Now suppose the household lives forNperiods, from Period 1 toN. Household receives an exogenous income stream{y1,y2, ...yN}, and accumulate their financial wealthatin each period. The return on real financial wealth isr. Let household's problem be

3 Optimal Consumption with Financial Wealth In lecture 2, we saw an example where the household only lives for two periods. Now suppose the household lives for N periods, from Period 1 to N. Household receives an exogenous income stream {y1,y2, ...yN}, and accumulate their financial wealth at in each period. The return on real financial wealth is r. Let household's problem be t= 1 max Egt-lin(ct) (1) Ct subject to at+1 = (1 +r)at + yt - ct (2) Ct 2 0 (3) aN+120 (4) where at is the financial wealth at the beginning of Period t and al = 0. 1. Interpret (1) (2) (3) and (4). 2. Write down the inter-temporal budget constraint and derive the Euler equation(s). 3. Assume B = 1, r = 0. Solve for the optimal consumption for each period, {ct }, t = 1, 2, ..., N. Explain how your results are related to permanent income theory