Question

At a student café, there are equal numbers of two types of customers with the following values. The café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate).

	Students with Early Classes	Students without Early Classes
Coffee	70	60
Banana	54	104

The marginal cost of coffee is 5 and the marginal cost of a banana is 20.

The café owner is considering three pricing strategies:

1.	Mixed bundling: Price bundle of coffee and a banana for 164, or just a coffee for 70.
2.	Price separately: Offer coffee at 60, price a banana at 104.
3.	Bundle only: Coffee and a banana for 124. Do not offer goods separately.

Assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle.

For simplicity, assume there is just one student with an early class, and one student without an early class.

Price Strategy	Revenue from Pricing Strategy	Cost from Pricing Strategy	Profit from Pricing Strategy
1. Mixed Bundling
2. Price Separately
3. Bundle Only

Pricing strategy   yields the highest profit for the café owner

Answer 1

Strategy 1: Mixed bundling: Price bundle of coffee and a banana for 164, or just a coffee for 70

The bundle of coffee and banana will be bought by the student without earliy classes whose maximum willingness to pay for coffee and banana together is 164. And the student with early classes will buy only coffee at 70 and the bundle is not affordable. Hence, total revenue from selling 2 coffee (1 with bundle and 1 without bundle) and 1 banana (with bundle) = 164 + 70 = 234. The cost for 2 coffee and 1 banana = 2*5 + 20 = 30. Hence, total profit = 234 - 30 = 204.

Strategy 2: Price separately: Offer coffee at 60, price a banana at 104.

Both type of students will buy coffee at 60 and the student without early classes will only buy banana. Hence, revenue from selling 2 coffee at 60 and 1 banana at 104 will be 2*60 + 104 = 224. The cost for 2 coffee and 1 banana = 30 as calculated above. Hence, profit with strategy 2 = 224 - 30 = 194.

Strategy 3: Bundle only: Coffee and a banana for 124. Do not offer goods separately.

Here both types of student will buy the bundle at 124. Hence, total revenue = 2 * 124 = 248. Cost for 2 coffee and 2 banana = 2 * ( 5+20) = 50. Hence, profit = 248 - 50 = 198.

The abouve discussed three strategy can be summarized below with their respective revenue, cost and profit.