers (offered coupons) = $16x2 - $12x2= $8

Thus combined profit from all customers $48+$8 = $56.

3. Under perfect price discrimination, the producer is able to charge each customer their reservation price. As a result, the entire consumer surplus is converted into producer surplus. But the producer will only cater to 7 customers because thereafter the Marginal Cost ($12) exceeds the relevant price ($8 and $4).

Combined profit: (36-12) + (32-12) + (28-12) + (24-12) + (20-12) + (16-12) + (12-12) = $84.

Thus combined profit from all customers is $84.