Consider an elaboration of the Cournot duopoly game in which firm 1 engages in advertising before the firms compete in the market.

2. (35 marks) Consider an elaboration of the Cournot duopoly game in which firm 1 engages in advertising before the firms compete in the market. Firm 1 selects an advertising level a, which is a number greater than or equal to zero. Advertising has a positive effect on the demand for the good sold in the industry, enhancing the price the consumers are willing to pay for the output of both firms. In particular, the market price is p = a q1 qz, where ql is the output of firm 1 and q2 is the output of firm 2. After firm 1 selects a, it is observed by the other firm. Then the two firms simultaneously and independently select their production levels. Assume for simplicity that the firms produce at zero cost. However, firm 1 must pay an advertising 3 cost of 28%. Find the subgame-perfect Nash equilibrium of this game, and report the profit-maximising choice of advertising level for firm 1, and the corresponding quantity choices of both the firms