A minor league baseball team called the Billings Mustangs attracts both students

Question

A minor league baseball team called the Billings Mustangs attracts both students and non-students as fans during the season, which runs from about mid-April through August. The Mustangs organization has estimated that, among students, weekly demand for tickets varies according to the equation Q 1200 200P, where Q is the quantity of tickets sold and P is the price in dollars. Among non-students, weekly demand is given by the equation Q 800-100P. The Mustangs organization earns marginal revenue from students according to the equation MR = 6-0.01Q and from non-students according to the equation MR = 8-0.02Q. The Mustangs incur a marginal cost of $3 among all fans. The Mustangs would like to charge different prices for students and non-students. How many tickets would the Mustangs sell to students, to maximize profit? What price would the team charge to students? How many tickets would the Mustangs sell to non-students, to maximize profit? What price would the team charge to non-students? b. Whether selling ticket packs to students or non-students, the Mustangs organization incurs total costs according to the equation TC 290 +3Q If the Mustangs succeed at price discrimination, how much economic profit (or loss) will the team earn selling tickets to students? How much will it earn selling tickets to non-students? How much total economic profit will the team earn? c. Suppose the Pioneer League, in which the Billings Mustangs play prohibits price discrimination in this way and forces the club to charge a single price to all fans. How many tickets would the Mustangs sell to non- students if they charged non-students the student price (part a)? Show that MR MC in this situation. How many tickets would the Mustangs sell to students if they charged students the non-student price (part b)? Show that MR MC in this situation d.

Explanation / Answer

a..)

Profit maximization:

MR = MC

6 – 0.01Q = 3

3 = 0. 01Q

Q = 3/ 0.01

= 300

Q = 1200 – 200P

300 = 1200 – 200P

900 = 200P

P = 900/200

= 4.5

b)

Profit maximization in case of non-students:

8 – 0.02Q = 3

5 = 0.02Q

Q = 5/0.02

= 250

Q = 800 – 100P

250 = 800 – 100P

550 = 100P

P = 550/100

= 5.5

c)

Profit = TR – TC

= 5.5*250 +300*4.5 -290 -3(550)

= $ 785

d)

Non Student = 800 – 100(4.5)

                     = 800 – 450

                      = 350

Student = 1200 – 200(5.5)

           = 1200 – 1100

       = 100

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