Before the MLB season begins, the Red Sox choose 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: AR(W) = P(W) = 160 W

It is costly to increase the number of wins because the team has to acquire better talent. The cost of an additional win is constant at MC = 80.

The total number of games in a regular MLB season is 162.

a) Find the Red Sox marginal revenue curve, MR(W).

b) If the Red Sox objective is to maximize profits, how many wins (W1) are chosen?

c) If the Red Sox objective is to maximize the number of wins, how many wins (W2) are chosen?

d) Repeat b) and c) if the total number of games in the MLB season is reduced to 60.

e) In response to the pandemic, the MLB's 2020 season was in fact reduced to 60 games. Do the results from this problem accurately describe the effects of this change on team decisions? Briefly explain your reasoning.