Consider a public project to build a bridge. The government is deciding whether

Question

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 = k + 10 t, [0, 30] Let t = 9.7; that is, each person pays the same amount for the project.

(a) Assume the government knows . For which values of it is socially optimal to build the bridge?

(b) Now assume that the government does not know . For which values of individuals 1 will have incentives to reveal his true valuation? Explain.

Explanation / Answer

Total Utility=Sum of utility for 10 people

Total utility=(10K+10-t)*9+ K+10-t

Total utility=90K+100-10t+K

K=1 If bridge is built and t=9.7

Total utility=90+100-10*9.7+

Total utility=93+

For bridge to be socially optimal

Total utility>=Total cost(C)

93+>=97

>=4

As mentioned E[0, 30]

Combining above

For 4<=<=30,it is social optimal to build the bridge

b)

If bridge is not build at all, the Utility of Individual 1= *0+ 10 – 0=10

If Bridge is built the utility of individual 1= + 10 – 9.7= +0.3

For individual 1

+0.3>=10

>=10.3

For 10.3<=<=30, the individual has incentive to reveal his true valuation

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