monetary policy in a small open economy - bank of canada€¦ · monetary policy in a small open...

odelsrsten-orssults

ian

to

ted

openmeilerally

ased,

Introduction

The past decade has seen widespread application of New Keynesian mto the study of monetary policy. These models are derived from fiprinciples and provide a rigorous setting in which to re-examine convtional wisdom and well-known puzzles in economics. A number of authhave examined the special case of small open economies, but their reare typically formulated in general theoretical terms.1 This paper applies theNew Keynesian modelling approach to the context of the Canadeconomy.

Canada is a small open economy with distinctive features; in particular,

(i) it is highly dependent on a single large foreign economy;

(ii) it comprises a significant primary goods sector geared largelyexports;

(iii) its other traded goods sector (e.g., manufacturing) is highly integrawith the United States.

Following the global trend, the Canadian economy has become moreand integrated, both domestically and with the rest of the world. The voluof foreign trade in non-primary goods has grown substantially, whprimary goods prices, and perhaps the size of that sector, have genefallen. Labour mobility between sectors and across countries has increand the exchange rate pass-through may well have declined.

1. See surveys in Lane (2001) and Bowman and Doyle (2003).

Monetary Policy ina Small Open Economy

Gabriel Srour

297

298 Srour

970s,ncepricelevele ledn theent

thetheange

ithcale

thefirms

r anes.

c andhowndckiate

e thethis

arerketother

ofme

ents

001).

ndulyn the

Canada has pursued a flexible exchange rate regime since the early 1and an inflation-targeting regime since 1991. While there is strong evidethat a flexible exchange rate has helped Canada to weather commodityshocks, the persistent decline of the Canadian dollar and the increasingof economic exchange between Canada and the United States, havsome economists to question the benefits of a floating exchange rate icurrent environment.2 Several authors have even argued that the currregime stifles productivity.

Accordingly, in this paper, we examine how some of the features ofCanadian economy might affect monetary policy and particularlyexchange rate. We ask whether past trends call for a less variable exchrate other than through the direct effect of transactions costs.3

We develop a simple one-period model of a small open economy wnominal-wage rigidities, price-taking firms, and decreasing returns-to-stechnology. Similar models have been used in the literature, althoughtechnology is usually assumed to have constant returns to scale, andare monopolistic-competitive and set their prices.4 We treat the equilibriumoutcome that obtains if wages were perfectly flexible as a benchmark foefficient monetary policy. For simplicity, we examine alternative casseparately,5 and focus on the monetary response to relative price shocks

We first consider a one-sector case, whereby there is only one domestione foreign good, and all prices are set in the world market. We then sthat the efficient monetary policy calls for a flexible exchange rate aconforms to conventional wisdom. Specifically, following a negative shoto the relative price of domestic goods, the local currency must deprecand domestic prices rise, to counteract the rigidity of wages and emulatdrop in real wages that would have obtained if wages were flexible. Incase, monetary policy can reproduce the flexible-wage outcome.

We go on to examine a two-sector model. The goods in one sectorthought of as primary goods, the prices of which are set in the world maand exogenously given. The goods in the other sector are consideredtraded goods (e.g., manufacturing) and have a relatively low elasticitysubstitution with foreign (non-primary) goods. We consider the two extre

2. See Courchene (1998), Harris (1993), Laidler (1999), and Murray (1999) for argumon both sides of the debate.3. For the effects of transactions costs, see Macklem, Osakwe, Pioro, and Schembri (24. See Devereux (2002) and Obstfeld and Rogoff (1999).5. It is possible to describe one model that nests many cases. However, this ucomplicates the presentation and algebra. Moreover, the functional specifications iextreme cases are more acceptable than a single artificial specification.

Monetary Policy in a Small Open Economy 299

woet inand

theency

ofodsnous,se,ter-andhentheome

areribedchutputtivertionlongould

ofent,. Intainvetary

hasels.Asionforticitypart,torsand

tion

cases of perfect labour mobility and no labour mobility between the tsectors, as well as two cases where prices of non-primary goods are sthe world market and where they adjust endogenously to make demandsupply equal.

We show that, when labour is mobile, monetary policy can reproduceflexible-wage outcome: as in the one-sector model, the domestic currneeds to depreciate following a negative shock to the relative priceprimary goods. Output and employment in the domestic non-primary gosector increase to take up the slack, and hence, if assumed endogeprices in that sector must fall relative to foreign goods. In this last cahigher economic integration, represented by a higher volume of innational trade or higher elasticity of substitution between domesticforeign (non-primary) goods, induces smaller currency depreciations. Wlabour is not mobile, it is shown that monetary policy cannot reproduceflexible-wage outcome at the sectoral level, but it can reproduce the outcat the aggregate level.

Finally, we again consider the one-sector model, but where firmsassumed to incur fixed costs in production along the same lines as descin Blanchard and Kiyotaki (1987). Aside from the literal interpretation, sufixed costs can also be thought of as a measure of a firm’s degree of oefficiency. The presence of fixed costs means that, following negashocks, some firms may not find it profitable to produce, and hence a poof the economy’s capacity may be left idle. Under these conditions, asas some capacity remains idle, an improvement of the terms of trade wraise capacity utilization and output, but not necessarily the markupdomestic prices over wages. We then show that in this environmmonetary policy cannot always reproduce the flexible-wage outcomefact, in some circumstances, monetary policy may have to susproduction in inefficient firms, that is, in firms that would make negatiprofits in a perfectly flexible environment. In this sense, therefore, monepolicy can stifle productivity.

The literature on New Keynesian open-economy macroeconomicsusually focused on one-sector (albeit monopolistic-competitive) modTwo papers by Tille (1999, 2002) are noteworthy in relation to our work.in our study, Tille (1999) examines the effect of the elasticity of substituton exchange rate policy. Our work extends Tille’s results in that we allowtwo domestic sectors, and we examine the effect of a change in the elasof substitution between the goods in one sector and its foreign counterkeeping the elasticity of substitution between the two domestic secunchanged. Tille, on the other hand, considers one domestic sectorexamines the effect of a country-wide change in the elasticity of substitu

300 Srour

entralthatthe

d intwo-

n istions

st ofhichthebe

medare

t andthe

tility

d

between domestic and foreign goods. In contrast, Tille (2002)6 examinesmonetary policy in a two-sector model, but his focus is on the differimplications for monetary policy between country-wide and sectoproductivity shocks. His model assumes a representative household, soissues of labour mobility do not arise, and the volume of trade as well aselasticity of substitution between goods are fixed.

The paper is organized as follows. The baseline model is describesection 1. The one-sector economy is examined in section 2, and thesector economy in section 3. The case of fixed costs in productioconsidered in section 4. The final section concludes and offers suggesfor future research.

1 The Baseline Model

We consider a one-period small open economy that trades with the rethe world. The domestic economy consists of a primary-goods sector, wtakes world prices as given, and a non-primary-goods sector,characteristics of which will be described below. Both types of goods cantraded.7 Home-produced and foreign-produced primary goods are assuto be perfect substitutes for each other, whereas non-primary goodsdifferentiated.

1.1 Households

The total number of households in the economy is assumed constannormalized to equal 1. Households have identical preferences overconsumption of goods, leisure, and real money balances. The periodic uof a household is

,

whereN is the number of hours worked, are real money balances, anCis consumption of a composite of goods:

,

6. We became aware of this study while working on our model.7. The model can easily be extended to the case that includes non-traded goods.

11 σ–------------C

1 σ– 11 φ+------------N

1 φ+– χ M

P-----

ln+

MP-----

CCX

γ X-------

γ X CT

γT-------

1 γ X–

=


ds,

after

ney

eeded

.

, , and denote, respectively, consumption of primary goohome-produced non-primary goods (H-goods), and imported non-primarygoods (F-goods). The elasticity of substitution, , betweenH-goods andF-goods is assumed to be greater than or equal to 1.8

Households choose consumption allocations and money balancesshocks are realized, subject to the budget constraint

,

where denotes dividends, and is the wage.

Standard optimization then implies that a household’s holding of mobalances and expenditures on the various types of good are:

,

,

,

,

and

,

where is the (domestic-currency) price of goods in sectori, P is theaggregate price index, and is the price index of non-primary goods,9

,

8. The limit case is identified with the Cobb-Douglas functional form.9. The price index of a composite good can be defined as the minimum expenditure nto buy one unit of the composite good.

