Consider two firms that compete according to the Bertrand model, and both have constant marginal costs equal to w. Demand is given by Q = 12 2P.

Suppose that either firm can engage in advertising. This advertising increases the demand for the product. Let a1 be the amount of advertising done by firm 1 and let a2 be the amount of advertising done by firm 2. Given these two amounts of advertising, suppose that demand is given by, Q = 12 + a1 + a2 2P. This advertising is not costless, however. The advertising is an additional fixed cost that must be sunk by the firm, and the cost to firm i is equal to 1/2(ai²). Suppose the two firms first simultaneously choose advertising levels in the first stage of the game. Then, in the second stage of the game they simultaneously choose prices. What is the unique equilibrium to this game? (Hint start with the second stage for a given (a1, a2) and work backwards).