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### Transcript of Monetary Theory: Price Setting - Harris Dellas competition, sets a price P t(i), ... Monetary...

• Monetary Theory: Price Setting

University of Bern

March 2011

(Institute) Monetary Theory: Price Setting March 2011 1 / 10

• Notation

Suppose the firm producing intermediate good i , in our setup withmonopolistic competition, sets a price Pt (i), and pays nominaldividends

Dt (i) = Pt (i)Yt (i)[Yt (i)]where [.] is the firms nominal cost function

Recall that demand for this firms output is related to aggregatedemand by

Yt (i) =[Pt (i)Pt

]eYt

We saw that with flexible prices, the optimal price satisfies

(1 e) [Pt (i)]e (Pt )e Yt = e [Pt (i)]e1 (Pt )e Yt[Yt (i)]

where [Yt (i)] [Yt (i)] is nominal marginal cost

(Institute) Monetary Theory: Price Setting March 2011 2 / 10

• Notation

Suppose the firm producing intermediate good i , in our setup withmonopolistic competition, sets a price Pt (i), and pays nominaldividends

Dt (i) = Pt (i)Yt (i)[Yt (i)]where [.] is the firms nominal cost functionRecall that demand for this firms output is related to aggregatedemand by

Yt (i) =[Pt (i)Pt

]eYt

We saw that with flexible prices, the optimal price satisfies

(1 e) [Pt (i)]e (Pt )e Yt = e [Pt (i)]e1 (Pt )e Yt[Yt (i)]

where [Yt (i)] [Yt (i)] is nominal marginal cost

(Institute) Monetary Theory: Price Setting March 2011 2 / 10

• Notation

Suppose the firm producing intermediate good i , in our setup withmonopolistic competition, sets a price Pt (i), and pays nominaldividends

Dt (i) = Pt (i)Yt (i)[Yt (i)]where [.] is the firms nominal cost functionRecall that demand for this firms output is related to aggregatedemand by

Yt (i) =[Pt (i)Pt

]eYt

We saw that with flexible prices, the optimal price satisfies

(1 e) [Pt (i)]e (Pt )e Yt = e [Pt (i)]e1 (Pt )e Yt[Yt (i)]

where [Yt (i)] [Yt (i)] is nominal marginal cost

(Institute) Monetary Theory: Price Setting March 2011 2 / 10

• One-period Price Rigidity

With flexible prices, as we saw, the optimal price is a markup overmarginal cost:

Pt (i) =(

e

e 1

)[Yt (i)]

Now suppose the firm sets Pt+1(i) at date t (there is one-period pricerigidity)Note the role of the markup and next-periods marginal costIf all firms set their price in this way, a change in aggregate demandwill affect outputAs a casual illustration, consider a binding cash-in-advance (CIA)constraint:

PtCt = Mt

Although one-period price rigidity implies non-neutrality of monetarypolicy, it cannot generate a persistent output response or sluggishprice response for several periods

(Institute) Monetary Theory: Price Setting March 2011 3 / 10

• One-period Price Rigidity

With flexible prices, as we saw, the optimal price is a markup overmarginal cost:

Pt (i) =(

e

e 1

)[Yt (i)]

Now suppose the firm sets Pt+1(i) at date t (there is one-period pricerigidity)

Note the role of the markup and next-periods marginal costIf all firms set their price in this way, a change in aggregate demandwill affect outputAs a casual illustration, consider a binding cash-in-advance (CIA)constraint:

PtCt = Mt

Although one-period price rigidity implies non-neutrality of monetarypolicy, it cannot generate a persistent output response or sluggishprice response for several periods

(Institute) Monetary Theory: Price Setting March 2011 3 / 10

• The firm sets Pt+1(i) to maximize

Et

[(t+1t

){Pt+1(i)Yt+1(i)[Yt+1(i)]}

]subject to

Yt+1(i) =

[Pt+1(i)

Pt+1

]Yt+1

The FOC is

Et

[(t+1t

){(1 ) [Pt+1(i)] (Pt+1) Yt+1 + [Pt+1(i)]1 (Pt+1) Yt+1[Yt+1(i)]

}]= 0

Multiply this by Pt+1(i) (which is not random at date t) and divide by (1 )to get

Et

[(t+1t

){Pt+1(i)Yt+1(i)