CT γ H

1η---

CH

η 1–η

------------

1 γ H–( )1η---

CF

η 1–η

------------

+

ηη 1–------------

=

CX CH CF

η

η 1=

PXCX PTCT M+ + WN Π T+ +=

Π W

PXCX γ XPC=

PTCT 1 γ X–( )PC=

PHCH

γ H

PH

PT-------

1 η–

PTCT

=

PFCF

1 γ H–( )PF

PT------

1 η–

PTCT

=

MP----- χC

σ=

PiPT

P PX

γ XPT

1 γ X–=

302 Srour

ede of. Ther aretors,s of

cale

r-

tputby a

for

.

1.2 Production

Production in sector ( ) requires a continuum of differentiattypes of labour, . Each household is associated with one typlabour, but several households may be associated with the same typenumber of households of each type and the number of firms in any sectoassumed constant. To examine the effect of labour mobility between secwe will consider the case where both sectors employ the same typelabour, i.e., typeXj and typeHj are identical. Otherwise, typeXj and typeHlare assumed to be different for allj andl.

All firms in a given sector are identical and have decreasing returns-to-sproduction technologies. Specifically, output by a firm in sector is

,

,

where is labour input of type , , , and is a sectowide technological shock.

Firms take prices and wages as given and choose their volume of ouafter shocks are realized. Profit maximization then implies that demandfirm in sectori for composite labour and individual labour of typeij is

and ,

where is the wage for labour of type , and is a wage indexlabour employed in sectori,10

10. can be interpreted as the minimum cost of a unit of composite labour.

PT γ HPH1 η–

1 γ H–( )PF1 η–

+[ ]

11 η–------------

=

i i X H,=ij j 0 1,[ ]∈,

i

Yi1

1 α–------------AiLi

1 α–=

Li l ij( )λ 1–

λ------------

jd0

1

∫

λλ 1–------------

=

l ij( ) ij 0 α 1<≤ λ 1≥ Ai

Li

AiPi

Wi-----------

1α---

= l ij( )Wi

W ij( )--------------

λLi=

W ij( ) ij Wi

Wi


arger

i.e.,as

s arebeer,

ds is

ointlypre-oldss areies

d for

alized

.

Thus, all else being equal, the higher the price markup over wages, the lthe demand is for labour and the larger output is by each firm.

1.3 Price determination

We assume throughout that the law of one price holds for all goods,, , where is the nominal exchange rate, expressed

the domestic price of a unit of foreign currency, andf superscript indicatesforeign variables. Furthermore, on the basis that the domestic marketsmall, prices of primary goods and foreign goods will be assumed todetermined in the world market and exogenously given. We will considhowever, the case where the price of home-produced non-primary gooendogenously determined.

1.4 Wage-setting

We assume that households of the same type pool their resources and jset their wages. We will also consider the case where wages aredetermined and the case where they are flexible. In the former, househare assumed to set wages at the beginning of the period, before shockrealized, to maximize expected utility. The first-order condition then impl

,

where is the expectations operator, and denotes the demanlabour per household of typeij.

In the case of flexible wages, households set wages after shocks are reto maximize their utility. The first-order condition then implies

.

Wi W ij( )1 λ–jd

0

1

∫

11 λ–------------

=

Pi SPif

= i X H F, ,= S

W ij( ) λλ 1–------------

E lh

ij( )1 φ+

[ ]

Elh

ij( )PC ij( )σ--------------------

-------------------------------=

E lh

ij( )

W ij( ) λλ 1–------------PC ij( )σ

lh

ij( )φ

=

304 Srour

omy,meds,therices

e inods

ameford

ignres

ate

2 One-sector economy

In this section, we assume that there is only one sector in the econidentified with the primary goods sector. Accordingly, households consuonly primary goods and imported non-primary goods or, in other wor

. The domestic price level is then completely determined byexchange rate and the exogenously given world prices, and relative pand the terms of trade are exogenously given:

.

Domestic monetary policy therefore has no effect on the terms of tradthis scenario, and the ratio of primary goods consumption to imported goconsumption depends only on world prices:

.

2.1 Equilibrium

We focus on symmetric equilibria, whereby all households supply the samount of labour and earn equal wages, i.e., andall j. (The subscriptX, which refers to the domestic sector, will be omittefrom now on when there is no ambiguity.)

The home country sells primary goods in the world market and buys foregoods in return. In equilibrium, prices adjust to equate total expendituwith income,

,

wheren is the number of firms in the sector. Hence, equilibrium aggregconsumption is

.

γ H 0=

P S PXf( )

γPF

f( )1 γ–

= γ γ X≡( )

PX

PF-------

PXf

PFf

-------=PX

P-------

PXf

PFf

------- 1 γ–

=

CX

CF-------

γ1 γ–-----------

PF

PX------- γ

1 γ–-----------

PFf

PXf

-------= =

L l ij( )= W W ij( )=

PC nPXY=

Cn

1 α–------------A

PX

P-------L

1 α– n1 α–------------ A

PX

P-------

1α---

PW-----

1 α–α

------------

= =


totalld is

our

erfor

t byrices

s

2.1.1 Flexible wages

Since there is only one sector in the domestic economy (and thenumber of households equals 1), the demand for labour per househo

, and therefore real wages are

.

Substituting the expressions for equilibrium consumption and labdemand, it follows that

,

,

,

,

where

.

All else being equal, a lower relative price of primary goods leads to lowincome from exports, hence lower consumption, output, and demandlabour. Under flexible wages, the lower demand for labour is partly offselower real wages. Nevertheless, wages relative to primary goods pincrease because of the higher marginal product of labour.

2.1.2 Predetermined wages

Substituting equilibrium aggregate consumption in , it followthat

,

lh

nL=

WP-----

λλ 1–------------C

σnL( )φ

=

WP-----

Θ λλ 1–------------

α 11 α–------------

ασ nα

APX

P-----------------

φ σ+

=

WPX-------

Θ λλ 1–------------

α 11 α–------------

ασn

αA( )

φ σ+ PX

P-------

α–( ) 1 σ–( )

=

CΘ λ 1–

λ------------

1 α– 11 α–------------

α ϕ+ nα

APX

P-----------------

1 ϕ+( )

=

LΘ λ 1–

λ------------ 1 α–( )σ 1

nφ σ+

-------------APX

P-----------

1 σ–

=

Θ 1 φ 1 σ–( ) 1 α–( )–+≡ φ α σ 1 α–( )+ +=

M χPCσ

=

Pα σ 1 α–( )+ χ α– 1 α–

n------------

σαAX

PX

P-------

σ–W

σ 1 α–( )M

α=

306 Srour

us,

,

.

From the first-order equation for predetermined wages,

,

it follows that

,

,

where

.

The above equations for , and permit one to derive variomonetary policies. In particular, a fixed exchange rate policy, sayrequires

PXα σ 1 α–( )+ χ α– 1 α–

n------------

σαAX

σ– PX

P-------

α 1 σ–( )

Wσ 1 α–( )

Mα

=

Sα σ 1 α–( )+ χ α– 1 α–

n------------

σαAX

σ– PX

P------

α 1 σ–( )

Wσ 1 α–( )

Mα

PXf( )

α σ 1 α–( )+( )–=

W1χ--- λ

λ 1–------------E nL( )1 φ+[ ]

EnLM------

------------------------------=

W

α φ+α

------------- 1χ--- λ

λ 1–------------

E n1 φ+

APX( )

1 φ+α

------------

En APX( )

1α---

M----------------------

-------------------------------------------------=

χW( )Θ

α σ 1 α–( )+-------------------------------

K

E APX

P-------

1 φ+( ) 1 σ–( )α σ 1 α–( )+

-----------------------------------

M

1 φ+α σ 1 α–( )+-------------------------------

E APX

P-------

1 σ–( )

α σ 1 α–( )+-------------------------------

M

1 α–( ) 1 σ–( )α σ 1 α–( )+

-----------------------------------

-------------------------------------------------------------------------------------=

Kλ

λ 1–------------ 1 α–( )

σφα σ 1 α–( )+-------------------------------

n

φα 1 σ–( )α σ 1 α–( )+-------------------------------

=

P PX S, , WS 1=


thatarybtains

theex,ch a

theyde.

fsetomycks

uchs ofd beratethe

w aentvel

e thethat

than

.

A policy that keeps the price of primary goods constant at requiresthe exchange rate fully offset any change in the world price of primgoods, but otherwise keeps the exchange rate constant. Such a policy oif

.

