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 and marginal revenue curves are:
PA = 9.6 - 0.08QA
MRA = 9.6 - 0.16QA
PCS = 4 - 0.05QCS
MRCS = 4 - 0.10QCS
where PA = adult price, PCS = children's/senior citizen's 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 the marginal cost to be zero.
Hint: Whenever inverse demand is P=a-bQ, marginal revenue is MR=a-2bQ
a. To start, what is the total revenue that would be collected if the zoo decides not to price discriminate?
b. If the zoo decides to price discriminate, what are the profit-maximizing price and quantity in each market? Calculate total revenue in each sub-market. How does the total compare to the total revenue from part (a)?
c. What is the elasticity of demand at the quantities calculated in (b) for each market. Are these elasticities consistent with your understanding of profit maximization and the relationship between marginal revenue and elasticity?
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 and marginal revenue curves are:
PA = 9.6 - 0.08QA
MRA = 9.6 - 0.16QA
PCS = 4 - 0.05QCS
MRCS = 4 - 0.10QCS
where PA = adult price, PCS = children's/senior citizen's 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 the marginal cost to be zero.
Hint: Whenever inverse demand is P=a-bQ, marginal revenue is MR=a-2bQ
a. To start, what is the total revenue that would be collected if the zoo decides not to price discriminate?
b. If the zoo decides to price discriminate, what are the profit-maximizing price and quantity in each market? Calculate total revenue in each sub-market. How does the total compare to the total revenue from part (a)?
c. What is the elasticity of demand at the quantities calculated in (b) for each market. Are these elasticities consistent with your understanding of profit maximization and the relationship between marginal revenue and elasticity?
