Suppose the local zoo hires you to assist them in setting admission prices. The
ID: 1203127 • Letter: S
Question
Suppose the local zoo hires you to assist them in setting admission prices. The zoo's managers recognize that there are two distinct groups of consumers for zoo admission: adults (A) and children/senior citizens (CS). The demand and marginal revenue functions for the two groups are as follows: P_A = 9.6 - 0.08Q_A MR_A = 9.6 - 0.016Q_A P_CS = 4 - 0.05Q_CS MR_CS = 4 - 0.10 Q_CS Suppose the zoo is large enough so that crowding is not a problem at the zoo. The managers therefore consider marginal cost to be zero. Answer the following questions: If the zoo decides to price discriminate, what are the profit-maximizing price and quantity in each sub-market? Calculate the total revenue in each sub-market. If the zoo decides not to price discriminate, it faces a combined demand and marginal revenue function of P = 6.15 - 0.03Q and MR = 6.15 - 0.06Q. What are the profit-maximizing price and quantity of admission if the zoo charges one admission price for all. Calculate the total revenue in this case. Would you recommend charging one admission price for all or different prices for adult and for children/senior citizens? Why do you make that recommendation?Explanation / Answer
(a) Sub-market I - For Adults
PA = 9.6 - 0.08QA
MRA = 9.6 - 0.16QA
MC = 0
Profit-maximizing condition -
MR = MC
9.6 - 0.16QA = 0
0.16QA = 9.6
QA = 60
PA = 9.6 - 0.08QA = 9.6 - 0.08*60 = 9.6 - 4.8 = 4.8
Total Revenue = PA * QA = 4.8 * 60 = 288
In Sub-Market I - For Adults
Profit maximizing price, PA = 4.8
Profit maximizing quantity, QA = 60
Total revenue = 288
In Sub-Market II - For Children/Senior Citizens
PCS = 4 - 0.05QCS
MRCS = 4 - 0.10QCS
MC = 0
Profit-maximizing condition
MR = MC
4 - 0.10QCS = 0
0.10QCS = 4
QCS = 40
PCS = 4 - 0.05QCS = 4 - 0.05*40 = 4 - 2 = 2
Total Revenue = PCS * QCS = 2 * 40 = 80
In Sub-Market II - For Children/Senior Citizens
Profit maximizing price, PCS = 2
Profit maximizing quantity, QCS = 40
Total revenue = 80
(b) P = 6.15 - 0.03Q
MR = 6.15 - 0.06Q
MC = 0
Profit-maximizing condition -
MR = MC
6.15 - 0.06Q = 0
0.06Q = 6.15
Q = 102.5
P = 6.15 - 0.03Q = 6.15 - 0.03 * 102.5 = 6.15 - 3.075 = 3.075
Total Revenue = P * Q = 3.075 * 102.5 = 315.18
When zoo charges one admission price for all -
Profit maximizing price, P = 3.075
Profit maximizing quantity, Q = 102.5
Total Revenue = 315.18
(c) We would recommend charging different prices for adult and for children/senior citizens.
We are making this recommendation because when different prices for adult and for children/senior citizens is charged then combined total revenue (288 + 80 = 368) is greater than the total revenue (315.18) when one admission price is charged from all. So, it is profitable for zoo to charge different prices for adult and for children/senior citizens.
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