Likewise, a policy that keeps the price level constant at requires thatexchange rate fully offset any change in the foreign price ind

, but otherwise keep the exchange rate constant. Supolicy obtains if

.

None of the three policies just described is efficient in general, althoughare all efficient regarding foreign shocks that do not affect the terms of traIndeed, in this particular case, it is best to let the exchange rate fully ofthe foreign shock and insulate domestic prices and the domestic econ(see below). A similar claim, however, cannot be made with regard to shoto the terms of trade, say a drop in the world price of primary goods. If sa shock is reflected fully in the exchange rate, and domestic priceprimary goods are kept constant, then the marginal cost of labour woultoo high, since employment is kept constant. Nor should the exchangebe kept constant and allow the shock translate in a one-for-one drop inhome-currency price of primary goods, because this would imply too lomarkup over wages, and therefore lead to an inefficient loss of employmand consumption. Likewise, a policy that targets a constant price lewould keep the real wage inefficiently constant.11

Nevertheless, monetary policy under predetermined wages can achievoutcome that obtains under flexible wages. To that effect, it can ensurereal wages under both regimes are equal, i.e.,

11. One can, in fact, show directly that household utility in each of these cases is lowerthe utility that obtains under flexible wages.

M χ 1 α–n

------------ σ–

Aσ PX

P-------

1 σ–( )–

W

σ– 1 α–( )α

------------------------

PXf( )

α σ 1 α–( )+α

-------------------------------

=

PX

M χ 1 α–n

------------ σ–

Aσ PX

P-------

1 σ–( )–

W

σ– 1 α–( )α

------------------------

PX

α σ 1 α–( )+α

-------------------------------

=

P

Pf PXf( )γ PF

f( )1 γ–≡

M χ 1 α–n

------------ σ–

AX

PX

P-------

σW

σ– 1 α–( )α

------------------------

P

α σ 1 α–( )+α

-------------------------------

=

308 Srour

rium

rade,fullyasesneyncy

esticstic

tput,stic

ge in

.

Hence,

and

.

Written differently,

,

where hat superscripts denote percentage changes from the equiliboutcome that obtains when no shocks occur. Note that

.

As expected, in response to a shock that does not affect the terms of tthe money supply is kept constant, and the exchange rate adjusts tooffset the effect on domestic prices. However, in response to decre(respectively increases) in the relative price of primary goods, the mosupply must expand (respectively contract), and the domestic curredepreciate (respectively appreciate), to offset the shock on the domsector. The larger the relative share, , of foreign goods in total domeexpenditures, or equivalently, the larger the share of exports in total outhe greater the effect of a change in primary goods prices on domeincome and consumption, and therefore the greater the required chanthe exchange rate and money supply.

WP-----

Θ λλ 1–------------

α 11 α–------------

ασ nα

AXPX

P---------------------

φ σ+

=

PΘ

WΘ λ

λ 1–------------

α– 11 α–------------

α– σ nα

AXPX

P---------------------

φ σ+( )–

=

MΘ χW[ ]Θ λ 1–

λ------------

α σ 1 α–( )+ 11 α–------------

σϕ nα

AXPX

P---------------------

ϕ– 1 σ–( )=

SΘ W

PXf

------- Θ λ

λ 1–------------

α– 11 α–------------

α– σn

αAX( )

φ σ+( )– PX

P-------

α 1 σ–( )

=

mφ– 1 σ–( )

Θ------------------------ aX 1 γ–( ) pX pF–( )+[ ]=

s pXf

–α 1 σ–( ) 1 γ–( )

Θ-------------------------------------- pX

fpF

f–( ) φ σ+

Θ-------------aX–+=

α 1 σ–( ) 1 γ–( )Θ

-------------------------------------- 1 γ– 1≤ ≤

1 γ–


tiveds,tors.allyre-y and

ary)WertedTheare

arkettheouslybour

e of

tions

profitically

Section 2 examined monetary policy in a one-sector economy. Relaprices referred to the price of all domestic goods relative to foreign gooand accordingly, a relative price shock is a shock across all domestic secOne would therefore expect monetary policy to respond fairly substantito such shocks. In the following section, we examine how monetarysponses are altered when there are two domestic sectors in the economthe shocks affect prices in one sector relative to the other.

3 Two-Sector Economy

We now suppose that the domestic economy consists of a (non-primtraded goods sector in addition to the primary goods sector (i.e., ).continue to assume that prices of primary goods and prices of impogoods are determined in the world market and exogenously given.mechanism by which prices of (non-primary) home-produced goodsdetermined, however, is more open to question, since the domestic mfor such goods is likely to be relatively important. We therefore examinecase where it is exogenously given and the case where it is endogendetermined. We also consider alternative scenarios regarding lamobility across sectors.12

All prices and wages are assumed equal in the long run,13 hence all firmsproduce the same output, and

,

where bar superscripts denote long-run values. The (long-run) sharexports of primary goods in total output is then

;

the share of exports of non-primary goods in total output is

12. Not treated in this paper, but not difficult to incorporate, are alternative assumpregarding labour mobility across national borders.13. This is reasonable, since all firms are identical and should therefore make equalin the long run; and labour is mobile in the long run, hence wages cannot be systemathigher in one sector.

γ H 0≠

CX

γ X-------

CT

1 γ X–---------------

CH

1 γ X–( )γH

---------------------------CF

1 γ X–( ) 1 γ H–( )----------------------------------------- C= = = =

nXYX nHYH+ nX nH+( )Y= =

αX

nXYX CX–

nX nH+( )Y----------------------------≡

nX γ X nX nH+( )–

nX nH+( )-------------------------------------------=

310 Srour

total

thecu-:

tive

e ofgn-

on-

orld

tionetary

;

the share of imports of non-primary goods must balance the share ofexports

;

whereas the share of the volume of trade in non-primary goods is

.

Given the changes over time in the composition of trade in Canada andevidence of greater integration with the United States, we will be partilarly interested in the implications for monetary policy of changes in the

• relative size of the primary goods sector driven by changes in the relanumber of firms;

• volume of trade in non-primary goods driven by changes in the sharconsumption of home-produced non-primary goods relative to foreiproduced goods; and

• elasticity of substitution between home-produced and imported nprimary goods.

We first examine the case where prices of all goods are set in the wmarket and labour is perfectly mobile across domestic sectors.

3.1 Prices of all goods set in the world market,and labour perfectly mobile

All relative prices are then exogenously given, and the ratios of consumpof the various products are independent of the exchange rate and monpolicy:

,

.

αH

nHYH CH–

nX nH+( )Y----------------------------

nH 1 γ X–( )γH

nX nH+( )–

nX nH+----------------------------------------------------------------= =

αF αX αH+CF

nX nH+( )Y---------------------------- 1 γ X–( ) 1 γ H–( )= = =

αH αF+ αX 2αH+nH

nX nH+------------------- 1 γ X–( ) 1 γ H–( ) 1 γ X–( )γ H–+= =

CX

CT-------

γ X

γT------

PT

PX-------=

CH

CF-------

γ H

1 γ H–---------------

PH

PF-------

η–

=


bour.lativeand

The domestic sectors are assumed to employ the same types of laWages are therefore equal across the domestic sectors, and reemployment and output across sectors depend only on relative pricestechnological shocks and not on the exchange rate policy:

,

.

Total demand for labour per household is

,

where

.

In equilibrium, total expenditures must equal total income:

,

hence

.


,

hence

nXLX

nHLH

--------------nX

nH------

AXPX

AHPH

---------------

1α---

=

nXYX

nHYH

--------------nX

nH------

AX

AH-------

1α---

PX

PH-------

1 α–α

------------

=

L nXLX

nHLH

+ Ω PW-----

1α---

= =

Ω nX

AXPX

P--------------

1α---

nH

AHPH

P---------------

1α---

+=

PC nXPX

YX nHPH

YH+=

C1

1 α–------------Ω P

W-----

1 α–α

------------

=

Wλ

λ 1–------------PC

σL

φ=

WP-----

Θ 11 α–------------

ασ λλ 1–------------

αΩα φ σ+( )

=

312 Srour

les,

thatreal

,

(recall ).

Note that the behaviour of governs the behaviour of the macro variaband


.

As in the one-sector model, monetary policy can reproduce the outcomeobtains under flexible wages: for this purpose, it suffices to ensure thatwages under both regimes are equal. This would require

,

hence

.

