Topics in Macroeconomic Policy: Optimal Monetary and Fiscalpolicies 复9大学经学院
Topics in Macroeconomic Policy: Optimal Monetary and Fiscal Policies
A Standard framework To Study Monetary Policy Production Technology y,=a,+n, Aa,=p △a41+E &s Monopolistic Competition mci=wt-pr-a-v=u Government Spending Assume GS is a fraction t of output and hence g=-In(1-t)I y=C+g,8P81→+E Household behavior maX ∑n(bmc-计+9」 A1=WN+(1+r1)A1-PC1+D The supply of labor satisfies p,=C+oon, 复9大学经 By some approximations. we also have s -(-Ex1-p)+ECHp=-hB虎
A Standard Framework To Study Monetary Policy ❖ Monopolistic Competition: a t t t t a t t y = a + n a = a + −1 • Production Technology: mct wt − pt − at −v = − • Government Spending [assume GS is a fraction τ of output and hence g = -ln(1-τ)]: g t t gt gt g gt t y = c + = + −1 • Household Behavior: ( ) t t t t t t t t t t t t A W N r A PC D st N C = + + − + + − + − = + 1 1 0 1 1 . . 1 max ln • By some approximations, we also have ct = −(rt − Et t+1 − )+ Et ct+1 −ln • The supply of labor satisfies: t t t nt w − p = c +
From the labor supply equation, we have +儿v2-a1-g The intertemporal equation vields 00y=-(-Ex1-)+Eym1+(-pnk,(2) Finally, assume money demand as Assume flexible price, from(1) and (2) one can see that money policy is neutral 巧=y++(3) 7=p+PAa1+(-v)-pk,(4) wher=(-)(G+o)y=1/(+0)复 °Note:(3) implies first best allocation人 can be achieved by setting v=u Moreover, (4)indicates optimal policy 4 rule of real interest rate(mechanism).i Finally,(3)and(4)show this is a model F with prominent Keynesian properties. F
• From the labor supply equation, we have • The intertemporal equation yields • Finally, assume money demand as mc (1 )(y a ) g v (1) t = + t − t − t − t t t t m − p = y −r (3) t at gt y = + + ( ) (1 ) (2) t t t t 1 t t 1 g t y = − r − E − + E y + − g + + • Assume flexible price, from (1) and (2) one can see that money policy is neutral: • Note: (3) implies first best allocation can be achieved by setting v = μ. Moreover, (4) indicates optimal policy rule of real interest rate (mechanism). Finally, (3) and (4) show this is a model with prominent Keynesian properties. (1 )(1 ) (4) t a t g t r = + a + − − g (v −)/( +), 1/(1+) • where
Staggering Price .Assume each firm resets price in any period only with probability 1-0. So g othe evolution of aggregate price can be approximated by the following ah1+(-0) Note that this is different from simple sticky price assumption. Firm solves the following programming to set p. max ∑",B(HR.-C Subject to (5)and p,-=p*. With the static price rule p =mc t u, we obtain n*=+(1-B02∑()E{mcn}o Here mcn denotes nominal marginal cost. 42 From(1)and(3), we know mc;-4=(1+)x1x1=y1-y
Staggering Price ❖ Assume each firm resets price in any period only with probability 1-θ. So the evolution of aggregate price can be approximated by the following (1 ) * (5) pt =pt−1 + − pt • Note that this is different from simple sticky price assumption. Firm solves the following programming to set pt * ( ) = − s t s s s max IR IC • Subject to (5) and pt = pt*. With the static price rule p = mc + μ, we obtain * (1 ) ( ) (6) 0 n t t s s s pt E mc + = = + − • Here mcn denotes nominal marginal cost. From (1) and (3), we know ( ) t t t t t mc − = 1+ x x y − y
Then from(5) and(6), one can obtain a New Phillips curve 11+1+Kx7 k is a positive parameter(?). From(2) and (4), one can further obtain x=(-Ex-)+Ex1(8) (7)and(8) characterize the dynamics of the model Note that there are 4 distortions in the mode First, money-holding cost(Friedman Rule).We ignore this because of the ad hoc money demand assumption. Second, static distortion from imperfect competition(solved by the subsidy v). The Third is firms inability to adjust prices and the Fourth is the relative x price distortion(due to the lack of synchronization in pricing), which induces si allocation inefficiency. Intuitively, the optimal monetary policy requires xt -T-0 to eliminate the last two distortions(mechanisms)
• Then from (5) and (6), one can obtain a New Phillips curve (7) t t t 1 t = E +x + • κ is a positive parameter (?). From (2) and (4), one can further obtain ( ) (8) t = − t − t t+1 − t + t t+1 x r E r E x • (7) and (8) characterize the dynamics of the model. • Note that there are 4 distortions in the model. First, money-holding cost (Friedman Rule). We ignore this because of the ad hoc money demand assumption. Second, static distortion from imperfect competition (solved by the subsidy v). The Third is firms’ inability to adjust prices and the Fourth is the relative price distortion (due to the lack of synchronization in pricing), which induces allocation inefficiency. Intuitively, the optimal monetary policy requires xt = πt = 0 to eliminate the last two distortions (mechanisms)