LO 2, 5 Suppose that all consumers are identical, and also assume that the real interest rate r is ixed.

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: (i)

a proportional tax of s per unit of savings, in that the tax collected per consumer is s(y - c); (ii) 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 s could be positive or negative. For example if consumers borrow, then s would need to be less than zero for the government to collect tax revenue. Show that option (ii) is preferable to option (i) if the government wishes to make consumers as well of as possible, and explain why this is so. [Hint: Show that the consumption bundle that consumers choose under option (i) could have been chosen under option (ii), but was not.]