Changes in output and the price level:

Mathematical

Social Sciences

22 (1991) 1-42

North-Holland

Changes

in output

An open-economy

and the price level:

mesoeconomic

analysis

K. Abayasiri-Silva Department

of Economics,

Communicated Received

This paper

develops

output

an open economy

changes

as well as foreign

reveals that the aggregate aggregate

of marginal

demand

revenue

model in order

to the exogenous

changes

to investigate in nominal

goods. The model focuses on the behaviour

firm that operates

of domestic

in nominal

the elasticity

Victoria, 3168, Australia

mesoeconomic

and the price level in response

petitive representative the effects

Clayion,

1991

in costs, and in the price of foreign

The analysis

University,

by Y.-K. Ng

28 February

aggregate

Monash

in the domestic demand

output

and the foreign

and price shocks

level of an open economy

in

demand,

of the non-perfectly

markets

com-

by taking

into account

on its profit-maximizing

deciGons.

may be affected

even if the price level is fully responsive

of the representative

the variations aggregate

firm with respect

by the exogenous

to such a change,

provided

to the price of foreign

goods

is non-zero. Key words:

Aggregate

output;

price level; open economy;

imperfect

competition;

mesoeconomics.

1. Introduction Recently, Ng (1982, 1986) has developed a new method of economic analysis, called mesoeconomics, which focuses on the microeconomics of a representative firm, taking into account the effects of macroeconomic variables such as aggregate demand, aggregate output, and the average price level of the economy. There are several important aspects in this method of analysis. First, the model he developed as a basis for macroeconomic analysis provides the microeconomic foundations for macroeconomics in the proper context of Marshallian economics of production, in the sense that the output and price decisions of the economy are mainly determined by the firm. Correspondingly, the model he developed is based on the non-perfectly competitive representative firm of the whole economy, which faces a demand curve as a function of its own price, the average price level of the economy, and the nominal aggregate demand. In view of this, the work of Ng can be distinguished from the well-known microeconomic foundations for the ‘augmented Phillips curve’ pioneered by Phelps et al. (1970) and the micronization of macroeconomics on the basis of a perceived kinked demand curve in the theory of oligopoly as developed by Negishi (1979). Secondly, Ng emphasizes the necessity of ‘working out 0165-4896/91/$03.50

0

1991-Elsevier

Science Publishers

B.V. All rights

reserved

2

K. Aba_vasiri-silva

a theory of demand and supply of in macroeconomic theory which develop in his General Theory, 1937). Thus, in making its output

/ Open-economy

mesoeconomics

output as a whole’ to deal with the unsolved issues was the main theme that Keynes attempted to and explored in his well-known paper (Keynes, decisions, Ng’s representative firm takes into ac-

count the marginal cost conditions as well as the demand conditions for its own output, which is affected by the aggregate demand of the whole economy. Moreover, by specifying the cost of production of the representative firm as a more general function of its own output, the average price level, the level of aggregate output and the exogenous factors such as government policy variables, Ng is able to capture the interaction of the representative firm with rest of the economy in a simple analysis. Finally, the adoption of non-perfect (imperfect) competition in Ng’s analysis’ is a significant departure from the previous work of most authors who explicitly or implicitly assumed perfect competition. This makes him the pioneer of the modern imperfectly competitive microfoundations of macroeconomic models2 (as noted by Marris, 1990, pp. 57 and 154).7 On the other hand, the adoption of non-perfect competition enables him to show that changes in the nominal aggregate demand associated with changes in the elasticities of demand curve facing the representative firm may have real effects with no changes in the price level, and no time lags, etc. generating a continuum of equilibria in the economy. This is in contrast not only with the perfectly competitive models, but also with the recent imperfectly competitive models such as Blanchard and Kiyotaki (1987).’ The purpose of this paper is to show that there are other possible cases where we may have real effects associated with changes in nominal aggregate demand by extending the work of Ng (1982, 1986, ch. 3) to an open economy model. In this model we investigate the short-run fluctuations of output and the general price level in

’ Recent

empirical

work

of Hall (1986) shows

siderable market power and hence lend support general case in the macroeconomic analysis. ’ The other modern

authors

imperfectly

who made a significant competitive

that

the majority

to the postulate contribution,

microeconomic

of U.S.

subsequent

foundations

industries

of non-perfect

to Ng (1980),

of macroeconomics

1986), Hart (1982), Solow (1986), Snower (1984), Dixon (1987, 1990) and Blanchard 3 Marris

(1990) states that ‘in 1980 Yew Kwang

Ng published

an article

manifest

competition

con-

as a more

in the field of

are Benassy and Kiyotaki

which effectively

(1982, (1987).

started

the

modern movement. But not being a resident of a town called Cambridge on either side of the Atlantic, and, if one has to be frank. possessing a certain profligacy in the presentation of equations, Y-K-N made less impact than his topic deserved’ (p. 154). J Blanchard and Kiyotaki (1987) claim that the monopolistic competition by itself could not explain why aggregate demand movements affect combined with monopolistic competition

output; but the small cost of changing may lead to the generation of output

prices (‘menu costs’) and welfare effects.

Nevertheless, their results mainly depend on two factors. First, they deliberately ignore the fact that ‘agdemand changes associated with changes in the demand elasticities facing fh-ms and workers will have real effects and these effects are likely to be different under perfect and monopolistic competition’

gregate

(see Blanchard

and Kiyotaki,

1987, p. 654). Secondly,

specifications in utility and production tiple equilibria.