Equivalently, in terms of the exchange rate,

CΘ 1

1 α–------------

α ϕ+ λ 1–λ

------------1 α–

Ωα 1 ϕ+( )

=

LΘ

1 α–( )σλ 1–λ

------------Ωα 1 σ–( )

=

Θ α φ σ 1 α–( )+ +=

Ω

αΩ αX pX pT–( )nH

nX nH+------------------- pH pT–( )

nXaX nHaH+

nX nH+---------------------------------+ +=

αX pXf αH pH

f αF pFf

–nXaX nHaH+

nX nH+--------------------------------- .+ +=

W1χ--- λ

λ 1–------------E L

1 φ+[ ]

ELM-----

----------------------=

PΘ

WΘ λ

λ 1–------------

α– 11 α–------------

α– σΩ α– φ σ+( )

=

MΘ χW( )Θ λ

λ 1–------------

α– σ– 1 α–( ) 11 α–------------

σϕΩ αϕ– 1 σ–( )

=


tiverts ofa netls atheturns

n theIn

odsice of

our,e that, non-hen

Not surprisingly, under flexible wages, the effect of changes in relaprices on the domestic economy depends on the share of imports/expothe goods directly affected. For instance, assuming the home country isexporter of primary goods, a lower relative price of primary goods entailower income from exports of that good, hence lower employment inprimary goods sector as labour shifts to the other sector. Decreasing reto scale then entail lower real wages and lower aggregate employment.

Accordingly, the monetary response to a relative price shock depends oshare of imports/exports of the good affected directly by the shock.particular, all else being equal, the volume of trade of non-primary gohas no bearing on the monetary response to changes in the relative prprimary goods.

3.2 Prices of all goods set in the world market,and no labour mobility

The domestic sectors are now assumed to employ different types of labso wages can be different across sectors. We nevertheless assumconsumption is the same across households, because of, for instancedistortionary taxes or transfers. A balanced account in equilibrium timplies

,

hence

.

s pX pXf– pX p– p pX

f–+ 1 γ X–( ) pXf

pTf–( ) α φ σ+( )

Θ----------------------Ω– pX

f–= = =

γ X pXf– 1 γ X–( ) pT

f–φ σ+( )

Θ----------------- αX pX

f αH pHf αF pF

f–nXaX nHaH+

nX nH+--------------------------------+ +

–=

γ Xφ σ+( )

Θ-----------------αX+ pX

f– 1 γ X–( )γ Hφ σ+( )

Θ-----------------αH+ pH

f– –=

α 1 σ–( )Θ

---------------------αF pFf–

φ σ+( )Θ

-----------------nXaX nHaH+

nX nH+-------------------------------- .–

PC nXPX

YX nHPH

YH+=

CnX

1 α–------------ AX

PX

P-------

1α---

PWX--------

1 α–α

------------ nH

1 α–------------ AH

PH

P-------

1α---

PWH---------

1 α–α

------------

+=

314 Srour

for

t tofrom

sultaryandtherealauseintoomeherand


.

Substituting the expressions for sectoral wages into the expressionequilibrium consumption,

,

,

,

where

.

Note that the variable is different from that in the previous section, bua first-order approximation, it has the same percentage deviationsinitial conditions,

.

Consequently, the outcome at the sectoral level is different from the rethat obtains when labour is mobile. Following a negative shock to primgoods prices, real wages for households in that sector fall more,employment falls less than it would if labour were mobile, assuminghome country is a net exporter of primary goods. By the same token,wages rise more and employment rises less in the other sector, becunemployment in the primary goods sector does not translate directlyan increased supply of labour in the other sector. Rather, the lower incfrom exports of primary goods, and increased transfers due to higunemployment, translate into lower wages, hence higher employment

Wi

P------

α φ+

α-------------

λλ 1–------------n

φC

σAi

Pi

P-----

φα---

=

CΘ 1

1 α–------------

α φ+n

φ λλ 1–------------

1 α–( )–Ωα 1 ϕ+( )

=

Wi

P------

Θ λ

λ 1–------------

αn

αφ 11 α–------------

ασΩ

α 1 ϕ+( ) ασα φ+-------------

Ai

Pi

P-----

φΘα φ+-------------

=

LiΘ λ 1–

λ------------n

φ–1 α–( )σΩ

1 ϕ+( )–ασ

α φ+------------- AiPi

P-----------

Θα φ+( )

------------------

=

Ωα 1 ϕ+( )nX AX

PX

P-------

1 φ+α φ+-------------

nH AH

PH

P-------

1 φ+α φ+-------------

+

α φ+

≡

Ω

αΩ αX pXf αH pH

f αF pFf

–nXaX nHaH+

nX nH+---------------------------------+ +=


level,

ils intill

ctors

Thus,ainsan,ct itunderl asuld beoy-ones in

arye-

al.d to

oods

output in the non-primary goods sector. Nonetheless, at the aggregateand to a first-order approximation, deviations in real wages,14 employment,consumption, and output are the same in both scenarios (see detaAppendix). Also, the volume of trade in the non-primary goods sector shas no bearing on the effects that such shocks have on the economy.


Note that under flexible wages, the ratio of wages across the two sedepends on relative prices,

,

whereas, under predetermined wages, the ratio is, of course, constant.in general, monetary policy cannot reproduce the outcome that obtunder flexible wages and no labour mobility at the sectoral level. It chowever, reproduce the outcome at the aggregate level. To that effesuffices to ensure that aggregate real wages equal those that prevailflexible wages.15 Under these conditions, output, in the aggregate as welin each sector, and hence consumption and aggregate employment, wothe same as in the flexible case with labour mobility. But naturally, emplment per household of each type will be different, since households insector would be called on to work more or less to offset the fluctuationemployment caused by inflexible wages in the other sector.

3.3 Prices of home-produced non-primary goods endogenous,labour fully mobile

In this scenario, prices of primary goods and foreign-produced non-primgoods are still determined in the world market; however, prices of homproduced non-primary goods adjust to make supply and demand equ16

Specifically, the demand for exports of non-primary goods is assumesatisfy

14. The aggregate wage index is

.

15. With or without labour mobility.16. An alternative scenario with similar consequences is that prices of imported gdepend on domestic demand, i.e., there is pricing to market by foreign firms.

WP-----

WX

P--------

nX

nX nH+-------------------

WH

P---------

nH

nX nH+-------------------

=

WX

WH---------

AX

AH-------

PX

PH-------

φα φ+-------------

=

316 Srour

,

ven.ced

non-gn

of

,

where is the volume of exports ofH-goods that obtain in the long-run, i.e.

.

The same derivations as in section 3.1 imply

,

,

with defined as in section 3.1.

Now, however, relative prices, and hence , are not exogenously giRather, the price ofH-goods adjusts so that total demand for home-produtraded goods equals supply, i.e.,

,

hence

.

All else being equal, an increase in raises output of home-producedprimary goods, which can be liquidated only if their price relative to foreinon-primary goods falls so that domestic consumption and exportsH-goods increase.


The same derivations as in section 3.1 give

EXH θPH

PT-------

η–

=

θ

θ αH1

1 α–------------

α φ+

Θ-------------

λ 1–λ

------------

1 α–Θ

------------

nX nH+( )α 1 ϕ+( )

Θ----------------------

=

L Ω PW-----

1α---

=

C1

1 α–------------Ω P

W-----

1 α–α

------------

=

Ω

Ω

CH EXH+ nHYH

=

1 γ X–( )γH

PPT------C θ+

11 α–------------nH AH

1α--- PH

PT-------

η PH

W-------

1 α–α

------------

=

PH

WP-----

Θ 11 α–------------

ασ λλ 1–------------

αΩα φ σ+( )

=


net

dropnsare,talandofg aricegateofary

renttion

.

Substituting into the market equilibrium condition forH-goods, it follows(see Appendix for details) that

,

and hence

,

where the coefficients and are positive if the home country is aexporter of primary goods.

