3. Suppose per-period utility over consumption and labor is given by: u(c, It) = However, now there are three periods instead of two. Assume the household's labor income = ItWe and that they have access to a bond, b that pays i every period. Note that By does not necessarily equal Ba- (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 = (G Ar) "wij = Y = q be the initial level of labor, output, and consumption. Suppose By increases. If nominal wages are downwardly rigid (they can't fall), what happens to Pi? Why? Holding P2, 62, and i constant, what happens to ci? Call the new level of consumption, ci. Is ci less than, equal to, or greater than cf? (d) Given e, and the same Wi, do workers want to work less? How much would they be willing to work? That is, what is ; 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