Question

The Duluth Science Museum, a non-profit organization, has hired you to assist them in setting admission prices. The museum’s managers recognize that there are two distinct demand curves for admission. One demand curve applies to adults and the other applies to children. Museum management would like you to maximize profit from museum visits to raise scholarship money for graduating local high school seniors.

Demand curve for adults: Pa = 9.6 - .08*Qa

Demand curve for children: Pc = 4 – 0.05*Qc

Where Pa and Pc are the prices charged per adult and child admission, respectively, and Qa and Qc are the quantities of tickets demanded per period for adults and children per hour, respectively.

Managers consider marginal cost of an admission to be $1.

If you use Excel, indicate the recommended prices and quantities in the spaces below, and indicate you have Excel work in a separate file.

1. What price will you recommend for adults? How many adults will attend each hour? Explain.

1. What price will you recommend for children? How many children will attend each hour? Explain.
2. Which group has the most price-elastic demand at the prices you set? How can you tell?
3. If you charged the same price to both groups, would you improve or reduce profits?

Answer 1

a. Profit maximizing quantity is where MC = MR, and we know MC = 1 for both.

MR for adults = 9.6 - 0.16Qa = 1, hence Qa = 8.6/0.16 = 53.75 (or say 54)

Price for adults = 9.6 - 0.08Qa = 9.6 - 0.08*54 = 5.28

b. Profit maximizing quantity is where MC = MR, and we know MC = 1 for both.

MR for children = 4 - 0.1Qc = 1, hence Qa = 3/0.1 = 30

Price for children = 4 - 0.05Qc = 4 - 0.05*30 = 2.5

c. elasticity of demand = (dQ/Q) / (dP/P) = (dQ/dP) / (Q/P)

for adults demand function = Qa = (9.6 - Pa) / 0.08

hence dQ / dP = -1/0.08

elasticity of demand for adults at profit maximizing price and quantity = (-1/0.08) / (54 / 5.28) = -1.2222

for children demand function = Qc = (4-Pc) / 0.05

hence dQ/dP = -1/0.05

elasticity of demand for children at profit maximizing price and quantity = (-1/0.05) / (30/2.5) = -1.66666

Demand by children is more price elastic

d. without any calculations we can say that charging the same price to both groups will reduce the profit since profit maximizing prices are different for the two groups