Consider a representative consumer with the following preferences over two goods, x1 and x2: U(x1, x2) = x .5 1 x .5 2 Initially, p1 = 1, p2 = 4, and income y = 8. Without any government intervention, the maximum utility such a consumer would reach is 2. Suppose the government wanted to improve each consumer's utility to a value of 3 (ignore the problem with measuring utility). How much of a per-unit subsidy on good 1 would be needed? How much would this program cost per person?