Consider an economy consisting of two firms, labeled 1 and 2. Each firm i = 1,2 chooses x₁ € [0,1], which yields a profi

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Consider An Economy Consisting Of Two Firms Labeled 1 And 2 Each Firm I 1 2 Chooses X 0 1 Which Yields A Profi 1 (49.56 KiB) Viewed 44 times

Consider an economy consisting of two firms, labeled 1 and 2. Each firm i = 1,2 chooses x₁ € [0,1], which yields a profit of 0₁(x)² 7₁ (x₁, x₁) = x₁- +₁, 2 where t, indicates a transfer from the government to firm i and 0, € [1,2] indicates the firm i's type. Assume that 0₁ and 2 are independently drawn from a common distribution F over the interval [1,2]. (a) Suppose that the firms choose the x simultaneously and independently. Assume there are no transfers: t₁ = t2 = 0. Compute a Bayesian Nash equilibrium of this game. (b) Suppose that the government can observe the firms' types (01,02), and that it seeks to max- imize 7₁ +7₂. Setting transfers equal to zero, compute the first-best allocation (x,x) as a function of the types. (c) Now suppose that the government cannot observe the firms' types. Design a direct reve- lation mechanism satisfying the following two properties: (i) the mechanism implements the first-best allocation in dominant strategies, and (ii) the mechanism always results in a balanced budget, i.e., t1 (01, 02) + t2 (01,02) = 0.