suppose the utility of John is given by u(x1x2=x1x2, his income is m, x1 and x2 are two commodities with prices p1 and p2 respectively. a) write down john's demand function for x1 and x2 b) Assuming p1 = 0.25, p2 =1, and m = 2, figure out John's optimal demand of commodity x1 and x2, and the corresponding utility. c) Assuming the government imposed an income tax that collected 0.5 from john, what is the optimal utility of John now? d) Assuming the government imposed a commodity tax rather than an income tax. Each unit of commodity x1 was taxed by 0.25, Now calculate the optimal consumption, the corresponding utility, and the amount of tax revenue. e) which type of tax is better for John, the income tax or the commodity tax?