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Firm 1 and Firm 2 are competing for a franchise. The present value of the net revenues generated by the franchise is equal to R. Each firm's probability of winning the franchise is given by its proportion of the total spent by the two firms on lobbying the local government committee that awards the franchise. That is, if 11 and 12 represent the lobby expenditures of Firm 1 and Firm 2, respectively, then Firm's 1's probability of winning is 11/01 +12) and Firm 2's probability of winning is 12/(11 +12). If each firm assumes that the other firm's spending is independent of its own, what is the equilibrium level of spending for each firm? Assume that the firms are risk neutral.3. Consider the following mechanism design problem. Let x E [0, 1] denote the level of a public good that affects the welfare of two individuals. Suppose both individuals receive utility v; from public good x and monetary transfer m = (m1, m2). Specifically, let v1(x, m1, 01) = 01 In(x) +m where 01 = 2 with probability 1/2 and 61 = 4 with probability 1/2, while v2(x, m2, 02) = 02a1/2 - x + m2 where 02 = 1 for sure. (a) Identify all possible states (i.e., type profiles) and find the first-best decision rule. (b) Find the pivotal mechanism transfer rule and verify that budget balancedness is not satisfied. (c) Find the expected externality transfer rule and show that budget balancedness is satisfied. (d) Verify that the expected externality mechanism you found above is incentive com- patible. (e) Verify that the expected externality mechanism you found above is individually rational