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	51	101

The marginal cost of coffee is 10 and the marginal cost of a banana is 40.

The café owner is considering three pricing strategies:

1.	Mixed bundling: Price bundle of coffee and a banana for 161, or just a coffee for 70.
2.	Price separately: Offer coffee at 60, price a banana at 101.
3.	Bundle only: Coffee and a banana for 121. 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

Consider the given problem here there are two students, “early classes” and “without early classes”. Now, their willingness to pay are given in the question.

1. Now, under “mixed bundling”, => students without early classes will buy the bundle having willingness to pay exactly equal to “161” and students with early classes will buy only “coffee”. Since “students with early classes” have total willingness pay for these both goods “70 + 51 = 121 < 161”. So, the “TR = 161 + 70 = 231”, “TC = 2*10 + 40 = 60”, because only “2” units of “coffee” and 1 unit of “banana” will be sold. So, “profit is given by, “ 231 – 60 = 171”.

2.

Now, under “Price Separately”, => students without early classes will buy both goods having total willingness to pay exactly equal to “161” and students with early classes will buy only “coffee”. Since “students with early classes” have lower willingness pay for “banana”, => only buy “coffee”. So, the “TR = 161 + 60 = 221”, “TC = 2*10 + 40 = 60”, because only “2” units of “coffee” and 1 unit of “banana” will be sold. So, “profit is given by, “ 221 – 60 = 161”.

3.

Finally, under “Bundle only”, => both the students will buy the bundle having both of the goods, because

“students without early classes” more willingness to pay for the bundle, 121 > 161, and ”students with early classes” will also buy the bundle having willing ness to pay exactly the price of the bundle. So, the “TR = 121*2 = 242”, “TC = 2*10 + 2*40 = 100”, because only “2” units of “coffee” and 2 units of “banana” will be sold. So, “profit is given by, “ 242 – 100 = 142”.

Consider the following table.

So, we can see the profit under the 1^st strategy is more compared to the other strategy, => “mixed bundle”.