Question is below:

1. There is a society consisting of n voters, and voters' utility function is given as u; (B) = log B + (1-t); where B is government spending on a public good, t is the income tax rate (proportional tax), and I; is voter i's income. The government's budget constraint is given as Eith = B (1) Find voter i's utility function excluding t by substituting the government's budget constraint and using n and the average income I. (2) As an illustrative example, create a rough graph where the horizontal axis is B, and the vertical axis is a voter's utility. (3) Find the amount of B to maximize the sum of n people's utilities. (4) Suppose that n = 3 and the amount of B is determined by the equilibrium of the Downs model of the two parties. Compare the amount of B between the cases when all three are I,=100 and when I1 = 40, 12 = 60, and /3 = 200