Question

Suppose that all kids attending the state fair have the same demand for carnival rides, which can be specified as: Q = 8 – 4P. The fair can be considered a monopolist in selling rides and the marginal cost of rides is effectively zero (since the ride setup and ride attendant can be considered fixed costs).

What price per ride should the fair charge to maximize profits? How many rides will each ride child purchase? How much revenue will be collected per child?

Can you think of a better way to sell rides (other than charging a uniform per-ride price like in part a.) that might allow the fair to earn higher profits? Describe your pricing scheme, explain how many rides each child will purchase, and show that the fair will collect more revenue per child than in part a.

Answer 1

Q = 8 - 4P

4P = 8 - Q

P = 2 - 0.25Q

Under single-pricing scheme, monopolist will maximize profit by equating Marginal revenue (MR) with MC.

Total revenue (TR) = P x Q = 2Q - 0.25Q²

MR = dTR/dQ = 2 - 0.5Q

Equating with MC,

2 - 0.5Q = 0

0.5Q = 2

Q = 4

P = 2 - (0.25 x 4) = 2 - 1 = $1

Revenue = P x Q = 1 x 4 = $4

However, profit can be increased using price discrimination. If the fair can effectively segment the market into different segments that have different elasticity of demand and no re-sale of tickets is possible across segments, the fair will increase its profits from current single-price level by charging a higher price in the less elastic segment and lower price in more elastic segment. Total revenue will be higher in this case.