Problem 2: You are a rock concert producer planning a rock concert. The demand schedule for tickets is P = 75 -0.005X where X is the number of people attending the concert. The marginal revenue function is MR = 75-0.01X.

The fixed cost of putting on the concert is $150,000. The marginal cost per person attending is zero. The capacity of the concert hall is 5,000. What price should you charge to maximize profits? How many people will attend the concert and what is the value of your profit or loss? What price should you charge to maximize attendance?

Set MR = MC... in this case 75 - .01x = 0. You'll find the profit-maximizing quantity to be 7500 and the profit-maximizing price to be $37.50. However, there aren't 7500 seats available; there are only 5000. Therefore, substitute 5000 for X in the original inverse demand function. This will yeild P = 50. This is the profit-maximizing price with a quantity of 5000. The rest should fall in place. Be sure you agree with my work as I'm only a grad student!!!

Do you not Multiple the .01 by 2

No, MR = a + 2bQ or 75 + 2(-0.005X) which gives you MR = 75 + .001X. I think you're on the right track though b/c you multiply the original inverse demand function (-0.005X) by 2 to get MR...

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asked by Bill

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