(

1

)Yt+1(i)[Yt+1(i)]

}]= 0

and

Pt+1(i) =

(

1

)Et {t+1Yt+1(i)[Yt+1(i)]}

Et [t+1Yt+1(i)]

1

• One-period Price Rigidity

With flexible prices, as we saw, the optimal price is a markup overmarginal cost:

Pt (i) =(

e

e 1

)[Yt (i)]

Now suppose the firm sets Pt+1(i) at date t (there is one-period pricerigidity)Note the role of the markup and next-periods marginal cost

If all firms set their price in this way, a change in aggregate demandwill affect outputAs a casual illustration, consider a binding cash-in-advance (CIA)constraint:

PtCt = Mt

Although one-period price rigidity implies non-neutrality of monetarypolicy, it cannot generate a persistent output response or sluggishprice response for several periods

(Institute) Monetary Theory: Price Setting March 2011 3 / 10

• One-period Price Rigidity

With flexible prices, as we saw, the optimal price is a markup overmarginal cost:

Pt (i) =(

e

e 1

)[Yt (i)]

Now suppose the firm sets Pt+1(i) at date t (there is one-period pricerigidity)Note the role of the markup and next-periods marginal costIf all firms set their price in this way, a change in aggregate demandwill affect output

As a casual illustration, consider a binding cash-in-advance (CIA)constraint:

PtCt = Mt

Although one-period price rigidity implies non-neutrality of monetarypolicy, it cannot generate a persistent output response or sluggishprice response for several periods

(Institute) Monetary Theory: Price Setting March 2011 3 / 10

• One-period Price Rigidity

With flexible prices, as we saw, the optimal price is a markup overmarginal cost:

Pt (i) =(

e

e 1

)[Yt (i)]

Now suppose the firm sets Pt+1(i) at date t (there is one-period pricerigidity)Note the role of the markup and next-periods marginal costIf all firms set their price in this way, a change in aggregate demandwill affect outputAs a casual illustration, consider a binding cash-in-advance (CIA)constraint:

PtCt = Mt

Although one-period price rigidity implies non-neutrality of monetarypolicy, it cannot generate a persistent output response or sluggishprice response for several periods

(Institute) Monetary Theory: Price Setting March 2011 3 / 10

• One-period Price Rigidity

With flexible prices, as we saw, the optimal price is a markup overmarginal cost:

Pt (i) =(

e

e 1

)[Yt (i)]

Now suppose the firm sets Pt+1(i) at date t (there is one-period pricerigidity)Note the role of the markup and next-periods marginal costIf all firms set their price in this way, a change in aggregate demandwill affect outputAs a casual illustration, consider a binding cash-in-advance (CIA)constraint:

PtCt = Mt

Although one-period price rigidity implies non-neutrality of monetarypolicy, it cannot generate a persistent output response or sluggishprice response for several periods

(Institute) Monetary Theory: Price Setting March 2011 3 / 10

• Two-period Price Rigidity

Consider next a firm setting the same price for two periods at date t

The optimal price depends on marginal cost at t and the expectationof marginal cost at t + 1

In the steady-state equilibrium with zero inflation , t is constantIn the neighborhood of a zero-inflation steady state, we get

pt (i) =(

11+

)t (i) +

(

1+

)Et t+1(i)

linking the price deviation to a weighted average of the currentmarginal-cost deviation and the current expectation of next-periodsmarginal-cost deviation

(Institute) Monetary Theory: Price Setting March 2011 4 / 10

• The firm sets Pt(i) to maximize

Pt(i)Yt(i)[Yt(i)] + Et[(

t+1t

){Pt(i)Yt+1(i)[Yt+1(i)]}

]subject to

Yt(i) =

[Pt(i)

Pt

]Yt

and

Yt+1(i) =

[Pt(i)

Pt+1

]Yt+1

The FOC is

0 = (1 ) [Pt(i)] (Pt) Yt + [Pt(i)]1 (Pt) Yt[Yt(i)]

+Et

[(t+1t

){(1 ) [Pt(i)] (Pt+1) Yt+1 + [Pt(i)]1 (Pt+1) Yt+1[Yt+1(i)]

}]Multiply this by Pt(i) and divide by (1 ) to get

0 = Pt(i)Yt(i)(

1

)Yt(i)[Yt(i)]

