Problem
Consider a cooperative of wheat producers in South Carolina, who sell their products to two types of customers: households, with demand q1 = 100 - 3p1; and to local millers, with demand q2 = 100 - 0.5p2. The cooperative operates as a monopolist in the area, and its cost function is C(q) = 1,300 + 4q, where q = q1 + q2 is the total output produced. There is no possibility of arbitrage between the two groups.
1. Because of different demands, the monopolist can practice third degree price discrimination. In this case, set up the profit-maximizing problem for the cooperative.
2. Find the optimal output levels and prices for each group of customers.
3. Calculate the cooperative's profit under third-degree price discrimination.
4. Assume now that the cooperative can practice first-degree price discrimination. Find the optimal output levels and prices for each group of customers.
5. Calculate the cooperative's profit under first-degree price discrimination. (Hint: The profit is the sum of the areas under the demand curve and above the marginal cost for each group of customers minus the fixed cost, $1300).
6. How do the profits for third-degree and first-degree price discriminations compare?
7. Why is it difficult to practice first-degree price discrimination?