3. There is widespread concern that Americans save too little. At an aggregate level, a lack of savings can lead to a lack of investment, which can attenuate the growth of the economy. At an individual level, a lack of savings can lead to inadequate re- tirement income. Leaving the first question to macroeconomics, we will examine the second. How might we ensure people have adequate retirement incomes? The answer to this question depends partly on income and substitution effects. Let us start with the utility function U(c1, C2) = 200ci - C + 20c2, where we now think of c, as the amount of money spent on current consumption and c2 the amount of money spent on future consumption. A more realistic model would require more periods, but we will think of period one as this person's working period and period two as retirement. Let the person's income be Mi in period one and M2 in period two. Under ordinary circumstances we would expect M, to be quite a bit smaller than Me, possibly with M2 = 0. Let the interest rate ber. 3.1 Write the budget constraint for this person, find the first-order conditions for utility maximization, and find the associated demand functions for consumption in period one and in period two