4. Promoters of a major college basketball tournament estimate that the demand f

Question

4. 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 $20. Determine the optimal price to charge adults and students. a. Adults pay $235.5 each; students pay $60 each b. Adults pay $257.5 each; students pay $65 each. c. Adults pay $257.5 each; students pay $57.5 each d. Adults pay $260 each; students pay $60 each

Explanation / Answer

demnand function for adults  

Q = 5000 - 10P

10P = 5000 - Q

P = 500 - Q/10

MR = 500 - Q/5

MR = MC

500- Q/5 = 20

500 - 20 = Q/5

480 = Q/5

Q = 2400

P = 500 - 2400/10

= 500 - 240

= 260

monopolist will charge for adults Rs 260

Demand function for students

Q = 10000 - 100P

100P = 10000 - Q

P = 100 - Q/100

So MR = 100 - Q/50

MR = MC

100 - Q/50 = 20

100 - 20 = Q/50

80 = Q/50

Q = 4000

P = 100 - 4000/100

= 100 - 40

= 60

monoplost will charge for students Rs 60

so option d is correct

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