Hershey Park sells tickets at the gate and at local municipal offices. There are
ID: 1194616 • Letter: H
Question
Hershey Park sells tickets at the gate and at local municipal offices. There are two groups of people. Suppose that the demand function for people who purchase tickets at the gate is QG = 10,000 – 100pG and that demand function for people who purchase tickets at municipal offices is QG = 9,000 – 100pG. The marginal cost of each patron is 5
If Hershey Park cannot successfully segment the two markets, what are profitmaximizing price and quantity? What is its maximum possible profit? b. If the people who purchase tickets at one location would never consider purchasing them at the other and Hershey Park can successfully price discrimination, what are the profit-maximizing price and quantity? What is its maximum possible profit?
Explanation / Answer
for people who purchase tickets at the gate:
Q = 10,000 -100P
The reverse demand function is: P = 100 - 0.01Q
TR = P xQ = 100Q - 0.01Q2
MR = 100 - 0.02Q
MC =5
For profit maximizing output MR = MC
100 - 0.02Q = 5
0.02Q = 95
So, Q = 4750 units
P = 100 - 0.01Q = 100 - 0.01 x4750 = $52.50
for people who purchase tickets at the muncipal office:
Q = 9,000 -100P
The reverse demand function is: P = 90 - 0.01Q
TR = P xQ = 90Q - 0.01Q2
MR = 90 - 0.02Q
MC =5
For profit maximizing output MR = MC
90 - 0.02Q = 5
0.02Q = 90
So, Q = 4500 units
P = 90 - 0.01Q = 90 - 0.01 x4500 = $45
Profit = TR - TC
= ($52.50 x 4750) + ($45 x 4500) - ($5 x (4750+4500)
= ($249,375 + $202,500) - $46,250 = $405,625
b. If the people who purchase tickets at one location would never consider purchasing them at the other and Hershey Park can successfully price discrimination, it means the firm is already changing discrminating price,i.e, $52.5 for those who purchaces at gate and $45 for those who purchaces at muncipal office.