functions,

they adopted

in their model,

constant

elasticity

to rule out the potential

of substitution source of mul-

K. Abayasiri-silva

/ Open-economy

3

mesoeconomics

response to exogenous changes in aggregate demand, in costs, in the price of imports, and in the price of foreign goods competing with domestic exports. Following Ng, this analysis focuses on the microeconomics of a non-perfectly competitive representative firm, while taking into account the effects of open economy macroeconomic variables such as domestic aggregate demand, domestic demand for imports, foreign demand for domestic exports, aggregate domestic output, domestic average price level, the price of imports, and the price of foreign goods competing with domestic exports, on the demand and cost functions of the representative firm. The representative firm is defined here as in Ng (1982, 1986). Thus, the firm in our model represents the whole economy in the following manner: (a) the elasticity of the marginal cost curve of the representative firm is the weighted average of the elasticities of marginal cost curves of all the firms in the economy; (b) the price determined by the representative firm, according to its own maximization calculus, will turn out to be equal to the average price of all the firms;’ (c) under the condition of (b), if there is an increase or decrease in real aggregate demand, the demand for the product of the representative firm will increase or decrease by the same proportion; (d) the representative firm is assumed to be small enough to have no effect on the average price level and the level of aggregate output; and (e) there is no implicit or explicit collusion between firms so that each firm has to maximize its objective with respect only to the variable under its own control. The short run is defined here, following Ng (1986, ch. 3), by the given number of firms. Thus, in the short run the number of firms is taken as fixed. Since the cost of setting up a new firm, as well as the cost of the exit of business for an existing firm, is substantial, the number of firms can only be changed in the long run, which allows a reasonable time period for entrepreneurs to rationalize their entry or exit decisions. The results of our analysis are important for several reasons. First, they reveal that when it is extended, Ng’s closed economy model can be viewed as a special case of our open economy analysis. Secondly, they show how the extension of the method of economic analysis developed by Ng to an open economy can yield insights not available through the traditional analysis based on perfect competition. Thirdly, our analysis deals with a non-perfectly competitive (representative) firm that operates in the domestic market as well as in foreign markets by taking into account the effects of international trade on its own maximizing decisions. Finally, our results show that the aggregate output level of an open economy may be affected by changes in nominal aggregate demand even if the price level is fully responsive to such a change, provided the elasticity of marginal revenue of the representative firm with respect to the price of foreign goods is non-zero. This last point is novel since, to our knowledge, it has not so far been discussed in the literature. s It is important tion and the fallacy

to note here that in the construction of attribution

of (a) and (b) we avoid the fallacy

(see Ng, 1982, for details).

of composi-

4

K. Abayasiri-silva

/ Open-economy

mesoeconomics

2. The model The representative

firm in our open economy

model produces

two goods:

home

(non-traded) goods and export (traded) goods. Traded goods are sold only to foreigners. These goods are produced according to the foreign market specifications and requirements and, hence, in the production process the firm has to bear special costs compared with the production of home goods. Thus, export goods do not sell in the domestic market because of the foreign market specifications and requirements embodied within them. If the firm needed to sell export goods in the domestic market it would have to ‘modify’ or ‘convert’ them into home goods, which would result in an additional cost to the firm. Thus, for simplicity, we treat the home goods and export goods as two different goods, and assume that there is no domestic demand for export goods. More realistically, one may assume that domestic market demands only a negligible amount of export goods. The home goods do not enter the world market and sell only to domestic households. This may be due to high transport costs or a prohibitive level of protection. Domestic households demand home goods as well as import goods.6 We assume that the prices of foreign goods are exogenously determined. The domestic prices of these goods are equal to their foreign currency prices multiplied by the exchange rate. Nevertheless, throughout the analysis of this paper we assume that the exchange rate of our economy is fixed, and equal to unity. The model developed in this paper includes the following variables: q” q1 ph p’ a”’ 8”

=quantity =quantity = price of =price of =price of = price of

demanded of home goods produced by the firm, demanded of export goods produced by the firm, home goods produced by the firm, export goods produced by the firm, imports in terms of domestic currency, foreign goods competing with domestic exports in terms of domestic

currency, price of home goods produced by all other domestic 7-r” =average TI-’ = average price of export goods produced domestically, Q” = total Q” = total

real output real output

of home goods, of export goods

produced

firms,

domestically,

’ A Gmilar type of model has been used by Grossman, Hanson and Lucas (1982) and Hicks (1953). Although the specification of our open economy model is the same as the Grossman, Hanson and Lucas (1982) model, their work is related to an extension of Barro and Grossman’s (1971, 1976) fixed-price macroeconomic model to a small open economy with traded and non-traded goods. Hicks’ modelling is slightly different, but has the same implications home goods, export goods, and imported goods.

as ours: each country consumes three commodities, Home goods do not enter the foreign market due to

natural immobility or cost of transport. There is virtually no substitution in consumption between home goods and export goods. The home goods are competing with import goods but they may not be the same goods.

K. A bayasiri-silva

Y =real

aggregate

output

/ Open-economy

of the domestic

rnesoeconotnics

economy,

Y*=real aggregate output of foreign countries, (nominal) aggregate demand for home goods, (X” =domestic &ll = (nominal) aggregate demand for imports, ns = foreign (nominal) demand for domestic exports (in

terms

of

domestic

currency), rV = fixed number of firms, B = balance of payments. The expected values of the respective variable are denoted with a circumflex. The representative firm has two perceived demand functions for its two products: home goods (h) and export goods (x): q/I +/Q#,

@$/?I, @),

q-I.= F,\ @.V,+V,j.r, d.I,j,

(1) (2)

where qh and q” are twice differentiable demand functions. The demand for home goods of the firm is a function of its own price (p”), the expected price of all other firms or the expected average price of the home goods (ii”), the expected price of imports in terms of domestic currency (J?“‘), and the expected (nominal) aggregate demand for home goods (6”). The inclusion of the domestic currency price of import goods in the demand function indicates that the home goods are competing with import goods in the domestic market. The demand for export goods of the firm is specified as a function of its own price (p”), the expected price of export goods of all other domestic firms (?j, the expected price of foreign goods competing with domestic exports in terms of domestic currency (J?“), and the expected foreign (nominal) demand for domestic exports (6,‘). Thus, the firm is competing in the production of export goods not only with domestic firms but also with foreign firms in the world market. In equilibrium we have the following relations: Pi1 = $1 = Tlh, PV = e.y ,,ll +,,l,

= =”

8” = P-‘-9

9

(3) (4) (5) (6)

and d 17= oh ) 6” = (yx.

(7) (8)

Since a proportional change in nominal aggregate demand and in all nominal prices does not affect the quantity demanded, equations (1) and (2) may be taken as homogeneous of degree zero in (p”, rch,$“, ah) and (p”, ~“,a’; a”), respectively, and then we have

K. Abayasiri-silva / Open-economy mesoeconomics

6

(9)

(10) Equation (9) indicates that the demand for home goods of the representative firm depends on the relative price of the home goods of the firm to the average price of home goods of the other firms in the economy, the relative price of imports in terms of home goods, and the real aggregate demand for home goods. Similarly, the demand for export goods of the firm depends on the relative price of export goods of the firm to the average price of domestic export goods of the other firms in the economy, the relative price of foreign goods competing with domestic exports in terms of the price of domestic exports, and the foreign (real) aggregate demand for domestic exports. For simplicity, we assume that (9) and (10) are homogeneous of degree one’ in ah/nh and ax/xx given ph/rrh, p”/nh and px/nx, pX/nX, respectively, and then we have

(11) (12) The total

revenue

of the representative

firm is given by

R=Rl’+R-‘,

(13)

where

and

The total cost function

of the firm is specified

as follows:

C=Ch+C”

(14)

where Ch = Ch(qh, 7r’l,Y, 8, EC”) and C” = C”(q”, Tch,rr”, Y, 8, EC‘). C” and C” are assumed to be twice differentiable cost functions for home goods and export goods, respectively; 0 and E represent the government policy variable and ’ Ng (1982, 1986, ch. 3) adopted show that the demand

for the product

this simplifying

assumption

of the representative

(which is relaxed

firm is of unitary

in Ng, 1986, ch. 4) to

aggregate

demand

elasticity.

