Question

Promoters of a major college basketball tournament estimate that the demand for tickets on the part of adults is given by Qad = 5,000 –10P, and that the demand for tickets on the part of students is given by Qst = 10,000 –100P. The promoters wish to segment the market and charge adults and students different prices. They estimate that the marginal and average total cost of seating an additional spectator is constant at $0.

a.For each segment (adults and students),find the inverse demand and marginal revenue functions.

b.Equate marginal revenue and marginal cost. Determine the profit-maximizing quantity for each segment.

c.Plug the quantities you found in (b) into the respective inverse demand curves to find the profit-maximizing price for each segment. Who pays more, adults or students?

d.Determine the profit generated by each segment, and add them together to find the promoter’s total profit.

e.How would your answers change if the arena where the event was to take place had only 5,000 seats?

Answer 1

a)

y Qad = 5,000 – 10P

P= 500 -(1/10)Q

TR= 500Q - (1/10)Q^2

MR = 500 - (1/5)Q

Qst = 10,000 – 100P.

P = 100 - (1/100)Q

TR = 100Q - (1/100)Q^2

MR = 100 - (1/50)Q

b)

Adult profit-maximizing output:

MR= MC

500 - (1/5)Q =0

Q = 500*5

= 2500

Student profit maximizing outut:

100 - (1/50)Q = 0

100 *50 = Q

Q = 5000

c)

Adult price:

P = 500 - (1/10)*2500

= 500 - 250

= 250

Student price:

P = 100 - (1/100)*5000

= 100 - 50

= 50

d)

Profit adult:

= 250*2500 - 0*2500

= 625000

Profit Student:

Profit = 50*5000 - 0*5000

=250000 - 0

=250000

e)

Qs +Qa = 5000

Qs = 5000 - Qa

500 - (1/5)Qa = 100 - (1/50)Qs

400 - (1/5)Qa = (1/50)(5000-Qa)

Qa =1666

Qs = 5000 -1666

= 3334