Consider the baseline NK model with the following log-linearized equilib- rium conditions. First, the household's log-linearized...

   

Transcribed Image Text:

Consider the baseline NK model with the following log-linearized equilib- rium conditions. First, the household's log-linearized Euler equation is given by: (4) CE[C+1]-(e-Ex[1]) The household's log-linearized labor supply is given by Wt - Pt = oCt + oNt = A firm i's log-linearized production technology is given by Yt(i) = u + N. where At - 1 = PA (At-1-1) + A, PA (0, 1), ~ N(0,0) (5) (6) (7) If prices were fully flexible in the absence of constraints on price ad- justment, firms would set a constant markup over marginal cost. With the Calvo-style pricing frictions, there is a new Keynesian Phillips curve (NKPC) in terms of the output gap: Tt = BEt [t+1] + KXt (8) Suppose that the government purchases (Gt) a fraction Tt of the output of each good, with Tt varying exogenously. Government purchases are financed through lump-sum taxes. where 6 > 0,8"> Gt Gt = te Tt-F = TtYt (9) Pr (Tt-1-7)+, &~ N(0,0) out capital (10) liza, on Assume that monetary policy is set according to the simple interest rate rule: (b) Solve for it = nt (11) (a) Derive a log-linearized version of the goods market clearing condition. (b) Determine the behavior of the natural level of output Y as a func- tion of ft and discuss the mechanism through which a fiscal expansion leads to an increase in output when prices are flexible. ay, and derive an expression Oft' (c) Define one possible fiscal multiplier as for it. What does it depend on? (U) (d) Derive the Dynamic IS equation of the following form: X = E[X] - = - E[Te+ - ) together with an expression for the natural rate, RN as a function of ft and t. R Consider the baseline NK model with the following log-linearized equilib- rium conditions. First, the household's log-linearized Euler equation is given by: (4) CE[C+1]-(e-Ex[1]) The household's log-linearized labor supply is given by Wt - Pt = oCt + oNt = A firm i's log-linearized production technology is given by Yt(i) = u + N. where At - 1 = PA (At-1-1) + A, PA (0, 1), ~ N(0,0) (5) (6) (7) If prices were fully flexible in the absence of constraints on price ad- justment, firms would set a constant markup over marginal cost. With the Calvo-style pricing frictions, there is a new Keynesian Phillips curve (NKPC) in terms of the output gap: Tt = BEt [t+1] + KXt (8) Suppose that the government purchases (Gt) a fraction Tt of the output of each good, with Tt varying exogenously. Government purchases are financed through lump-sum taxes. where 6 > 0,8"> Gt Gt = te Tt-F = TtYt (9) Pr (Tt-1-7)+, &~ N(0,0) out capital (10) liza, on Assume that monetary policy is set according to the simple interest rate rule: (b) Solve for it = nt (11) (a) Derive a log-linearized version of the goods market clearing condition. (b) Determine the behavior of the natural level of output Y as a func- tion of ft and discuss the mechanism through which a fiscal expansion leads to an increase in output when prices are flexible. ay, and derive an expression Oft' (c) Define one possible fiscal multiplier as for it. What does it depend on? (U) (d) Derive the Dynamic IS equation of the following form: X = E[X] - = - E[Te+ - ) together with an expression for the natural rate, RN as a function of ft and t. R

Answer rating: 100% (QA)

a To derive a loglinearized version of the goods market clearing condition we start with the production technology equation 6 Yi At Ne Summing over all firms i we get the aggregate output Y Y Yi At Ne ... View the full answer