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Real Rigidities, Predetermined Prices & A

New Classical Phi l l ips Curve

Jae Won Lee

February 16, 2011



Last topic: Static model of monopol istic com-

petition

1. A building block of NK model.

2. Even flexible-price output (natural output) is inefficient.

- Market power----+produce less than the socially optimal amount

3. Still monetary neutrality

- Imperfect competition alone does not lead to monetary nonneutrality

This time: develop a dynamic model, construct AD and AS (AD will be same,

more focus on AS)



Household00 01-a

max E o L{3 t ___:_t_I-a

t=OI + < p

1 01Pt(i)Gt(i)di + Et [Qt,t+1Dt+1J =WtNt + n , - PtTt +o,

=PtCt

Dixit-Stiglitz Conumption and Price index:

[

{I 8 - 1 ] 8 8 1c, J o c.;i)-8-di ,

(i) Optimal allocation of {Ot( i)} for a given c,

(ii) O ptim al choice of {Gt, Dt+1, N t} takin g {Pt, Qt,t+1, Wt, Tt, n .] as given



H H Op tim ality Cond itions

(3 E { O f P t}t of+1 Pt+ 1

Niof

M arkets C lear

Yt( i )

(3 E {~ O" P t }t ~ + 1Pt+ 1

NiYtO"

C ons um ption Euler Equation

Labor Sup p ly

( P ; t i)) -0Y t

1

1+ it

Wt

P t

Demand for Y( i )

IS equatio n

Labor Sup p ly



First Order Approximation

Log-linear Approximation of optimality conditions around zero-inflation steady

state

IS equation (AD)

A A A A.pN,+ aY t = = Wt - Pi Labor supply

Demand for Y(i)



where MGt is real marginal cost:

1 V V t 1 ~ aMGt = = - - - = = -Nt y t

At Pt At

"Natural Output":

_1 1+cp ()n _ (() - 1 ) a+cp A a+cp An _ 1+ < P A A

y t - t ----+y t - t

( ) a + < p

First order approximation of the FOe:

Pt(i) - Pt M otM ot = = Wt - Pt - At = = < p N t + aft - At = = (a + < p ) ft - (1+ < p ) At

M ot = ( 0 " + c p ) (ft - ft)Notional SRAS (Woodford, 2003, ch. 3):

Pt(i)-Pt=,(ft-ytn), , O " + c p



Notional SRAS and Real R igidit ies

Pt(i) - Pt ='" Y (ft - f in)

Indicates how much firm's relative price would vary with the level of aggregate

activity, if prices could be freely set (i.e. flexible)

• Purely notional in that it need not indicate how the prices are actually setin an economy with an economy where prices are sticky

• Sti I I usefu I to develop ani ntu ition

• Ball & Romer (1990): smaller the elasticity, is, bigger the" real rigidities"

• For a given degree of "nominal rigidities", slope of PC is smaller with a

smaller ,. (Review #7 in ps_O)



Strategic Complements vs. Substitutes

• Closely related concepts to real rigidities

• Pricing decisions are Strategic complements (substitutes) if an increase in

the prices charged for other goods increases (decreases) the price that it

is optimal to charge for one's own good.

• strategic complements - - - - + small r

• r is a measure (i) of strategic complementarity and (ii) of real rigidity

• The economy is characterized by a bigger degree of real rigidities when

pricing decisions are strategic complements.



One simple way to understand is to include the quantity equation:

A- A- A-

M, = = P,Y t : : : : : : : : }M, = = P,+ Y t

Combine this with the notional SRAS:

Pricing decisions are

strategic substitutes if r >

strategic complements if r <

Intuition: If prices are strategic completments, then the fraction of prices that

do not adjust in response to a disturbance to nominal spending lead even the

flexible-price firms to adjust their prices by less than they would otherwise



Keep in m ind ....

• Real rigidity alone does not cause monetary disturbances to have real ef-

fects

• If prices are flexible, money is neutral regardless of the degree of real rigidity

• Real rigidity magnifies the effects of nominal rigidity



Consequences of Prices Fixed in Advance

1. a fraction s E (0,1) of the prices are fully flexible

- can always adj ust prices after observi ng shocks

2. the remaining 1 - s set prices a period in advance

- shou Id set prices before observi ng shocks

- cannot adjust prices even if the realized shocks are different from theexpectations



Flexible-price firms:

log-linearized FOe: Pl,t - P t =I ( 9 t - f in)

(1)

Sticky-price firms:

(2 )

A ANote that P2 t = = Et-1Pl t, ,



Goal: Derive a Phillips-curve (AS) relation between aggregate price and output

Aggregate Price:

log-linearized: P t = = sPI , t + (1 - s )P 2,t (3)

First note that

P t - P 2 , t s ( P l, t - P 2 , t )

= = = = ? P t - E t - l P t = s ( P l, t - P 2 , t )

Now from (3), we get

P I,t - P t (1- s) ( P l , i - P 2 , t )

(A A ) 1 ( A A )= = = = ? PI t - P 2 t = = PI t - Pt, , 1- s '



Therefore,

8 ( A A n )====} 7rt - Et-l7rt = = r Y t - yt

1-8

A New Classical Phillips Curve (or Aggregate Supply):

7ft Et-l7ft + K, (ft - ft)

K, ( 1 ~ J IThe s lope r: is

(i) increas ing in 8 ( 1 ' nom inal rig id itie s - - - - + flatter P C)

(ii) increas ing in r ( 1 ' rea l ri g id i ti es - - - - + flatter P C)



Upward-sloping, Expectations-augmented Phillips curve (Phelps; Friedman)

Popular in the New Classical RE literature of the 1970s (Sargent and Wallas,

JPE 1975)

Implications:

- now real activity will not be independent of nominal variables (and monetary

policy)

- but only unexpected change in policy would have real effects

unexpected change in monetary policy impact on real activity



- 0nIy tra nsitory effect (no persistent effect)

Et ( " f t + k - " f t + k ) =0 Vk > 1



Impulse Responses of Output to Monetary Shock

Ceteris Paribus, how would output respond to a unexpected change in montary

policy (i.e. monetary polich shock)

AIgnore " Y tn (let's assume At is constant for the momentj-s- " Y tn = = 0

A A AEasier to construct IRF with the quantity equation: M; = = Pt + Y t

A AAssume money supply follows: M] = = Mt-l + Et and Et is white noise



Combine quantity equation and Phillips curve:

A

Y t1 ( A A )M: - Et-1Mt

1+K:

1

1+ K:Et

Impulse response function:

IRFy(k)

IRFy(k)

if k = = 0

otherwise

In the real world,

IRFy(k) > 0 for manay periods

The New Classical PC succeeds to generate monetary non-neutrality, but fails

to generate persistent real effect.

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