Question

Suppose a golf course manager is considering using the two-part pricing to charge consumers. Each consumer needs to become a member first. There is also a unit price per visit for using the golf course. For simplicity, assume that there are two consumers. Consumer 1 has the demand curve P = 80 - Q1, and consumer 2 has the demand curve P = 100 - Q2, where Q1 and Q2 are the numbers of times the consumer will use the golf course respectively in one year. There is no fixed cost, and marginal cost is a constant $10, which implies that the average total cost (ATC) is also $10. The goal of the manager is to maximize the sum of the membership fee and the profit from both customers, where profit = (P - ATC)xQ.

Suppose price discrimination is possible, and the manager can charge each customer with different membership fees, but the same unit price per visit. How much should the manager charge each consumer in terms of the membership fee and the unit price per visit? How much is the sum of the membership fees and profits from both customers? (You must show calculations.)

Answer 1

The manager should set the unit price per visit to equal the marginal revenue and marginal cost, then calculate the maximum membership fee as the consumer surplus for each consumer, and ultimately sum the membership fees and profits to determine total revenue.

Step-by-step explanation:

The golf course manager looking to employ two-part pricing with price discrimination must first determine the profit-maximizing output and price for each consumer, and then the maximum membership fee that could be charged.

For Consumer 1, the demand curve is P = 80 - Q1. To find the unit price, we set the marginal cost equal to the marginal revenue (MR) that comes from the demand function, or MR = MC. Since there's no fixed cost and the marginal cost is constant at $10, MR is also $10. Then, we use the inverse demand curve to find Q1 which gives us the quantity, and using the P = 80 - Q equation, we can find the price that maximizes profit per visit. Similarly, for Consumer 2, we use demand curve P = 100 - Q2, setting MR equal to $10 to find the optimal quantity and price per visit.

Next, we need to calculate the maximum membership fee that can be charged without Consumer 1 and Consumer 2 reducing their number of visits to zero. We do this by calculating the consumer surplus, which is the area under the demand curve and above the price line up to the profit-maximizing quantity. The consumer surplus represents the maximum membership fee.

Finally, we calculate the total revenue from both consumers, which is the sum of the membership fees and the profits from the visits, where profit = (P - ATC)xQ.