+Et

[(t+1t

){Pt(i)Yt+1(i)

(

1

)Yt+1(i)[Yt+1(i)]

}]Or

1k=0

kEt

[(t+kt

)Yt+k(i)

{Pt(i)

(

1

)[Yt+k(i)]

}]= 0

1

• Two-period Price Rigidity

Consider next a firm setting the same price for two periods at date t

The optimal price depends on marginal cost at t and the expectationof marginal cost at t + 1

In the steady-state equilibrium with zero inflation , t is constantIn the neighborhood of a zero-inflation steady state, we get

pt (i) =(

11+

)t (i) +

(

1+

)Et t+1(i)

linking the price deviation to a weighted average of the currentmarginal-cost deviation and the current expectation of next-periodsmarginal-cost deviation

(Institute) Monetary Theory: Price Setting March 2011 4 / 10

• Two-period Price Rigidity

Consider next a firm setting the same price for two periods at date t

The optimal price depends on marginal cost at t and the expectationof marginal cost at t + 1

In the steady-state equilibrium with zero inflation , t is constant

In the neighborhood of a zero-inflation steady state, we get

pt (i) =(

11+

)t (i) +

(

1+

)Et t+1(i)

linking the price deviation to a weighted average of the currentmarginal-cost deviation and the current expectation of next-periodsmarginal-cost deviation

(Institute) Monetary Theory: Price Setting March 2011 4 / 10

• Two-period Price Rigidity

Consider next a firm setting the same price for two periods at date t

The optimal price depends on marginal cost at t and the expectationof marginal cost at t + 1

In the steady-state equilibrium with zero inflation , t is constantIn the neighborhood of a zero-inflation steady state, we get

pt (i) =(

11+

)t (i) +

(

1+

)Et t+1(i)

linking the price deviation to a weighted average of the currentmarginal-cost deviation and the current expectation of next-periodsmarginal-cost deviation

(Institute) Monetary Theory: Price Setting March 2011 4 / 10

• 2 Approximation

In a steady-state equilibrium with zero inflation, we have

P (i)Y (i) (1 + ) =

(

1

)(i)Y (i) (1 + )

(implying that price is a markup over nominal marginal cost; and real marginalcost is the inverse of the markup)Approximating

Pt(i)

[Yt(i) + Et

(t+1t

)Yt+1(i)

]=

(

1

){Yt(i)t(i) + Et

(t+1t

)Yt+1(i)t+1(i)]

}near this state, we get

Y (i)(1+) [Pt(i) P (i)] =(

1

){Y (i)[t(i) (i)] + Y (i)Et[t+1(i) (i)]

}and

pt(i) =

(1

1 +

)t(i) +

(

1 +

)Et t+1(i)

2

• Staggered Price Setting

Taylors survey (summarized in Chapter 1) and subsequent work

Two-period Taylor contracts: half the firms set a new price Pt andthe other half keep the price Pt1 that they had set last period

The aggregate price level Pt follows

Pt =

10

[Pt (i)]1e di

11e

=

{12(Pt1)

1e +12(Pt )

1e} 1

1e

In the neighborhood of a zero-inflation steady state

pt =12pt1 +

12pt

Multi-period Taylor contracts

Calvo contracts (discussed below)

(Institute) Monetary Theory: Price Setting March 2011 5 / 10

• Staggered Price Setting

Taylors survey (summarized in Chapter 1) and subsequent work

Two-period Taylor contracts: half the firms set a new price Pt andthe other half keep the price Pt1 that they had set last period

The aggregate price level Pt follows

Pt =

10

[Pt (i)]1e di

11e

=

{12(Pt1)

1e +12(Pt )

1e} 1

1e

In the neighborhood of a zero-inflation steady state

pt =12pt1 +

12pt

Multi-period Taylor contracts

Calvo contracts (discussed below)

(Institute) Monetary Theory: Price Setting March 2011 5 / 10

• Staggered Price Setting

Taylors survey (summarized in Chapter 1) and subsequent work

Two-period Taylor contracts: half the firms set a new price Pt andthe other half keep the price Pt1 that they had set last period

The aggregate price level Pt follows

Pt =

10

[Pt (i)]1e di

11e

=

{12(Pt1)

