Delta faces a demand curve for seats for SFO-Athens tickets given by the followi

Question

Delta faces a demand curve for seats for SFO-Athens tickets given by the following equation P = 1000-2Q, where Q is the quantity of tickets demanded. The plane used holds up to 300 people. Assume the marginal cost for flying a passenger is $0 (literally just peanuts). What price per ticket will allow Delta to sell 250 seats? Write the marginal revenue equation using the numbers from this problem. What is the marginal revenue of the 250th ticket? Explain why the price for selling 250 tickets is NOT the same as the marginal revenue of the 250th ticket.

Explanation / Answer

a. Given Quantity = 250 seats

P = 1000 - 2Q

P = 1000 - 2 * 250

= 1000 - 500 = $500

Price per seat = 500 / 250 = $2

b. Total Revenue = Price * Quantity= (1000 - 2 Q ) * Q

= 1000 Q - 2 Q ^ 2

Marginal revenue = Differentiating TR with respect to Quantity

= 1000 - 4 Q

MR of 250th ticket = 1000 - 4 * 250 = 0

c. Since the demand curve is downward sloping, so to sell more units of the output the price has to be lowered. The price has to be lowered for all the previous units sold also. Thus, the MR of selling 250th ticket will be lower than the Price of the 250 tickets.

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