Question

Assume that a professional sports team is a profit-maximizing (but not a price-discriminating) monopolist. Assume the inverse demand for tickets is given by P = 12 – 0.75Q.

Assume that the marginal cost of selling another ticket is constant and equal to three ($3) per ticket sold and fixed costs $19. Assume there are no capacity constraints.

a) Draw a completely labelled graph of the situatIon described above.

b) Calculate the optimal price, number of tickets sold, consumer surplus, and team profits.
c) Calculate the amount of deadweight loss to society from not having perfect competition in tickets
d) Now, assume the team can identify the maximum willingness to pay for each unique consumer (that is, the team is a perfect price discriminating monopoly). How many tickets will it sell and at what price?

e) For the price discriminating monopoly, illustrate in your graph and calculate the consumer surplus and the deadweight loss.

Answer 1

To determine the monopoly's profit-maximizing price and quantity, we first need to find the point where marginal revenue (MR) equals marginal cost (MC). Once we have the price and quantity, we can calculate the total revenue, total cost, and profit. If the monopolist can price discriminate perfectly, it can sell each ticket at the maximum price every consumer is willing to pay.

Step-by-step explanation:

To determine the monopoly's profit-maximizing price and quantity, we first need to find the point where marginal revenue (MR) equals marginal cost (MC). In this case, the demand curve is given by P = 12 - 0.75Q. The marginal cost is constant at $3 per ticket. When MR = MC, we can solve for the quantity (Q) and then use the demand curve to find the corresponding price (P).

Once we have the price and quantity, we can calculate the total revenue, total cost, and profit. Total revenue is the price multiplied by the quantity sold, while total cost is the sum of fixed costs and variable costs. Profit is equal to total revenue minus total cost.

To calculate consumer surplus, we need to find the area between the demand curve and the price line. Deadweight loss can be calculated as the difference between the consumer surplus under perfect competition and the consumer surplus under monopoly.