1e +12(Pt )

1e} 1

1e

In the neighborhood of a zero-inflation steady state

pt =12pt1 +

12pt

Multi-period Taylor contracts

Calvo contracts (discussed below)

(Institute) Monetary Theory: Price Setting March 2011 5 / 10

• Staggered Price Setting

Taylors survey (summarized in Chapter 1) and subsequent work

Two-period Taylor contracts: half the firms set a new price Pt andthe other half keep the price Pt1 that they had set last period

The aggregate price level Pt follows

Pt =

10

[Pt (i)]1e di

11e

=

{12(Pt1)

1e +12(Pt )

1e} 1

1e

In the neighborhood of a zero-inflation steady state

pt =12pt1 +

12pt

Multi-period Taylor contracts

Calvo contracts (discussed below)

(Institute) Monetary Theory: Price Setting March 2011 5 / 10

• Let P t denote the new price set at t and

(Pt)1

=1

2(P t1)

1 +1

2(P t )

1

In a deterministic steady state with zero inflation, we have P = P , and nearthat steady state,

(1 ) (P ) (Pt P ) = (1 ) (P )[

1

2(P t1 P ) +

1

2(P t P )

],

andpt =

1

2pt1 +

1

2pt

3

• Staggered Price Setting

Taylors survey (summarized in Chapter 1) and subsequent work

Two-period Taylor contracts: half the firms set a new price Pt andthe other half keep the price Pt1 that they had set last period

The aggregate price level Pt follows

Pt =

10

[Pt (i)]1e di

11e

=

{12(Pt1)

1e +12(Pt )

1e} 1

1e

In the neighborhood of a zero-inflation steady state

pt =12pt1 +

12pt

Multi-period Taylor contracts

Calvo contracts (discussed below)

(Institute) Monetary Theory: Price Setting March 2011 5 / 10

• Staggered Price Setting

Taylors survey (summarized in Chapter 1) and subsequent work

Two-period Taylor contracts: half the firms set a new price Pt andthe other half keep the price Pt1 that they had set last period

The aggregate price level Pt follows

Pt =

10

[Pt (i)]1e di

11e

=

{12(Pt1)

1e +12(Pt )

1e} 1

1e

In the neighborhood of a zero-inflation steady state

pt =12pt1 +

12pt

Multi-period Taylor contracts

Calvo contracts (discussed below)

(Institute) Monetary Theory: Price Setting March 2011 5 / 10

• Calvos Model

A tractable way to model staggered price (or wage) setting with anyaverage duration

In each period, each firm gets to reset its price with a constantprobability (1 ), regardless of when the current price was setFocusing on a symmetric equilibrium, all the firms that get to set anew price at time t, choose the same price PtThe evolution of the aggregate price level is governed by

Pt =

10

[Pt (i)]1e di

11e

={

(Pt1)1e + (1 )(Pt )1e} 11e

(Institute) Monetary Theory: Price Setting March 2011 6 / 10

• Calvos Model

A tractable way to model staggered price (or wage) setting with anyaverage duration

In each period, each firm gets to reset its price with a constantprobability (1 ), regardless of when the current price was set

Focusing on a symmetric equilibrium, all the firms that get to set anew price at time t, choose the same price PtThe evolution of the aggregate price level is governed by

Pt =

10

[Pt (i)]1e di

11e

={

(Pt1)1e + (1 )(Pt )1e} 11e

(Institute) Monetary Theory: Price Setting March 2011 6 / 10

• Firms

Continuum of rms, indexed by i 2 [0; 1] Each rm produces a dierentiated good Identical technology

Yt(i) = At Nt(i)1

Probability of resetting price in any given period: 1 , independentacross rms (Calvo (1983)).