K. Abayasiri-silva

/ Open-economy

7

mesoeconomics

the effects of other exogenous factors. The costs of producing home goods and export goods of the firm vary with its respective output level, directly through its effects on the firm’s demand for labour and material inputs. The average domestic price levels of home goods and export goods may affect costs directly through the price of material inputs, and indirectly through its effects on the wage rate. The aggregate output of the economy may affect the cost function of the firm by raising the wage rate and the price of material inputs through an increase in the demand for labour and other inputs and through external economies or diseconomies. The effects of government policies on the firm’s cost function may be seen through its effects on wage rates (through direct and indirect taxes).’ The other exogenous factors that may affect the cost function of the firm include technological changes, trade union activities, and natural causes. The domestic (nominal) aggregate demand for home goods, the (nominal) aggregate demand for imports, and the foreign (nominal) demand for domestic exports are given by the following equations:

(15) (16) g=

a”(n”,pA;

y*,E"‘).

(17)

The (nominal) aggregate demand for home goods depends on the average price level of the home goods, the domestic currency price of imports, the aggregate output level (in equilibrium, which equals real income), the government monetary or fiscal policy (8), and the effects of other exogenous factors. The (nominal) aggregate demand for imports depends on the average price level of home goods, the domestic currency price of imports, the aggregate output level, the government monetary or fiscal policy, and the effects of other exogenous factors denoted by aam. The foreign (nominal) demand for domestic exports is specified as a function of the average price of domestic exports, the price of foreign goods competing with domestic exports, the real aggregate output of foreign countries, and other exogenous factors. In equilibrium, we also have the following relations:

(18) (19)

(20) Q” = W.

(21)

To complete the model we must specify the balance of payments. For simplicity, we abstract from the capital movements and other transactions of the current account. * We ignore the importance

of interest rates through

function of the firm because of this paper.

it needs a fully dynamic

which government analysis

policies can influence

of the firm,

which is beyond

the cost the scope

8

K. Abayasiri-silva

/ Open-economy

mesoeconotnics

Hence, it is made up from the balance of trade, which is described relation: B=cX-~-(X.:~~~, Y”, a.Y)_ (y”‘(TI/T,p’)i,Y, 0, Ef)I).

by the following (22)

In a fixed exchange rate regime since the exchange rate is fixed, the domestic money supply will be affected by changes in foreign exchange reserves as reflected in the balance of payments. Thus, we have

where hj” is the changes in foreign exchange reserves that constitute the foreign component of the domestic money supply. Correspondingly, the effect of the balance of payments on the domestic money supply raises two major problems, which need due consideration in maintaining the simplicity of the analysis without substantial loss of its generality. First, it restrains us from specifying monetary policy (0) as an exogenous variable because of its intrinsic form of endogeneity, which springs from the feedback between the foreign component of the money supply and the balance of payments. Secondly, it does not allow us to use the direct application of comparative statics by treating the balance of payments as an endogenous variable because it imposes an intrinsically dynamic structure to the system while all other behavioural relationships in our model are basically static. Methodologically there are two ways to overcome these two problems. First, we could define the level of foreign exchange reserves rather than its rate of change, as measured by the balance of payments, as the dependent variable and use comparative statics’ to investigate how it is affected by changes in other exogenous variables. Secondly, the feedback between the balance of payments and the domestic money supply could be eliminated by assuming that the government uses sterilization policies to neutralize completely the effect of foreign exchange reserve flows on its domestic money s~pply.‘~ The latter assumption will alter the dynamic adjustment mechanism pertaining to the foreign exchange reserves, and with the assumption of zero capital mobility in our model, it allows us to treat the monetary policy (0) as an exogenous variable. For this reason, and for simplicity, in what follows we maintain this assumption.” The representative firm, in our model, takes rrh, .TC’,p”‘, p”, Y, Y*, 8, and E as given and maximizes its profits (I7): II=R-C subject

to (ll),

(23)

(12), and (14).

Y This point was first made by Mundell (1968); Aghevli and Borts (1973) worked out the implications of comparative statics of this point for a two-country model. ‘” This assumption is also made by Aghevli and Borts (1973). ‘I We have developed a similar model to investigate the effects

of aggregate

demand

disturbances

under a flexible exchange rate. Apart from the additional effects of endogenous changes in the exchange rate on output and the price level, the qualitative results do not change substantially, although the algebra is much more tedious.

K. Abayasiri-silva

Using (13) and (14), the profit written as

function

n=P&A[!L?~ - C”(q”, Differentiating

/ Open-economy

mesoeconornics

(23) of the representative

9

firm could be

+Px$g($,$j 7rh, Y, 8, E”) - C”(q’,

2,

rr”,

Y, e, E”).

(24) with respect to ph and pr we obtain

+{d-ch(qh,d

the first-order

(24) conditions:

(25)

Y,B,d')}h,

+{pS-Cb(q.‘,~‘?,~.~,

(26)

Y,B,&“)}g,

where C” = X/aq/’ and c.\‘= X/aq.‘. From (25) and (26) we have

= ch(q”, d’, Y, e, Eh),

pl’ + 7l”

(27)

(28)

which indicates that the marginal revenues received from home goods (h) and export goods (x) by the firm are equal to the respective marginal costs of producing home goods and export goods. Totally differentiating (27) and (28), and using h/h, =(c”-p”)/n” and g/g, = (c-p”)/~*

from (27) and (28) and rearranging

(2+)

dph-

(2-

[

=$,,dqh+&dY+dch_

(2-F) =$

dpx-

dq”+c;dy+,j+

[

the terms we have

~)$_;++

(h1h2,““12)$Jdrrh

(h1h2,,h12) ,$,I,

(2_!!$)!$_;++

(29)

(g1g2,gg12)f]

&,.I

(g1g2;gg12)

Q”,

(30)

where ~$5, ci‘, c$, ci,, thy, and c^; denote the partial derivatives with respect to and dCh= c,hdtI + c$ de”, ds;-‘= cid0 + c$ de”. qh 4” 7t”, xx, and Y, respectively, Equations (29) and (30) show that the adjustments of the firm’s own prices of home

10

K. Abayasiri-silva / Open-economy mesoeconomics

goods and export goods depend on its expectations of changes in the average price levels of these two goods. Using equilibrium conditions of ph = nh, p”= 7cy, dph = dzh, dp”= drr”, on rearranging and dividing through cl’ =ph and c,‘=p”” (see the appendix for the details of A4 and X) we can have equations (29) and (30) in elasticity form:

(31)

