Question 3. (17 points) Hershey Park sells tickets at the gate and at local muni

Question

Question 3. (17 points) 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 Q-10,000-100P and that the demand function for people who purchase tickets at municipal offices us Q- 9,000 -100P. The marginal cost of each patron is 5. a. (7 points) If Hershey Park cannot successfully segment the two markets, what are the profit-maximizing price and quantity? What is its maximum possible profit? b. (10 points) If the people who purchase tickets at one location would never consider purchasing them at the other and Hershey Park can successfully price discriminate, what are the profit-maximizing price and quantity? What is its maximum possible profit? MR

Explanation / Answer

(a) If price discrimination is not possible,

Aggregate quantity (QA) = Tickets purchased at Gate + Tickets purhased at Municipal office

QA = 10,000 - 100P + 9,000 - 100P

QA = 19,000 - 200P

200P = 19,000 - QA

P = (19,000 - QA) / 200

P = 95 - 0.005QA

Proft is maximized when Marginal revenue (MR) is equal to MC.

Total revenue (TR) = P x QA = 95QA - 0.005QA2

MR = dTR / dQA = 95 - 0.01QA

Equating MR and MC,

95 - 0.01QA = 5

0.01QA = 90

QA = 9,000

P = 95 - (0.005 x 9,000) = 95 - 45 = 50

Profit = QA x (P - MC) = 9,000 x (50 - 5) = 9,000 x 45 = 405,000

(b) With price discrimination, profit is maximized when MR = MC for both customer segments.

For ticket purchased at Gates,

Q = 10,000 - 100P

100P = 10,000 - Q

P = 100 - 0.01Q

TR = P x Q = 100Q - 0.01Q2

MR = dTR / dQ = 100 - 0.02Q

Equating MR and MC,

100 - 0.02Q = 5

0.02Q = 95

Q = 4,750

P = 100 - (0.01 x 4,750) = 100 - 47.5 = 52.5

Profit = Q x (P - MC) = 4,750 x (52.5 - 5) = 4,70 x 47.5 = 225,625

For ticket purchased at municipality office,

Q = 9,000 - 100P

100P = 9,000 - Q

P = 90 - 0.01Q

TR = 90Q - 0.01Q2

MR = 90 - 0.02Q

Equating MR and MC,

90 - 0.02Q = 5

0.02Q = 85

Q = 4,250

P = 90 - (0.01 x 4,250) = 90 - 42.5 = 47.5

Profit = 4,250 x (47.5 - 5) = 4,250 x 42.5 = 180,625

Total profit from both customer segments = 225,625 + 180,625 = 406,250

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