2 [0; 1] : index of price stickiness Implied average price duration 11

• Calvos Model

A tractable way to model staggered price (or wage) setting with anyaverage duration

In each period, each firm gets to reset its price with a constantprobability (1 ), regardless of when the current price was setFocusing on a symmetric equilibrium, all the firms that get to set anew price at time t, choose the same price Pt

The evolution of the aggregate price level is governed by

Pt =

10

[Pt (i)]1e di

11e

={

(Pt1)1e + (1 )(Pt )1e} 11e

(Institute) Monetary Theory: Price Setting March 2011 6 / 10

• Optimal Price Setting

maxP t

1Xk=0

k EtQt;t+k

P t Yt+kjt t+k(Yt+kjt)

subject to

Yt+kjt = (Pt =Pt+k)

Ct+k

for k = 0; 1; 2; :::where

Qt;t+k kCt+kCt

PtPt+k

Optimality condition:1Xk=0

k EtQt;t+k Yt+kjt

P t M t+kjt

= 0

where t+kjt 0t+k(Yt+kjt) andM 1

• Calvos Model

A tractable way to model staggered price (or wage) setting with anyaverage duration

In each period, each firm gets to reset its price with a constantprobability (1 ), regardless of when the current price was setFocusing on a symmetric equilibrium, all the firms that get to set anew price at time t, choose the same price PtThe evolution of the aggregate price level is governed by

Pt =

10

[Pt (i)]1e di

11e

={

(Pt1)1e + (1 )(Pt )1e} 11e

(Institute) Monetary Theory: Price Setting March 2011 6 / 10

• Evolution of Calvo Prices

In a deterministic steady state with zero inflation,

(Pt )1e = (Pt1)1e + (1 )(Pt )1e

implies P = P, and we get

(1 e) (P)e (Pt P) = (1 e) (P)e [(Pt1 P)+(1 )(Pt P)]

andpt = pt1 + (1 )pt

So the inflation deviations (from the steady-state value of zero) satisfy

t pt pt1 = (1 )(pt pt1)

(Institute) Monetary Theory: Price Setting March 2011 7 / 11

• Evolution of Calvo Prices

In a deterministic steady state with zero inflation,

(Pt )1e = (Pt1)1e + (1 )(Pt )1e

implies P = P, and we get

(1 e) (P)e (Pt P) = (1 e) (P)e [(Pt1 P)+(1 )(Pt P)]

andpt = pt1 + (1 )pt

So the inflation deviations (from the steady-state value of zero) satisfy

t pt pt1 = (1 )(pt pt1)

(Institute) Monetary Theory: Price Setting March 2011 7 / 11

• Aggregate Price Dynamics

Pt = (Pt1)

1 + (1 ) (P t )1 11

Dividing by Pt1 :

1t = + (1 )P tPt1

1

Log-linearization around zero ination steady state

t = (1 ) (pt pt1) (1)

or, equivalentlypt = pt1 + (1 ) pt

• Implications of Staggered Price Setting

Cutting the nominal interest rate lowers the expected real interestrate and increases aggregate demand

With our iso-elastic utility function, this relationship is

ct = Et [ct+1]1[it Et (t+1) ]

Some firms react to an increase in aggregate demand by raising prices

Other firms (with rigid prices) end up increasing production

The difference in responses across firms raises interesting normativequestions (discussed in Chapter 4)

(Institute) Monetary Theory: Price Setting March 2011 8 / 10

• Implications of Staggered Price Setting

Cutting the nominal interest rate lowers the expected real interestrate and increases aggregate demand

With our iso-elastic utility function, this relationship is

ct = Et [ct+1]1[it Et (t+1) ]

Some firms react to an increase in aggregate demand by raising prices

Other firms (with rigid prices) end up increasing production

The difference in responses across firms raises interesting normativequestions (discussed in Chapter 4)

(Institute) Monetary Theory: Price Setting March 2011 8 / 10

• Implications of Staggered Price Setting

Cutting the nominal interest rate lowers the expected real interestrate and increases aggregate demand

With our iso-elastic utility function, this relationship is

ct = Et [ct+1]1[it Et (t+1) ]

Some firms react to an increase in aggregate demand by raising prices

Other firms (with rigid prices) end up increasing production

The difference in responses across firms raises interesting normativequestions (discussed in Chapter 4)

(Institute) Monetary Theory: Price Setting March 2011 8 / 10

• Implications of Staggered Price Setting

Cutting the nominal interest rate lowers the expected real interestrate and increases aggregate demand

With our iso-elastic utility function, this relationship is

ct = Et [ct+1]1[it Et (t+1) ]

Some firms react to an increase in aggregate demand by raising prices

Other firms (with rigid prices) end up increasing production

The difference in responses across firms raises interesting normativequestions (discussed in Chapter 4)

