Answer to Question #274095 in Microeconomics for Hazal3.4

Question

Hershey Park sells tickets at the gate and at local municipal offices to two groups of people. Suppose that the demand function for people who purchase tickets at the gate is QG = 10,000 - 100pc and that the demand function for people who purchase tickets at municipal offices is QG 9,000 - 100PG = The marginal cost of each patron is 5. a. If Hershey Park cannot successfully segment the two markets, what are the profit-maximizing price and quantity? What is its maximum pos sible 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 dis criminate, what are the profit maximizing price and quantity? What is its maximum possible profit?

Answer 1

Market demand function:

Q = 10000 - 100P +9000 - 100P

Q = 19,000 - 200P

Divide by 200

The inverse function:

$P = 95 - (\frac{Q}{200})$

$TR = P\times Q = 95Q - 0.005Q^2$

$MR = 95- (\frac{1}{100})$

Q = 95 - 0.01Q

Marginal cost (MC) = 5

At equilibrium MR = MC

95 - 0.01Q = 5

Q = 10,000

$P = 95- 0.005\times 10,000 =45$