K. Abayasiri-silva

&[ii

vl

) p,

p,

costs of producing rch and rr*, output

@/“,

ll(‘y

/ Open-economy

rnesoeconornics

11

yl’.“Y,

and q”“ are the elasticities of the marginal home goods and export goods with respect to their average prices qh and qx, and aggregate domestic output Y, respectively. M and

Xare the elasticities of marginal revenue with respect to the price of imports at given and rrh, and with respect to the price of foreign goods competing with domestic exports at given p.\’ and TC”.,D’ and ,D,”are the marginal revenues from home goods

ph

and export goods, respectively. The slope and the elasticity of the marginal cost curve (MCC) of the home goods are given by ach/aq” and Y$‘~“, respectively, while those of export goods are denoted by ac”/dq” and v(“~‘. The shifts in the marginal cost curve are caused by endogenous as well as exogenous factors, as shown in equations (31) and (32). The endogenous shifts in the MCC for home goods and export goods are represented by ach/ay, v(.“~, aP/aY, The exogenous shift in the and yl”“, respectively. marginal cost curve for home goods is caused by dch and that of export goods is due to d?. It can be seen from (31) and (32) that A4 and X are of ambiguous sign, which we shall discuss in detail in Section 3. Totally differentiating equations (15) and (17)-( 19) we obtain:

(33)

(34) dab dnh -=_+_ ah rr”

dQh

dczX drr” -=_+_ W” JP’

dQX

Qh ’ Q” ’

(35)

(36)

12

K. Abqvasiri-silvu

/ Open-economy

mesoeconomics

and

are the elasticities of aggregate (nominal) demand for home goods and of foreign (nominal) demand for domestic export goods with respect to average prices of home goods and domestic export goods (TC”and xX), total output (Y), the price of imports (@I’), and the price of foreign goods competing with domestic exports (a”).

are the exogenous changes in aggregate demand for home goods and in foreign mand for domestic exports. Using (35) and (36) in (33) and (34), respectively, we obtain:

de-

(37)

Note that we include in equation (33) the government policy variable (0) as an important factor which determines the exogenous shocks of aggregate demand for home goods. Similarly, real aggregate output of foreign countries (Y*) is included in equation (34) to capture the effects of exogenous shocks of foreign demand for domestic export goods. Moreover, the following reasonable restrictions are imposed on equations (37) and (38) to ensure the stability of the system: 1 > v”~~“> -1, is the most common one, 1 > qa’n’ >-1, and l>q a”“> - 1. The latter restriction which indicates that the marginal propensity to spend is less than one. The former two restrictions imply that the whole economy is facing downward-sloping demand curves for home goods and export goods. In the extreme case, when the whole economy faces a perfectly inelastic demand curve such as d0 in Fig. 1 then we have T*%n! = 1. This may also be true for q?““““. But for the general case, such as d’ in rl values for both Fig. 1, we have rl(r‘iT‘< 1 and v~“~” < 1, and hence positive (1 _ p ) and (1 - &““). At the initial equilibrium we may choose units such that the price of home goods and export goods are equal: PiI = PI

and

7~~’ = 71.‘.

K. Abayasiri-silva

From

/ Open-economy

this we may write the aggregate

output

rnesoeconomics

13

of the economy

as

Y = Qh + Q”. Totally

differentiating

(39)

(39) we obtain:

dY -_sShY

dQh Qh

sh
and

(40)

where .?=(l-sh)

are the shares of total output of home goods and export goods, respectively. The five equations (31), (32), (37), (38), and (40) can be used to solve the five endogenous variables drrh/rCh, drc”/n”, d Y/Y, dQh/Qh, and dQ”/Q”, as functions of the exogenous variables dEh/ch, dP/cl, doh/cWh, d&“/cr”, d$“/$“, and dpx/p”. For convenience we rewrite the above five equations, after rearranging, in matrix form: (1 _

).p” _ M)

_f"Y

0

(tiih

(l_&“‘-X)

-ul

_,p

_$‘Y

dnh

0

7rh drrX

+‘Y

0

7rx 0

0

(1 - &‘““)

0

0

1

-vl

d’Y

0

(l-&K‘)

-Sh

-s”

1

0

0

1

dY

*

Y

dQh Q” dQX Q”

L

ire, dji” vlap _x+p

da” a”

P

Denoting

the determinant

of the matrix

in (41*) as L?‘, we have

Q 1= [( 1 _ )?~W_ M)( 1 _ &./a” Y) + (vl’.“~”+ &L.” Y)( 1 _ qd”“)~ x [(l +‘nB x

[#+‘(&JY

_x)+rl(“41(l-~~‘n\)]+SX(l-_~‘“‘) +

v’.“q”va”Y)

+

$‘Y

(( l _

$+r”

_

M)

+

v(.‘ql

_

l?“‘w’>),

.

14

K. Abayasiri-silva

/ Open-economy

mesoeconomics

do

Fig.

I

We have already seen that (1 - v”‘“~) and (1 - $“‘) are both positive. Since sh 5 1 and 1~ vO”~ > - 1, we have a positive sign for (1 -s~v~“~). Although the signs of M and X are ambiguous, the necessary condition for the positive signs of M and X are explained in Section 3. Finally, we could take (1 - v“~“~) and (1 - v?“‘“‘) as non-negative. Thus, for the purpose of comparative static analysis, the sign of 52’ may be taken as positive. Applying Cramer’s Rule, we solve (41*) for dY/Y, dQ”/Q”, dQ”/Q”, dnh/nh, and drr‘/rC-’ and obtain the following five basic equations:

dab

K. Abayasiri-silva / Open-economy mesoeconomics

{?[(l

+

_ *) + ‘I(“y‘(l _ q‘n‘)] [@Y”“‘~‘(l _ p”)

-r#F

+ M(l _ $w

_ ula’ycs)] _SXpr’~(l

+ {SqrldJk(l

_ ~a’n’)()?‘.“4”)?a”P”‘_M)) fg

-ul”‘K’)+X(l-vla~i[~_~~‘p’)]

x [( 1 - $“Zh _ &f) + $“Y”( 1 - $“““)]}

x

Ql

dQX

-=

_

[)f”

Y

(1

_

15

f%”

5g)

A$,

-M)_vl”“Y(,_~a”n”)]}

([(&4’1 + Shyl'.f'Y)p”

+ Shf‘Y

(1

_

(41)

p’~

_

M)](,

(42) _

vu‘n‘)}

Q"

+{(l-

rp’ -~)[(,_shrla”Y)(,_~Il(.‘i~“_~)

+ (qchq” +

Shyl’.i’Y

)( 1 -

f”““)]}

_

([(l_Sh~a”Y)~‘.‘~“__hyl’.‘Y(I_~a”n”)l(l_~a’n’)}

_

{ [(#47”

+&f”

