Consider an economy with N population. Assume Y^i is the individual income and Ti is the tax paid by each of N members of society. Tax revenues are used to finance public good G and the price for each unit of G is $1. The utility function for each individual i is U^i = (Y^i - T^i)^(1-beta) G^beta, with 0 < beta < 1.

(a) If we can use the majority voting to find the outcome G, calculate the outcome G?

(b) Assume T^i = alphaY^i. Find outcome G as a function of mean income, y, and beta using the majority voting outcome.

(c) When income is uniformly distributed, which outcome is closest to the efficient outcome? What is the main element that the efficient level of provision is dependent on?