(Institute) Monetary Theory: Price Setting March 2011 8 / 10

• Implications of Staggered Price Setting

Cutting the nominal interest rate lowers the expected real interestrate and increases aggregate demand

With our iso-elastic utility function, this relationship is

ct = Et [ct+1]1[it Et (t+1) ]

Some firms react to an increase in aggregate demand by raising prices

Other firms (with rigid prices) end up increasing production

The difference in responses across firms raises interesting normativequestions (discussed in Chapter 4)

(Institute) Monetary Theory: Price Setting March 2011 8 / 10

• Price Setting in Calvos Model

Firms that get to set a new price at time t set it to maximize theexpect present value of profits over all future states in which this priceprevails

Note the similarities (and differences) with the FOC for our 2-periodprice setting problem:

1

k=0

kEt

[(t+k

t

)Yt+k (i)

{Pt (i)

(e

e 1

)[Yt+k (i)]

}]= 0

The link between new prices and real marginal cost

(Institute) Monetary Theory: Price Setting March 2011 9 / 10

• Optimal Price Setting

maxP t

1Xk=0

k EtQt;t+k

P t Yt+kjt t+k(Yt+kjt)

subject to

Yt+kjt = (Pt =Pt+k)

Ct+k

for k = 0; 1; 2; :::where

Qt;t+k kCt+kCt

PtPt+k

Optimality condition:1Xk=0

k EtQt;t+k Yt+kjt

P t M t+kjt

= 0

where t+kjt 0t+k(Yt+kjt) andM 1

• Price Setting in Calvos Model

Firms that get to set a new price at time t set it to maximize theexpect present value of profits over all future states in which this priceprevails

Note the similarities (and differences) with the FOC for our 2-periodprice setting problem:

1

k=0

kEt

[(t+k

t

)Yt+k (i)

{Pt (i)

(e

e 1

)[Yt+k (i)]

}]= 0

The link between new prices and real marginal cost

(Institute) Monetary Theory: Price Setting March 2011 9 / 10

• Price Setting in Calvos Model

Firms that get to set a new price at time t set it to maximize theexpect present value of profits over all future states in which this priceprevails

Note the similarities (and differences) with the FOC for our 2-periodprice setting problem:

1

k=0

kEt

[(t+k

t

)Yt+k (i)

{Pt (i)

(e

e 1

)[Yt+k (i)]

}]= 0

The link between new prices and real marginal cost

(Institute) Monetary Theory: Price Setting March 2011 9 / 10

• Equivalently,1Xk=0

k Et

Qt;t+k Yt+kjt

P tPt1

M MCt+kjt t1;t+k

= 0

where MCt+kjt t+kjt=Pt+k and t1;t+k Pt+k=Pt1

Perfect Foresight, Zero Ination Steady State:

P tPt1

= 1 ; t1;t+k = 1 ; Yt+kjt = Y ; Qt;t+k = k ; MC =

1

M

• Log-linearization around zero ination steady state:

pt pt1 = (1 )1Xk=0

()k Etfcmct+kjt + pt+k pt1gwhere cmct+kjt mct+kjt mc.Equivalently,

pt = + (1 )1Xk=0

()k Etfmct+kjt + pt+kg

where log 1.Flexible prices ( = 0):

pt = +mct + pt

=) mct = (symmetric equilibrium)

• Inflation Dynamics in Calvos Model

With a linear production function ( = 0), all the firms have the samemarginal cost

In this case, real marginal cost equals

WtPtAt

and an increase in aggregate demand increases real marginal cost byincreasing the real wage

With diminishing returns to labor (0 < < 1), firms with differentprices have different marginal costs; but aggregation across firms isfacilitated by the Calvo structure

In this case, an increase in aggregate demand increases real marginalcost through two channels: by increasing the real wage and reducingthe marginal product of labor

(Institute) Monetary Theory: Price Setting March 2011 10 / 10

• Particular Case: = 0 (constant returns)

=) MCt+kjt =MCt+kRewriting the optimal price setting rule in recursive form:

pt = Etfpt+1g + (1 ) cmct + (1 )pt (2)Combining (1) and (2):

t = Etft+1g + cmctwhere

(1 )(1 )

• Inflation Dynamics in Calvos Model

With a linear production function ( = 0), all the firms have the samemarginal cost