Y )(I

+(I-s”RV.Y)(I_~‘l~“_IM)](l-~*ll’)}~

_

#q

$y

$

$

K. Abayasiri-silva

/ Open-economy

_ { va”p”‘[(SI’f‘Y

(1 _ p”)

_ A,,f [( 1 _ p

mesoeconornics + pQ”q”

+shpj,

_ @“/”

+{[17a’P’(l_~~‘n\)+X(1_~~~n’ _ $“)‘)] ($“(lil

+

+

&p)(

[( 1 _

+ &f”Y

1 _

#+” _ M)

#““,I}

)(l -

$7,

s

_~'.I~'_-)(~7L."Y+~c"q'J~a"Y))

Is”(l

(43)

a” -X)+rl”‘Y‘(l-yl”‘“~](l-_~~~a”Y)

+{[(l-tp‘

!g

+S"f~Y(l_yla~n')}

_

(s”(l_rlCI’K1)(~CIY+)7’.Aq”~U”Y)~

c.’ +

(

[va~qf%”

+ Shyl’.“Y) _

M(1

_

&f”Y

),

[(I

$‘?7

_

_

X)

+~c'0'(1_nU'".l+r.~~c.Y(~'~q"~a"".'_~)(l_n".".)}~

+

x

{s-pf‘P’(l (#JOY

+

+f”‘)+X(l

-p_~a‘D‘)]

Q” ),/,'.'$fY"Y )) __,

(44)

P* Q

I

F = {&f‘Y + { [$w(l

(1

_

Ij7(.“d’_

M)

_&u”Y)

+ [v(.‘q’(vC”q” + &,f”Y)

+

+s”rl”‘q(l

h !cJ_

+ &pj}

pqvl(.“4”

_

+ sx#J’q”)?(.IY

p+‘_M) ,(I _ ul”“““)

+ sYyl’.‘n”(yl’.“Y + )?‘.“q”#Y” Y )} 5

+ { p”(l

_ S/?va”Y)

_ &PY

( 1 _ v”“““)}

$

K. Abayasiri-silva

/ Open-economy

+ {(prl(“4‘ +

(1

+hyldY

s"rl""Y)(l _ $“““)

_ x)[(yl’.“q”+ )(I

$“il”

_

+(II"'Y(l_)?cl'n"_

M)

_M),

+

17

mesoeconornics

)p7”(

+S.~.~n'P‘[yl'.~n"(yl'."Y pp) +

1 -

#““))]}

3.

These five equations are our basic comparative statics results. Since the nonperfectly competitive firm in our model represents the whole economy, these equations show us how the aggregate output, the output levels of home and export goods, and the average price levels of home goods and export goods must change in response to changes in domestic aggregate demand for home goods, in foreign demand for domestic exports, in marginal costs, in the price of imports, and in the price of foreign goods competing with domestic exports, in order for a new equilibrium to be established. An interesting feature of these five basic equations is that for the case where the foreign sector does not exist, so that we may take sX, yl(“4’, v”‘~‘, j?‘, and p”’ as zero, then they would reduce to the system of equations (15) and (16) of Ng’s (1982) model.12 Thus, it may be considered that Ng’s (1982) model is a special case of our open-economy model.

3. Effects

of changes in aggregate demand for domestic

output

In our open-economy model, exogenous changes in (nominal) aggregate demand for domestic output are caused by two main sources: first, exogenous changes in domestic aggregate demand for home goods (cJ?), and second, changes in foreign demand for domestic exports (a”). In the first case, a change in domestic aggregate demand may be generated by changes in the government policy variable (0) (i.e. monetary or fiscal policy) and in other exogenous factors captured by Ph. For the second case, changes in foreign demand for domestic exports may be caused by changes in aggregate output and income of foreign countries, and in other ex-

”

Equations

(15) and (16) of Ng’s (1982)

model are:

dY y’~c,-~~~,~-(I~n”“)~, a

c

dR=~(ri’U+~(Y)~+(,~~yY)~, rl ff where d”={(l~~‘~)(1~~“Y)+()7~~‘+~‘Y)(l~)?~~)}.

c

18

K. Ahuvasirr-silva

/ Open-economy

wzesoeconotnics

ogenous factors. Of these two cases, in this section we analyse the effects of exogenous changes in domestic aggregate demand on the level of aggregate output and the average price level. In the next section we shall analyse the price and output effects of changes in foreign demand for domestic exports. To isolate the effects of exogenous changes in domestic aggregate demand for home goods we set da-‘, d&‘, d?, d$“, and dj?’ equal to zero. This approach cannot be viewed as a partial equilibrium analysis because endogenous changes in cP, in costs, in the relative price of imports, and the relative price of foreign goods competing with domestic exports are taken into account and reflected in vaIni’, v”‘~‘, (,irilir , $“n‘, rf”‘, rf”, M, and X. vl Substituting d?” = 0, dP= 0, da-‘= 0, dp”’ = 0, and d@= 0 in equations (41)-(45) and rearranging, we have A y~‘i=~{~“(l-,l’l.*_M)[(l-II(.‘~‘_X) + p(l

+ /p”

_

+s\yl”‘Y

@/(“q

;,

_s.\.$“9”v?(.ql

_ @7‘)]

)(1

_

@ii‘)]

_

@K’)},

+ssp~‘.~n”(l

(46)

_ vd”‘)},

(47)

{[(yl’.‘J’/” + shv7("'Y )p/~

+,“~“‘y(l-vr“““i’-M)](l-vl~‘~‘)},

(48)

nliinii =~{(,i’.;“.‘+shi7~‘1~)[(1_B~l~l_X) ‘4 +vl(““‘(l_V?a’n‘)]

+S”~‘.“‘l”yl’.lY(l_yla\ir’)},

(49)

(50) where A

yO,‘_ dY =~.da”

AQ,,rx,,

_

n,,CI,,_

Y’

dQh

ah

da”

Q”’

AQ\a,, =--.-dQ’ A

CY’

ah

da”

Q”’

dn”

U”

=dd”‘rc”’

and A

n,Cr,,_ dn” =/I.-

da

cr” r?

