1. Two profit-maximising firms-call them firm 1 and firm 2- compete in quantities. Before the firms choose their quantities, firm 1 has the option to spend money on advertising, which allows differentiating the two products. That is, firm 1 chooses a [0, 1] (i.e., 0 a 1) and pays ca, with c> 0. The two firms then face the following inverse demand functions: P = 1-9-(1-a)q2 and p2=1-92-(1-a)g. There is no cost of production so the profit of firm 1 is 1 = P191 - ca and the profit of firm 2 is 2 = P292. (a) (10 points) Without doing any calculation, briefly explain what the market struc- ture would be if firm 1 one chose not to advertise at all (a = 0) and if it chose the maximal amount of advertising (a = 1). [max: 50 words] (b) (15 points) For any value of a [0, 1], calculate the equilibrium quantities. 1 (c) (15 points) Calculate the optimal level of advertising for firm 1. (d) (10 points) Briefly provide intuition for your results. [max: 50 words]