Suppose that a supermarket offers a product selection consisting of products A and B. Consumers are willing to pay 10 Euro for one unit of product A and 10 Euro for product B. Consumers have heterogeneous shopping cost z. This shopping cost is uniformly distributed over the interval [0, 10]. Consumers are of mass 10. The firm has marginal cost of 6 for product A and 0 for product B.

1. Calculate the profit-maximizing prices p_A and p_B. How much profit can the supermarket make.

2. Suppose that a discounter has entered the market who sells product A at its (lower) marginal costs of 4 Euro. Now consumers can opt for one- stop shopping at the supermarket, two-stop shopping at the supermarket and the discounter, or not to shop at all. The shopping cost z applies to each stop. Determine the profit maximizing prices of the supermarket. Determine the super-market’s profit.

3. Compare your results in (2) to those in (1). Interpret your findings.