Consider the linear Hotelling duopoly in which each firm produces a product with a firm-specific undesirable ingredient at zero marginal costs. Suppose that, absent advertising, consumers are not aware of this ingredient. In this case a consumer of type x derives utility r - tx - p₁ if she purchases product 1 and utility r - t(1 - x) - p₂ if she purchases product 2. If a consumer learns that product i has the undesirable ingredient utility is decreased by d. Suppose that parameter values are such that in the equilibria to be characterized below the market is fully covered. Firms set prices simultaneously.

1. Derive the equilibrium if firms cannot inform consumers that their product contains the undesirable ingredient.

2. Suppose that, at an initial stage, firm i simultaneously decide whether to inform consumers that its product contains an undesirable ingredient (suppose that such informative advertising is possibly cost less). Characterize the equilibrium of the two-stage game.

3. Suppose now that, at an initial stage, firms can simultaneously launch costly attack ads in which they reveal that their competitor’s product contains an undesirable ingredient. Characterize the equilibrium of the two-stage game depending on the advertising cost A. Are consumers better o¤ in this equilibrium compared to the solutions in (1) and (2). Explain your result.

4. Should attack ads be allowed in this setting?