Question

You are asked to assist the National Zoo in determining entry ticket prices. Assume that there are two different demand curves for a zoo visit. The first demand curve is for visitors aged 12 to 64, while the second demand curve is for children and the elderly. Both the demand and the marginal revenue curve are as follows:

PA = 9.6 - 0.08QA
MRA = 9.6 - 0.16QA
PCS = 4 - 0.05QCS
MRCS = 4 - 0.10QCS
PA is adult price, PCS is child and senior citizen, QA adult visitor demand and QCS = Child and senior visitor demand quantity. Marginal costs are assumed to be zero if the National Zoo decides to discriminate on ticket prices:

1) Calculate the revenue and profitability of each sub-market. 
2) State whether the price discrimination strategy benefits the National Zoo. 

Answer 1

(1)

For Adults,

Setting MRA = MC = 0,

9.6 - 0.16QA = 0

0.16QA = 9.6

QA = 60

PA = 9.6 - 0.08 x 60 = 4.8

Revenue = PA x QA = 4.8 x 60 = 288

Profit = Revenue (Since cost = 0) = 288

For Children,

Setting MRCS = MC = 0,

4 - 0.1QCS = 0

0.1QCS = 4

QCS = 40

PCS = 4 - 0.05 x 40 = 2

Revenue = PCS x QCS = 2 x 40 = 80

Profit = Revenue (Since cost = 0) = 80

(2)

(I) With price discrimination, Total revenue = Profit = 288 + 80 = 368

(II) Without price discrimination, PA = PCS = P

QA = (9.6 - P) / 0.08 = 120 - 12.5P

QCS = (4 - P) / 0.05 = 80 - 20P

Market demand (Q) = QA + QCS = 120 - 12.5P + 80 - 20P

Q = 200 - 32.5P

P = (200 - Q) / 32.5

TR = PQ = (200Q - Q²) / 32.5

MR = dTR/dQ = (200 - 2Q) / 32.5

Setting MR = MC = 0,

(200 - 2Q) / 32.5 = 0

200 - 2Q = 0

Q = 200/2 = 100

P = (200 - 100) / 32.5 = 3.07

Revenue = Profit = PQ = 3.07 x 100 = 307

Since profit is higher with price discrimination, the price discrimination strategy does benefit the zoo.