Consider the utility function U(x 1 , x 2 ) = x 1 + x 2 , where we now think x 1 as the amount of money spent on current consumption and x 2 the amount of money spent on future consumption. A more realistic model would require more periods, but we will think of period 1 as this person's working period and period 2 as retirement. Let the person's income be I 1 in period 1 and I 2 in period 2. Under ordinary circumstances we would expect I 2 to be quite a bit smaller than I 1 , possibly with I 2 = 0. Let the interest rate be r.