kindly show work for me to learn thanks

3. Suppose per-period utility over consumption and labor is given by: 1- -1+Y Ct Lt u(ct, Lt) = 1-o 1+y However, now there are three periods instead of two. Assume the household's labor income = LW, and that they have access to a bond, b that pays i every period. Note that 5 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 intra-temporal (labor supply) conditions. (c) Let Li = (cto W) = Y = c be the initial level of labor, output, and consumption. Suppose 3 increases. If nominal wages are downwardly rigid (they can't fall), what happens to P? Why? Holding P2, c2, and i constant, what happens to c? Call the new level of consumption, c. Is c less than, equal to, or greater than cf? (d) Given c and the same W, do workers want to work less? How much would they be willing to work? That is, what is L as a function of c and W? Is it greater or less than Li? (e) What is the definition 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? 3. Suppose per-period utility over consumption and labor is given by: 1- -1+Y Ct Lt u(ct, Lt) = 1-o 1+y However, now there are three periods instead of two. Assume the household's labor income = LW, and that they have access to a bond, b that pays i every period. Note that 5 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 intra-temporal (labor supply) conditions. (c) Let Li = (cto W) = Y = c be the initial level of labor, output, and consumption. Suppose 3 increases. If nominal wages are downwardly rigid (they can't fall), what happens to P? Why? Holding P2, c2, and i constant, what happens to c? Call the new level of consumption, c. Is c less than, equal to, or greater than cf? (d) Given c and the same W, do workers want to work less? How much would they be willing to work? That is, what is L as a function of c and W? Is it greater or less than Li? (e) What is the definition 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