Suppose that all consumers are identical, and also assume that the real interest rate r is fixed. Suppose that the government wants to collect a given amount of tax revenue R, in present-value terms. Assume that the government has two options: (1) a proportional tax of v per unit of savings, in that the tax collected per consumer is v(y - c); (2) a proportional tax u on consumption in the current and future periods, so that the present value of the total tax collected per consumer is uc + (uc') / (1 - r). Note that the tax rate v could be positive or negative. For example, if consumers borrow, then v would need to be less than zero for the government to collect tax revenue. Show that option 2 is preferable to option 1 if the government wishes to make consumers as well off as possible, and explain why this is so. [Hint: Show that the consumption bundle that consumers choose under option 1 could have been chosen under option 2, but was not.] The proportional tax, v, on savings results in a consumer's lifetime budget constraint given by O A. C' y' C+ 1 +r 1+v (1+ r)(1+v) O B. c' y' v(y - c) C+ - 1+r =y + 1 + r 1 + r O C. C' y' C + (1+ r)(1-v) =y+ (1 + r) ( 1 - v ) OD. c (1 - v) y'(1 - v) C+ 1 + r Fy + (1 + r) ( 1 + v)