Promoters of a major college basketball tournament estimate that the demand for tickets for *adults* and by *students* are given by:

\[\begin{aligned} q_a&=5,000-10p_a\\ q_s&=10,000-100p_s\\ \end{aligned}\]

where \(a\) represents adults and \(s\) represents students. They estimate that the marginal and average total cost of seating an additional spectator is constant at $10.

## 1.

The promoters wish to segment the market and charge adults and students different prices.

### a.

For each segment of the market, find the inverse demand function and marginal revenue function.

### b.

Find the profit-maximizing quantity and price for each segment.

### c.

How much total profit would the tournament earn if they could price discriminate?

## 2.

Now suppose they could not price discriminate, and were forced to charge the same price for all attendees.

### a.

Find the total market demand function.

### b.

Find the inverse demand function for the total market, and then the marginal revenue function.

### c.

Find the profit-maximizing quantity and price for the whole market.

### d.

How much total profit would the tournament earn if they could not price discriminate?