The demand for Bruce Springsteen at the Meadowlands stadium is given by ... Q= 1
ID: 1187433 • Letter: T
Question
The demand for Bruce Springsteen at the Meadowlands stadium is given by ... Q= 120,000 - 2000 P
For this concert the stadium holds 60,000 people. The marginal cost of each additional concert goer is essentially zero up to 60,000 fans, but becomes infinite beyond that point.
1) Determine marginal revenue and marginal cost functions
2) What is the profit maximizing number of tockets and price per ticket? Please show work!!
3) Suppose the local government imposes a tax $10 per ticket on the concert promoters. Assuming nothing else changes, determine the profit maximizing ticket price. Please show work!!
Explanation / Answer
1) P = 60 - Q/2000
Total Revenue(TR) = P*Q = 60Q - Q^2/2000
Marginal Revenue = dTR/dQ = 60 - Q/1000, Q >= 0
Marginal Cost = 0 , if Q<60000 else infinity if Q>60000, Q >= 0
2) Total Cost = Fixed Cost, as marginal cost = 0 if Q<60000
Total Revenue = 60Q - Q^2/2000
for profit max, d(TR-TC)/dQ = 0
=> MR = 0
=> 60 - Q/1000 = 0
=> Q = 60000
(Note: If marginal cost = 0, profit is maximized at the highest attainable output)
Price = 60 - 60000/2000 = 30
3) Total Cost = Fixed Cost + 10Q
Total Revenue = 60Q - Q^2/2000
for profit max, d(TR-TC)/dQ = 0
=> 60 - Q/1000 = 10
=> Q = 50000
Price = 60 - 50000/2000 = 35
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