K. Abayasiri-silva / Open-economy

Before we go into the detailed

analysis

the following

i.e. (21) and

two equations,

19

mesoeconomics

of these equations,

we compare

them with

(22) of Ng’s (1982) closed-economy

model:

dY

(Y

da

Y’

/1YCr,_._

It is not difficult to observe that if we take sI=O, v(“~ =O, $“ =O, X=0, and M=O, then equations (46) and (49) are equal to the above two equations of Ng’s (1982) model. Hence, it indicates that Ng’s (1982) analysis of the effects of exogenous changes in aggregate demand is a special case of the present analysis of our model. In addition, it indicates the applicability of the parallel line of analysis as used in Ng (1982) to our open-economy model. Equations (46), (49), and (50) indicate how and to what extent an exogenous change in domestic aggregate demand for home goods (ah) affects the level of aggregate output and the average price level (of home goods and export goods) of the economy, depending on the values of (1 - $li”’ - M)( . ), s”(y~‘.“~“~‘.‘~“)(~), (yl’.“q”+ &f”Y)(. ), and s-‘+f”Y” $‘I’)(. ). Equations (47) and (48) provide a detailed explanation for changes in the aggregate output level by highlighting how each sector (home goods and export goods) of the economy will be affected by an exogenous change in domestic aggregate demand. Let us first consider the effects of exogenous changes in domestic aggregate demand (a”) on the level of aggregate output. In our open economy, the aggregate domestic output level will be affected by two main sources. First, there are direct effects on the aggregate output level that occur through changes in the level of output of home goods and are equal to the case where (1 - uCbR’- M)( . ) > 0 in equation (46). Secondly, there are indirect effects on it that emerge through changes in the level of output of export goods, that is where .s”ylciiq”ylc’“ii(.)>O. An increase in ah has negative effects on the output level of the export goods sector, as indicated by the negative sign of equation (48). Correspondingly, the second expression of equation (46) has the correct negative sign, which captures the indirect effects on the level of aggregate output that occur through the reduction in output of export goods. The mechanism for this may be explained as follows. An increase in ah may shift the demand curve for home goods of the representative firm

20

horizontally

K. Abyvasiri-silva

to the right,

/ Open-economy

mesoeconomics

such as from do to d’ in Fig. 2. This horizontal

shift in

the demand curve will result in a primary increase in the price level as well as the output level of home goods, if the elasticity of marginal cost with respect to output quantities of the firm is positive, i.e. $‘lQii>O, in other words if the marginal cost curve (MCC) for home goods is upward sloping. Following Ng (1982, 1986, ch. 3), the changes that may occur in the output and the price level due to changes in the slope of the MCC may be called the primary cost effects. On the other hand, the increase in the output level of home goods may result in an increase in the aggregate output level and enhance the competition among the firms to hire more inputs to maintain the higher level of output by bidding up the prices they paid for their inputs. This may cause an upward shift in the MCC of home goods if v’.~‘>O, and generate secondary cost effects (i.e. changes due to shifts in the MCC) on the price level of home goods. Moreover, an increase in the price of home goods may generate further secondary effects on the marginal cost curve of the export goods through its effects on the money wage rate, and on other material inputs. Hence, we may also have $““’ >O. The secondary effects on the marginal cost curve of the export goods that may occur through the primary and secondary cost effects on the price of home goods are shown in the first expression (yl’.“ll +~~yl’.~~)$‘~~ in equation (48). In other words, the two terms in the parentheses explain the cause of the rise in the price level of home goods which makes an upward shift in the MCC of export goods. Yet, as far as the indirect effects, through which changes in the output of

Fig. 2.

K. Abayasiri-silva

/ Open-economy

21

mesoeconomics

export goods may have on the aggregate output level, are concerned, the slope of the marginal cost curve of home goods is more prominent than its shifts as a cause of secondary effects on the MCC of export goods. Hence, we have .~“yl’.“~“yl’.‘~“(~ ) in equation (46). Given the demand for export goods, a shift in the MCC of export goods will result in an increase in the domestic price of export goods. As a result, since we have (1 - qa“‘) > 0, the quantity demanded for export goods will fall. This would generate a negative effect on the level of aggregate domestic output. These results are consistent with the analysis based on the perfectly competitive as well as the non-perfectly competitive firm. An exogenous change in oh has positive effects on the output level of the home goods sector if (1 - v”‘~” -M)( . ) and (or) .~~$“~yl’.‘~“(~ ) are (is) positive as shown in equation (47). The effects of changes in the output of home goods on the aggregate output level of the economy are captured by the first expression, (l“i’“i’-M)(. ), in equation (46). In the traditional analysis, including closedV economy models with a non-perfectly competitive firm (see Ng, 1982, 1986, ch. 3) these output effects are captured by the term (1 - v”~“~). Instead, we have (l-M)(. ). Accordingly, the output effects on home goods in our model may vl be caused by two sources. First, to what extent does a change in oh influence the marginal cost curve for home goods of the representative firm by an increase in the price of home goods (i.e. the secondary cost effects of the increase in the price of home goods)? Thus, if the marginal cost of home goods is fully responsive to the primary increase in rrh, that is if yl“iii[il= 1, then we have (1 - ~“l’“~) =O, and it is expected to have no effect on the output level of home goods. This result in our model is consistent with the traditional analysis. Secondly, the output of home goods may also be affected by the changes in the elasticity of marginal revenue of the representative firm with respect to relative price of imports, i.e. depending on the value of &f in (1 _ $“n” -M)(. ). This latter point makes a new contribution to the analysis of output effects of nominal aggregate demand disturbances. In this context the role played by the value of M in determining the output effects of home goods needs further elaboration. As shown in the appendix, M is defined and derived with respect to the relative price of imports in terms of home goods $“/z/’ with a given p’ and T? It is also shown in the appendix that M=$“i”i lp”, =‘I 1G yip”@”I#, 7~”/ , where ,i =$“/T[“. Using v~“~” as own price elasticity also show that

m

a(~“(1 + l/~q”P”)}

P

am

of demand

of the representative

firm we can

IP”, n”I

(51) It is clear

from

(51),

since

the marginal

revenue

of the representative

firm

is

K. Abayasiri-srlva / Open-economy mesoeconomics

Fig. 3

A4Rh =ph =ph(l + l/~~l’~*), that as the (absolute) demand elasticity (-qqhpl’) increases (decreases), the marginal revenue of the firm (ph) increases (decreases) at a given p”. Thus, A4 may be either positive or negative if an increase in $“/rch increases or decreases the absolute demand elasticity. For further illustration of this point let us consider an increase in the price of imports at a given price of home goods. This will raise the relative price of imports in terms of home goods and enhance the demand for home goods through its increased competitiveness in the domestic market. How does this affect the elasticity of marginal revenue of the representative firm? If the demand for home goods increases (decreases), the demand curve of the representative firm must shift to the right (left). If this horizontal shift in the demand curve is equi-proportional at each jY’/nh such as the movement of do to d’ in Fig. 3, the absolute demand elasticity will remain unchanged at points A and B. In other words, an increase in $“/rch does not change the absolute demand elasticity (--v”‘~‘) of the firm. This phenomenon is equal to the case where M=O. In such a case we could apply the traditional analysis, for our model, in which the output effects are solely based on the value of (1 - $‘llZiir). What would be the case where Mf O? At a given ph, a rise (fall) in the price of imports may shift the demand curve of the representative firm to the right (left), horizontally, but not in the same proportion such as movements of do to d’ in Figs. 4(a) and 4(b). In Fig. 4(a), since the rightward shift in the demand curve is not equi-proportional the elasticity of d’ at B is greater than the elasticity of do at A, with a given ph, and hence we have M>O since MR is higher at given ph. The

K. Abayasiri-silva

/ Open-economy

mesoeconomics

23

reverse case is depicted in Fig. 4(b), where the elasticity of d’ at B is lower than the elasticity of do at A and MC 0. Thus, it is not difficult to observe from Figs. 4(a) and 4(b) that there is a positive relationship between the direction of changes in the elasticity of demand from the initial point A to the new point B and the sign of M.

