Question

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–TC≥0. Compare your answer to (a).

Answer 1

a.

WP	TR	TC	Profit	MC	MR
0.1	9.5	6	3.5	60	90
0.2	18	12	6	60	80
0.3	25.5	18	7.5	60	70
0.4	32	24	8	60	60
0.5	37.5	30	7.5	60	50
0.6	42	36	6	60	40

At WP = 0.4 or 40% and where MC=MR the profit becomes maximum

b.

WP	TR	TC	Profit
0.1	9.5	6	3.5
0.2	18	12	6
0.3	25.5	18	7.5
0.4	32	24	8
0.5	37.5	30	7.5
0.6	42	36	6
0.7	45.5	42	3.5
0.8	48	48	0
0.9	49.5	54	-4.5
1	50	60	-10

WP becomes maximum at 0.8 or 80% where TR-TC=0

So when compared with a, the winning percentage increase with the decrease in profit