27.2* In exercise 27.1, we extended our analysis of subsidized voluntary giving from 2 to N people. In the process, we simply assumed the government would set t to cover its costs, and that individuals would take t as given when they make their decision on how much to give. We now explore how the strategic setting changes when individuals predict how their giving will translate into taxes.

A. Consider again the case where N identical people enjoy the public good.

a. First, suppose N 5 2 and suppose the government subsidizes private giving at a rate of s. If individual n gives yn to the public good, what fraction of the resulting tax to cover the subsidy on his giving will he have to pay?

b. Compare the case where the individual does not take the tax effect of his giving into account to the case where he does. What would you expect to happen to n’s best response function for giving to the public good in the former case relative to the latter case? In which case would you expect the equilibrium response to a subsidy s to be greater?

c. Explain the following true statement: When N 5 2, a subsidy s in the case where individuals do not take the balanced-budget tax consequence of a subsidy into account will have the same impact as a subsidy 2s in the case where they do.

d. Given your answer to

(c) (and given that the optimal subsidy level when N 5 2 in exercise 27.1 was 0.5), what do you think s would have to be to achieve the efficient level of the public good now that individuals think about balanced-budget tax consequences?