Thus, as expected, a drop in the world price of primary goods causes ain the price ofH-goods relative to foreign goods. Numerical approximatioshow that the larger the volume of foreign trade (induced by a smaller sh

, of consumption of home-produced non-primary goods in toconsumption of non-primary goods), the smaller the coefficients

(in ). And therefore, the smaller the drop in the pricehome-produced non-primary goods relative to imported goods followinnegative shock to the price of primary goods, the larger the drop in the pof primary goods relative to wages, and the smaller the drop in aggrereal wages, employment, and consumption. A higher elasticitysubstitution, , between home-produced and foreign-produced non-primgoods, has the same effects as a larger volume of trade, but for differeasons. A higher elasticity of substitution implies that a smaller reduc

CΘ 1

1 α–------------

α ϕ+ λ 1–λ

------------1 α–

Ωα 1 ϕ+( )

=

LΘ

1 α–( )σλ 1–λ

------------Ωα 1 σ–( )

=

Ψ pX pF–( ) 1 ϕ+( )Θ

-----------------αH nX nH+( )

nH-------------------------------

nXaX nHaH+

nX nH+--------------------------------

1α---aH Γ pH pF–( )+ +=

αΩ αX αHΨΓ----+

pX pF–( ) 1αH

Γ------- 1 ϕ+( )

Θ-----------------

αH nX nH+( )nH

--------------------------------–+=

nXaX nHaH+

nX nH+---------------------------------

αH

Γ------- 1

α---aH–

w pX–φ σ+

Θ-------------αX 1 γ X–( )–

φ σ+Θ

-------------nH

nX nH+------------------- α 1 σ–( )

Θ---------------------

1 γ X–( )γ H+ΨΓ----+ pX pF–( ) +=

φ σ+Θ

-------------φ σ+

Θ-------------

nH

nX nH+------------------- α 1 σ–( )

Θ---------------------

1 γ X–( )γ H+ 1 ϕ+( )

ΓΘ-----------------

αH nX nH+( )nH

-------------------------------–nXaX nHaH+

nX nH+--------------------------------

+

φ σ+Θ

-------------nH

nX nH+------------------- α 1 σ–( )

Θ---------------------

1 γ X–( )γ H+ 1

Γα-------aH ,–

Ψ Γ

γ H ΨΓ----

αX αHΨΓ----+ αΩ

η

318 Srour

as as of

etaryain,s arergerionargertiveould

olicyivethatandicydsodel

.

odelt of).

d toon,nces

r ofsing

nity

in prices is needed to clear the market for non-primary goods, wherelarger volume of trade implies that a drop in prices is more costly in termincome, and therefore induces greater labour supply.


As in section 3.1, since labour is assumed mobile between sectors, monpolicy can reproduce the equilibrium outcome under flexible wages. Agit suffices to ensure that real wages equal those that obtain when wageflexible. The results above showed that when wages are flexible, the lathe volume of foreign trade and the larger the elasticity of substitutbetween home-produced non-primary goods and imported goods, the lthe drop in the price of primary goods relative to wages following a negashock to the price of primary goods, and therefore the exchange rate shoffset the shock to a lesser degree.

In all the cases considered so far, there is no sense in which monetary ppromotes low productivity in the primary goods sector following a negatshock. When labour was assumed to be perfectly mobile, it was foundmonetary policy can, in fact, reproduce the flexible-wage outcome,when labour was not mobile, it was found that, if anything, monetary polwould sustain higher marginal productivity of labour in the primary goosector than in the flexible-wage case. The next section describes a mwhereby monetary policy can sometimes sustain inefficient productivity

4 One-Sector Economy with Fixed Costs in Production

In this section, we make the same assumptions as in the one-sector mdescribed in section 2, except that now firms can incur a fixed cosproduction along the same lines as in Blanchard and Kiyotaki (198717

Specifically, output by a firm in the domestic sector is now given by

,

where is a fixed cost (expressed in the firm’s own good) that is allowebe different from one firm to another. Aside from the obvious interpretatidifferences in fixed costs between firms can also be thought of as differein efficiency of production.18

17. One difference in our model, with important implications, is that the total numbefirms in the sector that can potentially produce output is fixed and firms have decreareturns-to-scale technology.18. In a partial-equilibrium setting, the fixed cost can also be thought of as an opportucost for doing business in a particular sector.

Y1

1 α–------------AL

1 α–c–=

c


ot toth

ro-

uiv-

talve

The presence of fixed costs means that some firms may choose nproduce following a negative shock. More formally, profits by a firm wifixed costsc are

.

It follows that such a firm admits non-negative profits, and therefore pduces output if

,

i.e., if the price markup over wages is above a certain threshold or, eqalently, if

,

i.e., if the fixed cost is below a certain threshold.

The total domestic output following a shock is

,

where is now the number of firms that do produce output,19 which may besmaller than the total number of firms in the sector, and is the tofixed cost of production incurred in the sector (e.g., if firms haidentical fixed costs). Accordingly, market equilibrium is now written as

,

and the equilibrium level of aggregate consumption is

.

19. To simplify the derivations, this number is allowed to be a fraction.

Π PXY WL–α

1 α–------------AX

1α--- PX

W-------

1α---

W PXc–= =

PX

W------- 1 α–

α------------c

α

1 α–------------

AX

11 α–------------–

≥

cα

1 α–------------A

X

1α--- PX

W-------

1 α–α

------------

≤

totYn

1 α–------------AXL

1 α–totc–=

nn totc

totc nc=

PC PXtotY=

Cn

1 α–------------AX

PX

P-------L

1 α– PX

P-------totc–

n1 α–------------ AX

PX

P-------

1α---

PW-----

1 α–α

------------PX

P-------totc–= =

320 Srour

rof in

ration

4.1 Flexible wages

Households are assumed to take the number,n, of firms in operation as givenwhen they set their wages.20 The first-order equation for wages is

.

Substituting equilibrium consumption gives

.

On the other hand,

.

It follows that the markup satisfies

.

The larger the number,n, of firms in operation, the higher the demand folabour, the higher the real wage and the smaller the markup (see proAppendix). If the threshold for positive profits is binding for some valueof the fixed cost, then

.

(In particular, if all firms admit the same fixed costs, then

.)

20. It would be interesting to examine the case where households take into considethe effect of their wage demands on the subsistence of the firm.

Wλ

λ 1–------------PC

σnL( )φ

=

Wλ

λ 1–------------P

n1 α–------------AX

PX

P-------L

1 α– PX

P-------totc–

σ

nL( )φ=

LAPX

P-----------

1α---

PW-----

1α---

=

PX

W-------

α ϕ+ασ

-------------

n

ϕσ--- n

1 α–------------A

1α--- PX

W-------

1 α–α

------------

totc– λ

λ 1–------------

1σ---–

A

ϕασ-------– PX

P-------

1 σ–( )

σ-----------------

=

c

nϕ nc

α------ totc–

σ λ 1–λ

------------ 1 α–

α------------c

α ϕ+( )–1 α–

---------------------

A

1 ϕ+( )1 α–

----------------- PX

P-------

1 σ–( )

=

nϕ σ+ λ 1–

λ------------

1 α–α

------------c

α ϕ+( ) σ 1 α–( )+1 α–

----------------------------------------------–

AX

1 ϕ+( )1 α–

----------------- PX

P-------

1 σ–( )

=


costise,nrmsle. Buttheent

hede.long

bein thectionms,agese

notes.gesin)tstheir

olicyy tothat

er or, thethe

If the total number of firms in the sector, , is smaller than the numbern thatsatisfies the equation above with the highest possible value of the fixedchosen for , then all the firms in the sector produce output. Otherwthere is an upper limit onc, such that only firms with fixed costs less thaor equal to can make non-negative profits, and the number of such ficannot exceed the numbern that satisfies the equation above. A favourabchange in the terms of trade increases the number of firms in operationas long as this number is no greater than the total number of firms insector with fixed costs less than or equal to , the markup and employmper firm remain constant at

and .

More generally, if the firms’ fixed costs do not differ too much, then tmarkup ought to change relatively little with changes in the terms of traAggregate production would have close to constant returns to scale asas some firms remain idle, and changes in the terms of trade wouldpassed on to wages. However, once the economy reaches capacity,sense that all the firms are in operation, then higher aggregate producan obtain only by means of increases in the production of individual firin which case, domestic goods prices would increase faster than wbecause of decreasing returns to scale.21 The Appendix illustrates the caswhere firms’ fixed costs are distributed uniformly on the interval [0,1].


One can think of two reasons why, in the flexible-wage case, a firm mayproduce output following a negative shock to the terms-of-trade pricEither its fixed costs are too high to operate at the level to which waadjust in equilibrium, or the level of wages at which it can attract (or retalabour is too high. If firms are sufficiently differentiated by their fixed cosso that those firms that choose not to produce do so strictly because ofhigher fixed costs, then, as in the case without fixed costs, monetary pcan reproduce the flexible-wage outcome by causing the local currencdepreciate and domestic prices to rise until real wages equal thoseobtain under flexible wages.

