Consider an industry that consists of Mo rms, Firm I and Firm A. The inverse demand function in this industry is p = l ql (1,1, and the cost functions are C; = V2 (11 and CA = 1/: qn. Suppose that Firm I is the leading rm in this industry, and hence, Firm I designs the strategic environment, i.e., Firm 1 determines the game stages and the sequence of moves. The strategic environmunt is as follows. In Stage 1, Firm 1 makes a non-binding announcement about its output level. It may announce that unless Firm A produces no goods and leaves the market (thus allowing Firm I to be a monopolist), it will \"ood the market\" by producing an output of l and will therefore drive the price to zero; or, it may announce its intention to share the market with Firm A by producing an output of U6. In Stage 2, after observing Firm I's announcement, Firm A decides whether to remain in the market and produce an output of No, or to leave the market. Firm A's decision is observed by Finn I. If Firm A decides to leave the market, the game ends. Otherwise, Stage 3 starts. In Stage 3, F inn I chooses its output level. It may decide to fulll its announcement and produce and output of l; or it may decide to produce an output of U6. a. Represent this strategic environment in an extensive form and characterize the SPNE for this game. Provide intuitive explanation regarding your results. b. Suppose that Firm I has the ability to redesign the duopolistic market and hires you as a business consultant. Would you recommend any,r changes in the strategic environment? Explain