14. (20 points) Information disclosure and adversting. 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 consumer of type x derives utility r-tx-p if she purchases product 1 and utility rt (1-x)-p2 if she purchases product 2. If a consumer learns that product i has the undesirable ingrediente, utility is decreased by d (with d < 3t). Suppose that parameter values are such that in the equilibria to be characterized below the market is fully covered. Firms set price simultaneously. a. (4 points) Derive the equilibrium if firms cannot inform consumers that their product contains the undesirable ingredient. b. (6 point) Suppose now that, at an initial stage, firm i simultaneously decides whether to inform consumers that its product contains an undesirable ingredient (suppose that such informative advertising is costless). Characterize the equilibrium of the two-stage game. (Hint: there are three subgames to consider: both firms do not advertise the undesirable ingredient, both firms advertise it and only one firm advertises it; construct a normal form game where the two actions in the initial stage are Inform (I) and Not Inform (NI), payoffs are profits and find the subgame perfect Nash equilibrium).Explain c. (6 points) Suppose now that, at an initial stage, firms can simultaneously launch costly attack adverts in which they reveal that their competitor's product contains an undesirable ingredient. Characterize the subgame perfect Nash equilibrium of the two-stage game depending on the advertising cost size of A. (Hint: construct a normal form game where the two actions are Attack advert against competitor as A and No attack advert as NA) d. (4 point) Are consumers better off in this equilibrium compared with the solutions in parts a) and b)? Should attack adverts be allowed in this setting? Explain your result. 2