3. Suppose per-period utility over consumption and labor is given by: 4.1-sz 10 1+? (cts Lt) = However, now there are three periods instead of two. Assume the household's labor income = LtWt and that they have access to a bond, b that pays every period. Note that B2 does not necessarily equal 3. (a) What is the household's new lifetime budget constraint? (b) Solve the household's problem to get their 2 inter-temporal (Euler) condi- tions and 3 intratemporal (labor supply) conditions. (c) Iet LI = (CIE%1)1_ = Yf' = of be the initial level of labor, output, and consumption. Suppose ,82 increases. If nominal wages are domwnm'ly rigid (they can't fall), what happens to P1? Why? Holding P2, c2, and i constant, what happens to c1? Call the new level of consumption, Cl- ls Cl less than, equal to, or greater than of? (d) Given 0'1 and the same W1, do workers want to work less? How much would they be willing to work? That is, what is L1 as a function of 01 and W1? Is it greater or less than L? (e) What is the denition of potential output? Is output above or below poten- tial output now? Explain. (f) If the Federal Reserve is following a Taylor rule, how should they respond to this shock? \fWe'll show that the Central Bank can achieve its policy goals by following a Taylor Rule of the form (by and (, are both positive): it = it by ( Y + - Y ) + DT ( Tit ) Where Y is 'potential output' and Y - Y is the 'output gap