Nonetheless, monetary policy ought to be different depending on whethnot the economy has reached full capacity. Since, under flexible wageselasticity of the markup to changes in the terms of trade is lower when

21. To see this, differentiate the expression for wages in terms of .

n

cc

c

c

PX

W-------

1 α–α

------------c

α1 α–------------

AX

11 α–------------–

= LAXP

X

W--------------

1α---

=

PX

P------

322 Srour

re in

rval

h,uldvetaryan

allarlyn byy all

Theme

ffsetlevelces,elbe

whenks of

omeng asage

Overld beo bermal

ne

economy is below full capacity, the exchange rate must depreciate moresponse to the negative shock in that case.22 The Appendix illustrates thecase where the fixed costs of firms are distributed uniformly on the inte[0,1].

If firms are not sufficiently differentiated by their fixed costs to begin witthen fixing the real wage to that which prevails under flexible wages wosustain production in inefficient firms, i.e., in firms that would not haproduced if wages could adjust. Under such conditions, therefore, monepolicy cannot reproduce the flexible-wage outcome. What then, isefficient policy?

If, in fact, all firms have equal fixed costs, then following a shock, eitherfirms produce output or none does. However, the latter outcome clecannot be efficient since it entails no income and hence no consumptiohouseholds. In this case, monetary policy always sustains production bfirms, even if some firms are inefficient.23

This result depends, however, on all firms having equal fixed costs.presence of firms with different fixed costs makes it possible that for sorange of the terms of trade it is optimum, as in the previous case, to oshocks to the terms of trade and keep the price of primary goods at athat sustains inefficient production. For another range of relative prihowever, it is optimum to allow the price of primary goods to fall to a levthat thwarts production in certain firms in spite of the fact that they wouldefficient if wages could adjust.24

22. By the same token, this also implies that prices must be allowed to change morethe economy is at full capacity. Of course this does not take into consideration the risinflation. One must introduce dynamics in the model to tackle such questions.23. Heuristically, the policy that seems closest to reproducing the flexible-wage outcis the policy that keeps the price of primary goods (hence the markup) constant as lothe terms of trade are below the threshold that entails positive profits in the flexible-wcase, i.e., as long as the potential number,

,

of firms that can be sustained is no greater than the total number of firms in the sector.that range of values for the terms of trade, employment is therefore higher than it wouunder flexible wages. Conversely, for the equilibrium to exist, employment likely has tlower than it would be under flexible wages for values above the threshold. A more foproof of this claim is outside the scope of this paper.24. Alternatively, one can obtain similar outcomes even if all firms are identical, if oincorporates a second sector in the economy that can provide a substitute income.

nϕ σ+ λ 1–

λ------------

1 α–α

------------c

α ϕ+( ) σ 1 α–( )+1 α–

----------------------------------------------–

AX

1 ϕ+( )1 α–

----------------- PX

P------

1 σ–( )

=


oachForpening

cienta

ncytwo-s ofdedas ining ally,ter-andns.inthe

meat its in

tions,t ofhileo aan

Conclusions

This paper applies the New Keynesian open-economy modelling apprto examine monetary policy in the context of the Canadian economy.that purpose, it develops a simple one-period model of a small oeconomy with nominal-wage rigidities, price-taking firms, and decreasreturns-to-scale technology.

The paper first looks at a one-sector case and shows that the effimonetary policy conforms to conventional wisdom. Specifically, followingnegative shock to the relative price of domestic goods, the local curremust depreciate to counteract the rigidity of wages. Next, it examines asector model, with one sector standing for primary goods, the pricewhich are set in the world market, and another sector standing for tranon-primary (e.g., manufactured) goods. It is subsequently shown that,the one-sector model, the domestic currency needs to depreciate follownegative shock to the relative price of primary goods, but that typicahigher economic integration, represented by a higher volume of innational trade or higher elasticity of substitution between domesticforeign (non-primary) goods, would induce smaller currency depreciatioFinally, the paper considers a one-sector model with fixed costsproduction, and shows that monetary policy cannot always reproduceflexible-wage outcome in such an environment. In fact, in socircumstances, monetary policy may stifle productivity, in the sense thmay have to sustain production in firms that would make negative profita perfectly flexible environment.

The model can be easily extended to examine a number of other quesfor instance, the effect of labour mobility across countries on the conducmonetary policy, or the effects of adjustment costs in labour markets. Wit allows one to abstract from dynamics, the restriction of the model tsingle period strongly limits the breadth of the results. Extension toinfinite horizon is the natural next step in this research.

324 Srour

torent

t theder

lly in

AppendixTwo-Sector Economy

All prices set in the world market, labour not mobile

Claim: Under flexible wages, real wages in the primary goods secfollowing a shock to prices in that sector deviate less, and employmdeviates more when labour is mobile than when it is not, assuming thahome country is a net exporter of primary goods. However, to a first-orapproximation, aggregate real wages and employment deviate equaboth scenarios.

Indeed, real wages (in either sector) when labour is mobile are

,

and hence, in percentage deviations from initial conditions,

;

whereas, when labour is not mobile,

,

hence

Recall that, in either case,

Thus, the elasticity of real wages with respect to is

WP-----

Θ 11 α–------------

ασ λλ 1–------------

αΩα φ σ+( )

=

Θ w p–( ) α φ σ+( )Ω φ σ+( ) αX pXf αH pH

f αF pFf–

nXaX nHaH+

nX nH+--------------------------------+ +

= =

Wi

P------

Θ λ

λ 1–------------

αn

αφ 11 α–------------

ασΩ

α 1 ϕ+( ) ασα φ+-------------

Ai

Pi

P-----

φΘα φ+-------------

=

Θ wi p–( ) α 1 ϕ+( ) ασα φ+-------------Ω φΘ

α φ+------------- ai pi p–+( )+=

1 ϕ+( ) ασα φ+------------- αX pX

f αH pHf αF pF

f–nXaX nHaH+

nX nH+--------------------------------+ +

φΘα φ+------------- ai pi p–+( ) .+=

αΩ αX pX pT–( )nH

nX nH+------------------- pH pT–( )

nXaX nHaH+

nX nH+---------------------------------+ +=

αX pXf αH pH

f αF pFf

–nXaX nHaH+

nX nH+---------------------------------+ +=

pXf


te

when labour is mobile, and

when labour is not mobile, and their difference is negative:

The claim for sectoral employment follows immediately, since

under either scenario.

The deviation in aggregate real wages when labour is not mobile is

which is identical to that when labour is mobile; similarly for aggregalabour.

Prices of home-produced non-primary goods endogenous

The same derivations as above give

φ σ+( )αX

1 ϕ+( ) ασα φ+-------------αX

φΘα φ+------------- 1 γ X–( )+

1α φ+------------- φ σ+( ) α φ+( ) 1 ϕ+( )ασ–[ ]αX φΘ 1 γ X–( )–

1α φ+------------- φ α φ σ 1 α–( )+ +( )αX φΘ 1 γ X–( )– =

φΘα φ+------------- αX 1 γ X–( )– φΘ

α φ+-------------–

nH

nX nH+------------------- .= =

Li

AiPi

P-----------

1α---

AiP

Wi---------

1α---

=

Θ w p–( ) ΘnX

nX nH+------------------- wX p–( )

nH

nX nH+------------------- wH p–( )+=

1 ϕ+( ) ασα φ+-------------αΩ

nX

nX nH+------------------- φΘ

α φ+------------- aX pX p–+( )

nH

nX nH+------------------- φΘ

α φ+------------- aH pH p–+( )+ +=

1 ϕ+( ) ασα φ+-------------αΩ φΘ

α φ+-------------αΩ+ φ σ+( )αΩ ,= =

WP-----

Θ 11 α–------------

ασ λλ 1–------------

αΩα φ σ+( )

=

CΘ 1

1 α–------------

α ϕ+ λ 1–λ

------------1 α–

Ωα 1 ϕ+( )

=

326 Srour

.

Equilibrium in the market forH-goods requires

.

It follows

.

