1. Consider a monopolistic team that chooses attendance, Q (measured in millions

Question

1. Consider a monopolistic team that chooses attendance, Q (measured in millions), to maximize profit. Let its demand be

  P = 100 – 20Q which results in marginal revenue of

  MR = 100 – 40Q

Also, suppose its total cost function is

  TC = 50 + 4Q

which entails a marginal cost of MC=4. Find the team’s optimal attendance, Q*, and ticket price, P*. Also compute its total profit (P•Q–TC).

2. Now consider a team that chooses winning percentage, WP, as its choice variable. Let its total revenue and total cost functions be given by TR = 100WP – 50WP2

TC = 60WP

The resulting marginal revenue and marginal cost expressions are

                    MR = 100 – 100WP

MC = 60

a.) Find the optimal winning percentage of a team that maximizes profit.

b.) Find the optimal winning percentage of a team that maximizes WP subject to TR–TC0. Compare your answer to (a).

Explanation / Answer

(1) Profit is maximized when MR equals MC.

100 - 40Q = 4

40Q = 96

Q* = 2.4 (Million)

P* = 100 - (20 x 2.4) = 100 - 48 = $52

TR ($Million) = P* x Q* = 52 x 2.4 = 124.8

TC ($Million) = 50 + (4 x 2.4) = 50 + 9.6 = 59.6

Profit ($Million) = TR - TC = 124.8 - 59.6 = 65.2

NOTE: As per Chegg answering guideline, first question is answered.

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