Question

The local zoo has hired you to assist them in setting admission prices. The zoo's managers recognize that there are two distinct demand curves for zoo admission. One demand curve applies to those ages 12 to 64, while the other is for children and senior citizens. The two demand curves are:

PA = 9.6 - 0.08QA
PCS = 4 - 0.05QCS

where PA = adult price, PCS = children's/senior citizens' price, QA = daily quantity of adults, and QCS = daily quantity of children and senior citizens. Crowding is not a problem at the zoo, so that the managers consider marginal cost to be zero.

a) If the zoo decides to price discriminate, what are the profit maximizing price ____ and quantity ____ for adults? What is the total revenue ____ in this sub-market?

b) What are the profit maximizing price ____ and quantity ____ for children/seniors? What is the total revenue ____ in this sub-market?

c) What is the elasticity of demand for adults ____ at the price and quantity calculated? What is the elasticity of demand for children/seniors ____ at the price and quantity calculated? (Think about why this may be the case.)

Clearly label each answer.

Answer 1

For optimal price discrimination the zoo should set MRA= MRCS= MC=0

MRA = 9.6- 0.16QA =0 , Therefore, QA = 60. Hence PA= $4.8 Profit maximizing price for adults = $4.8 and quantity =60.

MRCS = 4-0.1QCS=0. Therefore, QCS =40. Hence PCS =$ 2.  Profit maximizing price for children/seniors = $2 and quantity =40.

TRA = 60*4.8 = $288. Total revenue for adults = $288

TRCS = 40*2= $80. Total revenue for children/seniors =$80

Total revenue for zoo = 288+80 = $368

PA = 9.6 - 0.08QA

120 - 12.5PA = QA

DQA/DPA = -12.5

Elasticity of demand for adults = (DQA/DPA) *(P/Q) = -12.5 *(4.8/60) = -1

PCS = 4 - 0.05QCS

80-20PCS = QCS

DQCS/DPCS =-20

Elasticity of demand for children/seniors = -20 *(2/40) = -1