Econ425 Homework 5 Intertemporal choices 1 1. (8 points) Tax on saving Mr. Jones' life time utility is given by the following, (cf1) + 0.9(c2_1). (a) Suppose that his rst period income is $80,000 and second period income is $0. Suppose that the real interest rate is 7%. Solve Mr. Jones's optimal consumption allocation. Find the size of his saving. (b) Suppose that government collects income tax on the interest income Mr. Jones receives on his saving in the second period. This type of tax is called the capital income tax. If Mr. Jones save $100, he will have $7 interest income. Suppose that the tax rate is 15%. Government will take away 15% ' $7 = $1.05 from him and he is left with 85% - $7 = $5.95. Such tax makes saving less rewarding; it also changes the relative price between c1 and c2. We need to dene the after tax interest rate, 7" = (1 15%) - 0.07 = 0.0595. The two equations becomes . 1 MRSC1,.:2 = 1+1" or MRS\