Taking log deviations from initial conditions,

hence

,

or equivalently

LΘ

1 α–( )σλ 1–λ

------------Ωα 1 σ–( )

=

1 γ X–( )γH

PPT------C θ+

11 α–------------nH AH

1α--- PH

PT-------

η PH

W-------

1 α–α

------------

=

1 γ X–( )γH

PPT------ 1

1 α–------------

α ϕ+

Θ-------------

λ 1–λ

------------

1 α–Θ

------------

Ω

α 1 ϕ+( )Θ

----------------------

θ+

nH AH

1α--- PH

PT-------

1 α– αη+α

--------------------------PT

P------

1 α–α

------------1

1 α–------------

α ϕ+

Θ-------------

λλ 1–------------

1 α–( )Θ

-----------------–

Ωα 1 ϕ+( )

Θ---------------------- 1–

=

1α---

αH nX nH+( )nH

--------------------------------– γ X pX pT–( )[ ] 1α---aH

1 α– αη+α

-------------------------- pH pT–( )+=

1α---–

1 ϕ+( )Θ

-----------------αH nX nH+( )

nH--------------------------------+

+ αΩ ,

1α--- γ X αX+( )

αH nX nH+( )nH

-------------------------------- γ X1 ϕ+( )

Θ-----------------αX+

– pX pT–( )[ ] =

1α---

nX

nX nH+------------------- 1 ϕ+( )

Θ-----------------αH η 1–+ +

+ pH pT–( ),

1α---–

1 ϕ+( )Θ

-----------------αH nX nH+( )

nH--------------------------------+

nXaX nHaH+

nX nH+--------------------------------- 1

α---aH+ +

Ψ pX pT–( ) 1 ϕ+( )Θ

-----------------αH nX nH+( )

nH-------------------------------

nXaX nHaH+

nX nH+--------------------------------

1α---aH Γ1 pH pT–( )+ +=


,

where

,

and

.

In particular, if , then

,

while if , then

,

, and

.

It follows

Ψ pX pF–( ) 1 ϕ+( )Θ

-----------------αH nX nH+( )

nH-------------------------------

nXaX nHaH+

nX nH+--------------------------------

1α---aH Γ pH pF–( )+ +=

Γ11α---

nX

nX nH+------------------- 1 ϕ+( )

Θ-----------------αH η 1–+ +=

Γ Γ1 1 γ H–( ) Ψγ H+=

Ψ 1α---

nX

nX nH+( )------------------------ 1

1 γ X–( )γ H nX nH+( )nH

---------------------------------------------------– 1 ϕ+( )

Θ-----------------

nX

nX nH+------------------- 1 α–( ) 1 σ–( )

Θ-----------------------------------γ X–

–=

αH 0=

Ψ 1α---

nX

nX nH+( )------------------------= Γ1

1α---

nX

nX nH+------------------- η 1–+=

Γ 1α---

nX

nX nH+------------------- η 1–( ) 1 γ H–( )+=

αX αHΨΓ----+ αX=

γ H 0=

Ψ ϕ σ+( ) 1 α–( )αΘ

------------------------------------nX

nX nH+------------------- 1 α–( ) 1 σ–( )

Θ-----------------------------------γ X+=

Γ11α---

nX

nX nH+------------------- 1 ϕ+( )

Θ-----------------

nH

nX nH+------------------- η 1–+ += Γ Γ1=

αX αHΨΓ----+ αX

nH

nX nH+-------------------

ϕ σ+( ) 1 α–( )αΘ

------------------------------------nX

nX nH+------------------- 1 α–( ) 1 σ–( )

Θ-----------------------------------γ X+

1α---

nX

nX nH+------------------- 1 ϕ+( )

Θ-----------------

nH

nX nH+------------------- η 1–+ +

---------------------------------------------------------------------------------------------------------+=

αΩ αX pX pF–( ) αH pH pF–( )nXaX nHaH+

nX nH+--------------------------------+ +=

αX αHΨΓ----+

pX pF–( ) 1αH

Γ------- 1 ϕ+( )

Θ-----------------

αH nX nH+( )nH

-------------------------------–nXaX nHaH+

nX nH+--------------------------------

αH

Γ------- 1

α---aH–+=

328 Srour

ons

and

Recalling , and , one alsohas

Thus, , , and are positive. Furthermore, numerical approximatishow that

increases, and

w pX– w p– 1 γ X–( ) pX pF– γ H pH pF–( )–[ ]–=

φ σ+Θ

-------------αXφ σ+

Θ-------------α

H1 γ X–( )γ H+

ΨΓ----+ 1 γ X–( )– pX pF–( ) +=

φ σ+Θ

-------------φ σ+

Θ-------------αH 1 γ X–( )γ H+

1 ϕ+( )ΓΘ

-----------------αH nX nH+( )

nH-------------------------------–

nXaX nHaH+

nX nH+--------------------------------

+

φ σ+Θ

-------------αH 1 γ X–( )γ H+ 1

Γα-------aH–

φ σ+Θ

-------------αX 1 γ X–( )–φ σ+

Θ-------------

nH

nX nH+------------------- α 1 σ–( )

Θ---------------------

1 γ X–( )γ H+ΨΓ----+ pX pF–( )=

φ σ+Θ

-------------φ σ+

Θ-------------

nH

nX nH+------------------- α 1 σ–( )

Θ---------------------

1 γ X–( )γ H+ 1 ϕ+( )

ΓΘ-----------------

αH nX nH+( )nH

-------------------------------–nXaX nHaH+

nX nH+--------------------------------

+

φ σ+Θ

-------------nH

nX nH+------------------- α 1 σ–( )

Θ---------------------

1 γ X–( )γ H+ 1

Γα-------aH .–

αX

nX

nX nH+------------------- γ X–= αH

nH

nX nH+------------------- 1 γ X–( )γ

H–=

Ψ ϕ σ+( ) 1 α–( )αΘ

------------------------------------1 ϕ+( )

Θ-----------------


--------------------------------------------------- +

nX

nX nH+( )------------------------=

11 γ X–( )γ H nX nH+( )

nH---------------------------------------------------–

1 α–( ) 1 σ–( )Θ

-----------------------------------γ X +


--------------------------------------------------- γ X1 ϕ+( )

Θ-----------------αX+

1 α–( )Θ

----------------- 1 σ–( )γ Xϕ σ+( )

α------------------

nX

nX nH+( )------------------------++=

Γ11α--- 1 ϕ+( )

Θ-----------------–

nX

nX nH+------------------- 1 ϕ+( )

Θ-----------------

nX

nX nH+-------------------

nH

nX nH+------------------- 1 γ X–( )γ H–+

η 1–+ +=

1 α–( ) ϕ σ+( )αΘ

------------------------------------nX

nX nH+------------------- 1 ϕ+( )

Θ----------------- 1 1 γ X–( )γ H–( ) η 1 .–+ +=

Ψ Γ1 Γ

ΨΓ----

αX αHΨΓ----+


the

decreases with . It follows that the elasticity,

of

with respect to , which is negative, is larger in absolute value asdecreases.

Note too that is independent of, while and increase with,elasticity of substitution . Thus

and

decrease with .

One-sector economy with fixed costs in production

Flexible wages

Claim: The larger the number,n, of firms in operation, the higher thedemand for labour and the higher the real wage.

Recall the expression for the markup,

,

.

Differentiating both sides with respect ton, and lettingd denote the partialderivative of

,

γ H

φ σ+Θ

-------------αX 1 γ X–( )–φ σ+

Θ-------------

nH

nX nH+------------------- α 1 σ–( )

Θ---------------------

1 γ X–( )γ H+ΨΓ----+

WPX-------

PX

PF------- γ H

Ψ Γ1 Γη

ΨΓ---- αX αH

ΨΓ----+

η

DPX

W-------

α ϕ+ασ

-------------–

n

ϕσ--- n

1 α–------------AX

1α--- PX

W-------

1 α–α

------------

totc–

=

Dλ

λ 1–------------

1σ---–

AX

ϕασ-------–

PX

P-------

1 σ–( )

σ-----------------

=

PX

W-------

330 Srour

we obtain

hence

hence,

hence,

where is the largest fixed cost of a firm that is in operation and

.

Dα ϕ+

ασ-------------–

PX

W-------

α ϕ+ασ

-------------– 1–

dϕσ---n

1–D

PX

W-------

α ϕ+ασ

-------------–

=

n

ϕσ--- 1

1 α–------------AX

1α--- PX

W-------

1 α–α

------------1 α–

α------------ n

1 α–------------AX

1α--- PX

W-------

1 α–α

------------ 1–

dn∂

∂totc–+ ,+

dPX

W------

1–

Dα ϕ+

ασ-------------–

PX

W------

α ϕ+ασ

-------------–

n

ϕσ--- n

α---AX

1α--- PX

W------

1 α–α

------------

–ϕσ---n 1–

DPX

W------

α ϕ+ασ

-------------–

=

n

ϕσ--- 1

1 α–------------AX

1α--- PX

W------

1 α–α

------------

n∂∂

totc– ,+

d1α---

PX

W-------

1–n–( )AX

1α--- PX

W-------

1 α–α

------------α ϕ 1 α–( )σ+ +

1 α–( )σ-----------------------------------------

α ϕ+σ

-------------+ totc

=ϕσ---n

1– n1 α–------------AX

1α--- PX

W-------

1 α–α

------------

totc–

11 α–------------AX

1α--- PX

W-------

1 α–α

------------

n∂∂

totc–+

d–1α---

PX

W-------

1–n

cα--- k+

1 α–( ) α ϕ+σ

-------------+ ncα--- totc– nk+

=ϕσ---n

1–n

cα--- totc– nk+ c

α--- k

n∂∂

totc–+ ,+

c

k1

1 α–------------A

X

1α--- PX

W-------

1 α–α

------------

cα---–≡


t

hus,

o afits.the

hecesion.

t of

ctor.

