Consider the Slappers, a hockey team that plays in an arena with 12,000 seats. The only cost associated with staging a hockey game is a fixed cost of $6,000. The team incurs this cost regardless of how many people attend a game. The demand curve for hockey tickets is Q = 12,000 - 1000P and the marginal revenue curve associated with this demand curve is MR = 12 - 0.002Q.
a. The owner’s objective is to maximize the profit per hockey game. He does this by deciding how many tickets to sell (how many seats to fill … some may be left empty). At the profit maximizing output level, how many tickets will be sold?
Always always always. Marginal cost=Marginal revenue. In this amazing arena where there are no marginal cost MC=0=MR.
To find the profit-maximizing output level, we need to set the marginal cost (MC) equal to the marginal revenue (MR). In this case, the marginal cost is zero because there are no additional costs incurred when selling more tickets.
The marginal revenue is given as MR = 12 - 0.002Q, where Q represents the quantity of tickets sold.
Setting MC = MR:
0 = 12 - 0.002Q
Solving for Q:
0.002Q = 12
Q = 12 / 0.002
Q = 6000
Therefore, the profit-maximizing output level for the Slappers hockey team is 6000 tickets, which means they should sell 6000 seats.