Question

Suppose major league baseball consists if two types of teams: profit maximizing teams (e.g., Rays) and win maximizing teams (e.g., Red Sox). Before the season, each team decides the number of expected wins they are going to get that season by constructing a roster of players. Fans enjoy wins, but the additional revenue of each win is decreasing and given by the following average revenue inverse demand) curve: P(W) = AR(W) = 320 - 2W It is costly to increase the expected number of wins because the team has to acquire better talent. The cost of an additional win is constant at: MC(W) = 100 (You can think of this as being in millions of dollars in order to make it (slightly) more realistic. The total number of games in a season is 162 (i.e., the maximum number of wins is 162). 1. First, consider market where there are no salary restrictions. (a) Solve for the number of expected wins for the profit maximizing teams. (b) Solve for the number of expected wins for the win maximizing teams. (c) Compare the consumer surplus, profit (producer surplus) and total payroll of profit maximizing teams and win maximizing teams. (d) Is there parity (equal number of expected wins across teams) in this league? Explain. (hint: ignore the fact that the total number of games played across teams has to equal the total number of games in the league)

Answer 1

Answer:

a) Normal income for both benefit amplifying groups and win augmenting groups are given as AR(W) = 320-2W

Hence, all out income is TR(W) = 320W-2W2

furthermore, negligible income work is MR(W) = 320-4W......(1)

Likewise minor expense of extra win is MC(W) =100 .......(2)

For benefit amplifying wins, MR(W) = MC(W)

or on the other hand, 320-4W=100,

4W=320-100

4W= 220

W=220/4

W=55

In this manner, anticipated number of wins of benefit boosting groups = 55

b) The success boosting state of group is MR(W)=0

or on the other hand, 320-4W=0

   4W=320

W=320/4

   W=80

In this way, anticipated number of wins of win augmenting groups = 80

c) the compensation top doesn't accomplish equality between anticipated number of wins of the two groups. All out number of games in a season is 162, anticipated number of wins of benefit expanding groups is 55 also, expected number of wins of win amplifying groups = 80.

Along these lines, 162-55-80= 27 games would wind up in a draw.

d) The normal income capacity of anticipated number of wins is

AR(W) = 420-2W

In this way, Negligible income capacity of anticipated number of wins is

MR(W) = 420-4W

Likewise Negligible expense of extra win (W) is McC(W) = 100

Accordingly for benefit amplifying condition, MR(W) =MC(wW)

or then again, 420-4W=100

4W=420-100

4W=320

W=320/4

W=80

Thusly, anticipated number of wins of benefit augmenting groups is 80

Again for win augmenting condition,

MR(W) = 420-4W= 0

or on the other hand, W= 105 yet the most extreme number of expected successes =80.

Thusly, anticipated number of wins of win boosting groups is 80.

Right now, top accomplish equality of anticipated number of wins of the two groups. Since win augmenting groups won't attempt to win more than 80 games as it will build their expenses of extra wins.