Question

Suppose you are a boba-tea monopolist on an island. You are considering multiple scenarios in order to maximize your profit. The demand for a representative consumer is given by: P = 80 − 16b b represents a serving of boba-tea. You also face a variable cost of 4b. Lastly, suppose that there are 50 individuals.

If this were a two-part tariff setup, what is your price, quantity, and profit?

Answer 1

(e)

Since individual demand: P = 80 - 16b,

b = (80 - P) / 16 = 5 - 0.0625P

As there are 50 consumers,

Market demand (Q) = 50b

b = Q/50

Q/50 = 5 - 0.0625P

Q = 250 - 3.125P

P = (250 - Q) / 3.125 = 80 - 0.32Q [Market demand]

For two-part tariff, P = MC, and Profit = Consumer surplus (CS)

P = MC = 4

80 - 0.32Q = 4

0.16Q = 76

Q = 475

When Q = 0, P = 80 (vertical intercept of demand curve)

Profit (CS) = Area between demand curve and price = (1/2) x (80 - 4) x 475 = (1/2) x 76 x 475 = 18,050