AO

a

d

sh(97

0

b

A>B M
@(ax)

0 Fig. 4.

24

K. Abayasiri-silva

/ Open-economy

rnesoeconomics

Geometrically, this confirms the deduction we drive from (51), namely of M depends on whether an increase in .D”‘/TC~increases or decreases elasticity of demand at a given ph.

that the sign the absolute

In addition, the relative value of p”‘/n” may increase or decrease with a given p”’ as 7~‘~increases or decreases, endogenously. This case is more important in the analysis of the effects of exogenous changes in domestic aggregate demand on aggregate output and the price level of our economy. Let us consider a situation where an increase in domestic aggregate demand for home goods will result in an increase in the price of home goods through the primary and secondary costs effects. We have already seen that if the marginal cost of the home goods is fully responsive to the change in rch there will be no output effects since (1 -r,JhXi’)=O. Nevertheless, in our model there is still a possibility of having output effects on the home goods sector through changes in the elasticity of marginal revenue of the representative firm with respect to the relative price of imports, if Mf 0. Correspondingly, since there is a minus sign before A4 in (1- #‘h’iii-M) there may be a positive or negative effect on the output level of home goods, depending on whether M is negative or positive, as follows. A rise in TC’ as a consequence of primary and secondary costs effects on home goods will decrease the $“/rrh at a given p”‘. According to the traditional analysis a decrease in the relative price of imports will strengthen the relative competitiveness of import goods in the domestic market and may have a negative effect on the demand for the home goods of the firm. Thus, a decrease in the level of output of home goods is expected. However, in our analysis whether a decrease in the relative price of imports will result in a fall or rise in the output level of home goods will also depend on its effects on the absolute demand elasticity of the firm at a given increase in ph. Thus, if the decrease in jYT’/rch increases the absolute demand elasticity (-yly”P” ) the value of M will be negative and, since we have the minus sign before M in (1 - I?(“‘~ - M), the output level of home goods will increase. On the other hand, as JY’/r?’ decreases, if -$“p” decreases, the sign of M will be positive and the output level of home goods will fall. These results suggest that most of the deductions of traditional analysis are implicitly or explicitly based on the assumption of perfect competition and hence ignore the importance of endogenous changes that may occur in the elasticity of the demand curve of the firm. It may be noted here that even in our analysis the shift in the demand curve of the representative firm, as czh/rrh changes, is assumed as the value of A4 in isoelastic or equi-proportional (see’equation (11)). I3 Nevertheless, our analysis captures how the initial equi-proportional shifts in the demand curve of the firm may endogenously change non-isoelastically through changes in the relative price of imports. In our model these non-traditional results are generated through the introduction of the relative price of imports in terms of home goods

I3 In chapter 4 of Ng (1986) this assumption has been changed to take into account isoelastic shifts in the demand curve as real aggregate demand changes.

the effects of non-

K. Abayasiri-silva

as a variable firm.

in the demand

/ Open-economy

25

mesoeconomics

curve of the non-perfectly

competitive

representative

Another way of looking at our non-traditional results is to compare them with the results of Ng’s closed-economy model. In his model, Ng (1982, 1986, ch. 3) identified four cases in the analysis of price and output effects of an exogenous change in aggregate demand. Of these four cases, in case (a) an increase in aggregate demand increases only the price level without affecting the output level when (1 - qCii) = 0 and ~1”~+ qCY> 0. On the other hand, in case (b) the output increases with an unchanged price level when (1 - v”~)>O and ~1”~+ qCy= 0.14 In contrast to case (a) of his closed-economy model, in our open-economy analysis as aggregate demand increases, the aggregate domestic output level will increase (decrease) even if (1 _ vl”“““) = 0 and ~(liq” + sl’~?‘.“Y >O, provided M>O (A4<0), and the sum of expansionary effects on the level of output of home goods and the contractionary effects on the level of output of export goods is positive (negative). Moreover, even if we compare our results with case (b) of Ng’s (1982, 1986, ch. 3) model (ignoring the impact of the export goods sector on the aggregate level of output), the output effect of our open-economy model differs owing to the importance of A4 in determining the impact on the home goods sector. Thus, our non-traditional results that emerge with M, the elasticity of marginal revenue of the firm with respect to the price of imports, have important implications for the theory of aggregate supply and provide a reasonable ground to review the major conclusions of the existing theory on that basis. The effects on the prices of home goods and export goods of exogenous changes in domestic aggregate demand are represented by the two expressions ““rl” + .~“#‘l’~)(. ) and #“‘(. ) of equations (49) and (50). An important fact that (rl is revealed by these two expressions is that in our model the price effects and the output effects are not completely independent of each other compared with Ng’s closed-economy model. To elaborate this fact, let us consider the following two cases. Case I: (1 - q”““” - M)( +) > 0 and (yl’.“‘l”+ .Y~$‘~‘~ )(. )=0, which is equal to case (a) of Ng’s model, where there are only output effects without having any effects on the price level. However, in our open-economy model, as a result of the expression (I _ $“X” -M)(. ) appearing in the price equation for export goods, the output effects are not completely independent from the price effects. Case 2: (1 - q?(‘+”_ M)( . ) = 0 and (qc”q”+ s”q’.“Y )(. )> 0, which is equal to case (b) of Ng’s model, where there are only price effects without having any changes

” In determining the price effects, the elasticities of marginal costs with respect to the firm’s own output and to the aggregate output level of the economy, that is /qi’ + 7““‘. play a major role in our model. It is interesting to note here that McDonald and Solow (1981) found that ‘fluctuations in real product demand at the firm and industry level to be accompanied by large correlated fluctuations in employment (output) and small changes in real wage rates (costs) that could go in either direction’ (p. 908). That is, q”‘Q” + $‘“) may well be zero over a certain range.

