Consider a public project to build a bridge. The government is deciding whether
ID: 1189926 • Letter: C
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