Note, , (otherwise a firm with fixed cost would noproduce), and

,

since all firms with fixed cost less than must already be in operation. Tall the terms in brackets in the equation above are positive, andd is negative.In other words, a marginally lower number of firms in operation leads thigher markup, which in turn implies higher, hence non-negative, proIt follows that, as claimed, the lower the number of firms in operation,higher the markup and the lower the real wage.

Claim: Suppose that firms’ fixed costs are distributed uniformly on tinterval [0,1]. Then the markup grows faster with changes in relative prionce the economy is at full capacity, i.e., once all the firms are in operat

Indeed, ifn is the number of firms in operation, then the highest fixed cosa firm that does produce output isn and

.

Recall that

.

It follows

,

hence

,

as long as this number is smaller than the total number of firms in the seIt follows that a 1 per cent increase in the relative price

totc ncncα------≤ ≤ k 0≥ c

n∂∂

totc c≥

c

totcn

2

2-----=

nϕ nc

α------ totc–

σ λ 1–λ

------------ 1 α–

α------------c

α ϕ+( )–1 α–

---------------------

AX

1 ϕ+( )1 α–

----------------- PX

P-------

1 σ–( )

=

nϕ n

2

α----- n

2

2-----–

σ λ 1–

λ------------

1 α–α

------------n

α ϕ+( )–1 α–

---------------------

AX

1 ϕ+( )1 α–

----------------- PX

P-------

1 σ–( )

=

n

α ϕ+( ) 2σ ϕ+( ) 1 α–( )+1 α–

----------------------------------------------------------------- 1α--- 1

2---–

σ

λ 1–λ

------------ 1 α–

α------------

α ϕ+( )–1 α–

---------------------

AX

1 ϕ+( )1 α–

----------------- PX

P------

1 σ–( )

=

PX

P-------

332 Srour

ches

hes

raises the number of firms by

and the markup by

,

as long as some capacity is idle. Whereas, once the economy reacapacity, the markup grows by

,

which ranges over the interval

[ , ],

since

ranges over

[1, ] as .

In particular, the markup grows more rapidly once the economy reaccapacity.

1 σ–( ) 1 α–( )α ϕ+( ) 2σ ϕ+( ) 1 α–( )+

----------------------------------------------------------------

α 1 σ–( )α ϕ+( ) 2σ ϕ+( ) 1 α–( )+

----------------------------------------------------------------

α 1 σ–( )

α ϕ+( )

11 α–------------AX

1α--- PX

W-------

1 α–α

------------

11 α–------------AX

1α--- PX

W-------

1 α–α

------------12---–

-----------------------------------------------------σ 1 α–( )+

----------------------------------------------------------------------------------------------------

α 1 σ–( ) 2 α–( )2 α–( ) α ϕ+( ) 2σ 1 α–( )+

-------------------------------------------------------------------- α 1 σ–( )α ϕ+( ) σ 1 α–( )+

----------------------------------------------

11 α–------------AX

1α--- PX

W-------

1 α–α

------------

11 α–------------AX

1α--- PX

W-------

1 α–α

------------12---–

-----------------------------------------------------

22 α–------------ 1

1 α–------------AX

1α--- PX

W-------

1 α–α

------------1α---≥


aln inlow

ges

p ofthe

Predetermined wages

Claim: Assuming firms’ fixed costs are distributed uniformly on the interv[0,1], a negative shock to the terms of trade calls for a smaller expansiothe money supply when the economy is at full capacity than when it is becapacity.

From the market equilibrium,

.

Substituting this expression into , it follows that

.

When the economy is at full capacity, the markup under flexible wasatisfies

,

hence

,

and therefore the money supply must expand by the percentage drothe markup in response to a change in relative prices. It follows fromprevious results that the money supply should expand by at most

.

Whereas, when the economy is below capacity,

,

Cn

1 α–------------ AX

PX

P-------

1α---

PW-----

1 α–α

------------PX

P-------totc–=

M χPCσ

=

M χPX

P-------

σ 1– n1 α–------------AX

1α--- PX

W-------

1 α–α

------------

totc–

σPX

W-------W=

n1 α–------------AX

1α--- PX

W-------

1 α–α

------------

totc– λ

λ 1–------------

1σ---–

AX

ϕασ-------–

PX

P-------

1 σ–( )

σ-----------------

PX

W-------

α ϕ+ασ

-------------–

n

ϕσ---–

=

M χ λλ 1–------------

1–A

X

ϕα---–

PX

W-------

ϕα---–

nϕ–W=

ϕα---

ϕ 1 σ–( )α ϕ+( ) σ 1 α–( )+

----------------------------------------------

PX

W-------

1 α–α

------------c

α1 α–------------

AX

11 α–------------–

=

334 Srour

tage

is at

hence

,

and therefore the money supply must expand by the percendrop of the markup in response to a change in relative prices, hence by

,

which is greater than the upper bound in the case where the economyfull capacity.

M χPX

P-------

σ 1– ncα------ totc–

σPX

W-------W χ

PX

P-------

σ 1– 2 α–( )n2

2α-----------------------

σPX

W-------W= =

ϕα--- 2 α–( )

ϕ 2 α–( ) 1 σ–( )α ϕ+( ) 2σ ϕ+( ) 1 α–( )+

----------------------------------------------------------------


he

els

t.the

y.”

ic

s

of

References

Blanchard, O.J. and N. Kiyotaki. 1987. “Monopolistic Competition and tEffects of Aggregate Demand.”American Economic Review 77 (4):647–66.

Bowman, D. and B. Doyle. 2003. “New Keynesian, Open-Economy Modand Their Implications for Monetary Policy.” This volume.

Courchene, T.J. 1998. “Towards a North-American Common Currency:An Optimal Currency Area Analysis.” Queen’s University. Manuscrip

Devereux, M. 2002. “Is the Exchange Rate a Shock Absorber? EvaluatingCase for Flexible Exchange Rates.” University of British Columbia.Manuscript.

Harris, R.G. 1993. “Trade, Money, and Wealth in the Canadian EconomC.D. Howe Institute Benefactors Lecture.

Laidler, D. 1999. “The Exchange Rate Regime and Canada’s MonetaryOrder.” Bank of Canada Working Paper No. 99–7.

Lane, P.R. 2001. “The New Open Economy Macroeconomics.”Journal ofInternational Economics 54 (2): 235–66.

Macklem, T., P. Osakwe, H. Pioro, and L. Schembri. 2001. “The EconomConsequences of Alternative Exchange Rate and Monetary PolicyRegimes in Canada.” InRevisiting the Case for Flexible Exchange Rate,3–35. Proceedings of a conference held by the Bank of Canada,November 2000. Ottawa: Bank of Canada.

Murray, J. 1999. “Why Canada Needs a Flexible Exchange Rate.” BankCanada Working Paper No. 99–12.

Obstfeld, M. and K. Rogoff. 1995. “Exchange Rate Dynamics Redux.”Journal of Political Economy 103 (3): 624–60.

———. 1999. “New Directions for Stochastic Open Economy Models.”NBER Working Paper No. 7313.

———. 2000 “The Six Major Puzzles in International Macroeconomics:Is There a Common Cause?” NBER Macroeconomics Annual 15.

Tille, C. 1999. “The Role of Consumption Substitutability in theInternational Transmission of Monetary Shocks.”Journal ofInternational Economics 53 (2): 421–44.

———. 2002. “How Valuable Is Exchange Rate Flexibility? OptimalMonetary Policy under Sectoral Shocks.” Federal Reserve Bank ofNew York. Staff Report No. 147.

monetary policy in a small open economy - bank of canada€¦ · monetary policy in a small open...

Documents