Consider a public project to build a bridge. The government is deciding whether to undertake it or not. Let k = 1 if the bridge is built and k = 0 if the bridge is not built. The cost of building the bridge is C = 97. There are 10 individuals, such that 9 of them have utility of the form: Ui = 10k + 10 − t, i = 2, ..., 10 where t is the payment for the project. Individual 1 has utility: U1 = θk + 10 − t, θ ∈ [0, 30] Let t = 9.7; that is, each person pays the same amount for the project.
(a) Assume the government knows θ. For which values of θ it is socially optimal to build the bridge?
(b) Now assume that the government does not know θ. For which values of θ individuals 1 will have incentives to reveal his true valuation? Explain.