Question

Nebula Doles is the owner of an independent coffee shop. She wants to design a nonlinear pricing menu for selling cups of coffee. The following table shows the WTP for 3 representative customers, for up to 3 cups in a day. In your calculations, assume that the per-unit variable cost is zero.

	WTP for each Customer
Cups of Coffee a Day	Customer 1	Customer 2	Customer 3
1st Cup	2.5	3	4
2nd Cup	2	2	2.5
3rd Cup	1	1	1.5

A. If Nebula were to charge one single price for each cup, what is the optimal price she should charge?

b.

1. If Nebula were to design a multi-block pricing with P1>P2>P3, where P1 is the price of the 1^st cup for a day, P2 is the price of the 2^nd cup, and P3 is the price for the 3^rd cup, what are the optimal {P1, P2, P3} and the resultant total profits? Assume that for each cup, customers will only purchase if the price is equal to or less than the WTP.

Answer 1

A. Single price would be $2.
reason: The following table presents the WTP of the three customers in a demand schedule.

When price = $4, only Customer 3 will buy 1 cup of coffee as his WTP equals the price. When price = $3, Customer 2 and 3 will buy 1 cup of coffee each (total demand 2) as their WTP matches this price. When price = $2.50, 2 more cups will be bought (demand =4); at price = $2, 2 more (demand = 6); at price= $1.50, 1 more will be demanded (total demand = 7); and at price = $1, 2 more cups of coffee will be demanded (total demand at this level = 9).

Revenue is maximum when price = 2 (demand at this level = 6; revenue = 2*6 = 12). So, if Nebula were to charge a single price, she would charge $2.

B. P1 = $2; P2 = $1.50; P3 = $1
  Condition: P1>P2>P3.
As seen in part (A), highest revenue is earned when price = $2 (revenue = 12). So, P1 = $2. Next is when price = $1.50 (revenue = 10.50). So, P2 = $1.50. Third is when price = $2.50 (revenue = 10), but due to the condition of P2>P3, price of the third cup of coffee must be lower than P2. So, she will charge $1 for the third cup.