(Don't copy the answer)Consider the situation of private provision of a public good. Assume there are H households, each with a utility function of the following form:

Uh = x^h + ^hln(G)

where x^h is private consumption of household h, G is public consumption, and h is a preference parameter: ¹ < ² < ... < ^H . Total public consumption is the sum of the households' private provision: G = g¹ + g² +...+ g^H. Each individual is facing the budget constraint

x^h + g^h = ^h

where ^h is the endowment of individual h.

a) Show that, in a Nash equilibrium, only household H contributes to the public good (i.e. only the household with the largest ), and all the other contribute 0.

b) What is the economic intuition behind the result in a)?