Assume that there are two goods, 2 and 2, and the consumer has a utility function u(1,2). Prices are p = 1 and p2 = p, and the consumer has wealth w. The government can raise revenues in one of two ways: (i) a lump-sum tax, where the government directly takes some amount T of the consumer's wealth, or (ii) a sales tax on good 2 at a rate 7 per unit of good 2 purchased. The government must raise amount R regardless of the method is uses. Show that a lump- sum tax leaves the consumer better off.