In this case, real marginal cost equals

WtPtAt

and an increase in aggregate demand increases real marginal cost byincreasing the real wage

With diminishing returns to labor (0 < < 1), firms with differentprices have different marginal costs; but aggregation across firms isfacilitated by the Calvo structure

In this case, an increase in aggregate demand increases real marginalcost through two channels: by increasing the real wage and reducingthe marginal product of labor

(Institute) Monetary Theory: Price Setting March 2011 10 / 10

• Inflation Dynamics in Calvos Model

With a linear production function ( = 0), all the firms have the samemarginal cost

In this case, real marginal cost equals

WtPtAt

and an increase in aggregate demand increases real marginal cost byincreasing the real wage

With diminishing returns to labor (0 < < 1), firms with differentprices have different marginal costs; but aggregation across firms isfacilitated by the Calvo structure

In this case, an increase in aggregate demand increases real marginalcost through two channels: by increasing the real wage and reducingthe marginal product of labor

(Institute) Monetary Theory: Price Setting March 2011 10 / 10

• Generalization to 2 (0; 1) (decreasing returns)Dene

mct (wt pt)mpnt (wt pt)

1

1 (at yt) log(1 )

Using mct+kjt = (wt+k pt+k) 11 (at+k yt+kjt) log(1 ),

mct+kjt = mct+k +

1 (yt+kjt yt+k)

= mct+k

1 (pt pt+k) (3)

Implied ination dynamics

t = Etft+1g + cmct (4)where

(1 )(1 )

1 1 +

• Inflation Dynamics in Calvos Model

With a linear production function ( = 0), all the firms have the samemarginal cost

In this case, real marginal cost equals

WtPtAt

and an increase in aggregate demand increases real marginal cost byincreasing the real wage

With diminishing returns to labor (0 < < 1), firms with differentprices have different marginal costs; but aggregation across firms isfacilitated by the Calvo structure

In this case, an increase in aggregate demand increases real marginalcost through two channels: by increasing the real wage and reducingthe marginal product of labor

(Institute) Monetary Theory: Price Setting March 2011 10 / 10

• Real Marginal Cost and Inflation Dynamics in CalvosModel

An increase in real marginal cost increases inflation because it erodesthe monopoly markup

To protect their markups, firms setting new prices choose a higherprice, which leads to inflation

The response coeffi cient in

t = Ett+1 + mc t

is inversely related to the degree of price rigidity

Iterating forward,the bounded solution for inflation is

t = Et

j=0

j mc t+j

(Institute) Monetary Theory: Price Setting March 2011 11 / 11

• Real Marginal Cost and Inflation Dynamics in CalvosModel

An increase in real marginal cost increases inflation because it erodesthe monopoly markup

To protect their markups, firms setting new prices choose a higherprice, which leads to inflation

The response coeffi cient in

t = Ett+1 + mc t

is inversely related to the degree of price rigidity

Iterating forward,the bounded solution for inflation is

t = Et

j=0

j mc t+j

(Institute) Monetary Theory: Price Setting March 2011 11 / 11

• Real Marginal Cost and Inflation Dynamics in CalvosModel

An increase in real marginal cost increases inflation because it erodesthe monopoly markup

To protect their markups, firms setting new prices choose a higherprice, which leads to inflation

The response coeffi cient in

t = Ett+1 + mc t

is inversely related to the degree of price rigidity

Iterating forward,the bounded solution for inflation is

t = Et

j=0

j mc t+j

(Institute) Monetary Theory: Price Setting March 2011 11 / 11

• Real Marginal Cost and Inflation Dynamics in CalvosModel

An increase in real marginal cost increases inflation because it erodesthe monopoly markup

To protect their markups, firms setting new prices choose a higherprice, which leads to inflation

The response coeffi cient in

t = Ett+1 + mc t

is inversely related to the degree of price rigidity

Iterating forward,the bounded solution for inflation is

t = Et

j=0

j mc t+j

(Institute) Monetary Theory: Price Setting March 2011 11 / 11

Monetary Theory: Price SettingNotationOne-period Price RigidityTwo-period Price RigidityStaggered Price SettingCalvo's ModelEvolution of Calvo PricesImplications of Staggered Price SettingPrice Setting in Calvo's ModelInflation Dynamics in Calvo's Model