Consider the Hotelling model in which consumers are uniformly distributed on the [0, 1]-interval and firms A and B are located at the extreme points. Firms produce a product of quality s_i. Consumer x ∈ [0, 1] obtains utility u_A = (r - tx) s_A - p_A if she buys one unit of product A and u_B = (r – t (1 - x)) s_B - p_B if she buys one unit of product B. Each consumer buys either one unit of product A or one unit of product B.

1. Describe the property of the utility function with respect to quality in two or three sentences.

2. Determine the demand for products A and B at given prices and given qualities.

3. Suppose that qualities s_A and s_B are given and that marginal costs of production are zero. Determine the Nash equilibrium in prices under the assumption that qualities are not too asymmetric implying that both firms have a strictly positive market share in equilibrium.

4. Suppose that qualities are symmetric and that the cost of quality C(s_i) is increasing and strictly convex in s_i. How does the equilibrium profit depend on quality?

5. Compare this finding to the standard quality-augmented Hotelling-model in which consumer x obtains utility u_A = r + s_A - tx - p_A if she buys product A and u_B = r + s_B – t (1 - x) - p_B if she buys product B.