26

K. Abayasiri-silva

/ Open-economy

mesoeconomics

in the level of output. Yet, in our model, ignoring the possible effects that may occur through s~‘)?‘.~~” q““(. )>O, we cannot have any price effects on home goods unless at least one of the terms in (1 - Y](‘~*‘-X)+ $“q‘(l)?a”‘)15 is positive in (49), which again shows that the price effects are not independent of the output effects. The interdependency between output and the price effect in our model could be explained as follows. In Case 1, if (1 - qci’“l’-M)( . )>O, there will be an increase in the output level of home goods (Qh). But as Qh increases it will generate secondary cost effects, by the increase in Y, in the export goods sector and will raise the price of export goods if v(“’ >O. Since we have (1 - qa“‘) >O, this will result in a fall in the output level of export goods. Thus, in the final equilibrium a rise in Qh may not necessarily increase the aggregate output Y. Similarly, in Case 2 when (ylch4”+ ?v“~~)(. )>0, the increase in the price level of home goods will have negative effects on the output level of export goods if q”“’ >O (see equations (48) and (49)) and hence will offset the initial increase that may occur in the aggregate domestic output level. We obtain these results partly due to the two-sector analysis of our open-economy model and partly as a result of introducing non-perfect competition into the analysis. The inclusion of the influence of the export goods sector, i.e. (1 - $““‘-X), in the price equation of home goods and the influence of the home goods sector, i.e. (1 _ @r* -M), in the price equation of export goods, reflects the interdependency between the two sectors. On the other hand, the endogenous changes in czh have the same qualitative results as in the case of exogenous changes and hence their effects only alter the magnitude of the total effects. Although this is similar to the point highlighted in Ng (1982, 1986, ch. 3), an additional fact is that the inclusion of endogenous changes in ax due to exogenous changes in ah may offset the magnitude of the total effects. Thus, in the case where there are price effects as well as the output effects, an endogenous change in ah reinforces the increase in the price of home changes in ax if goods if @@Khis positive, but is partially offset by the endogenous the net outcome of the output effects depends on whether rl “A’>O. Therefore, rla%? is greater or less than or equal to qa“‘. Thus, the interdependency of the price and output effects in our model is another important feature that has different implications for the theory, compared with Ng’s model (1982, 1986, ch. 3). These results would strongly support the New Keynesian case that the government fiscal and monetary policies may have output effects as well as price effects. 4. Effects

of changes in foreign

demand

Changes in foreign (nominal) demand caused by changes in the price of foreign ” This expression equation

(46).

is equal

to the (.

for export goods for domestic export goods (a”) may be goods competing with domestic exports,

) of the second bracketed

expression

in (I - r/n”

- ,+f)(

) in

K. Abayasiri-silva

/ Open-economy

27

mesoeconornics

in aggregate income and aggregate demand of foreign countries, and in other exogenous factors such as geo-political disputes. To isolate the effects of changes in foreign demand for domestic export goods on the level of output and prices in our economy, we set da” = 0, d&’ = 0, dP’= 0, d$” = 0, and dp-‘= 0. Since we do not igCT”Y nore the endogenous changes in ah, ch, and cX, which are reflected in ylahn’, q , ciiiiii , rl C”Y , ,,,(“d’, $‘d, and ,,,l”Y, this cannot be considered as a partial equilibrium vl analysis. arranging

Thus, imposing our restrictions terms, we obtain:

_)f”Y(l nQ‘“‘_

into

equations

-f+_M)]},

(41)-(45)

and

after

re-

(53)

’ _n’{(l-a”“‘_x)[(l_s”rln”Y)(l_~~i’6”_M)

+

()?&”

+ Shtl(.”

Y )( 1 _

11”%“)])

)

(54) (55)

(56) where dY -da”

/lyal=_.

AQ,,a‘ _ dQh

AQta\ _ -

&a’

ax

_

y’ ax

da”

Qh’

dQ”

a”

dc”

Q”’

drrh _=~.da”

uX nh

and

An increase in foreign demand for domestic export goods may have ambiguous effects on the output level of home goods, as shown in equation (53). A rise in the

28

K. Ahuyusrri-silva

/ Open-economy

mesoeconoinics

output share of export goods, as the foreign demand for domestic export goods increases, may result in an increase in total output of the economy if (1 - qcii[ X)(. ) is positive, as indicated in (52). Yet, the increase in Y will have negative effects on the output level of home goods if v“~’ is positive since we have (l@““)>O. On the other hand, an increase positive effects on the (share of the) output aggregate demand for home goods with ($““) is positive, provided (1 - q”““” -M) >

in aggregate output (Y) may generate level of home goods if the elasticity of respect to the aggregate output level 0. In the previous section we discussed the possibility of having a positive sign for the latter term depending on the values of rl<.““” and M. Thus, whether in general an increase in cP has a negative, positive, or neutral effect on the output level of home goods depends on whether $l”(. ) is greater than or less than or equal to qaily(. ). The effect of an increase in foreign demand for domestic exports on the output level of export goods, as shown in equation (54), is positive if (1- v”~’ X)(. )>O. The value of q”““, which shows the degree of responsiveness of the marginal cost of export goods as z-v increases, may be taken as less than unity, since the export sector does not use solely the export goods as inputs. Nevertheless, for the extreme case, even if $““ = 1, the value of (1 -q”‘““ -X) will be positive (negative) iff X is negative (positive). The role of X, the elasticity of marginal revenue of the representative firm with respect to the relative price of foreign goods competing with domestic exports in terms of the price of domestic exports, in determining the output effects on export goods in equation (54) is similar to the role of M in determining output effects on home goods, which we discussed in the previous section. Thus, using the same analysis we could show that since ,$= MR‘=ps(l + l/$‘J“), at a given p.‘, as the absolute demand elasticity (-q”“” ) increases, the marginal revenue of the firm ($) increases and hence the sign of X may be positive or negative if an increase (decrease) in $/n.’ increases (decreases) or decreases (increases) the absolute demand elasticity. Correspondingly, since there is a minus sign before X in (l1.‘n’-X), an increase in foreign demand for domestic exports may increase :d ecrease) the domestic output of exports even though the domestic price of exports increases endogenously (due to secondary cost effects), if the decrease (increase) in p-‘/n-‘ increases (decreases) -$lil-“, since we have a negative (positive) value for X. Moreover, since we may take (1- v(“~~)>O for the general case, in the following analysis it is assumed that (1 - $‘I“ -X)> 0. The two expressions in the square brackets in (54) explain the effect on the output level of export goods that may occur through changes in the output level of the home goods sector as (Y.’increases. Thus, if (1 -shqa”r)> 0, there will be positive effects on the export goods sector, provided (1 - &““-M) is positive. On the other hand (since (1 - ~“““l’) is positive), if ($“‘4”+.s”yl”‘y)>0, a decrease in the output level of home goods reinforces the positive effects that may have on the output level of export goods as (Y-’increases. The aggregate output effects of changes in foreign demand for domestic export

K. Abayasiri-silva

goods are shown of changes that Thus, aggregate of export goods The effect of

/ Open-economy

29

mesoeconomics

in equation (52). This can be viewed as an illustration of the sum may occur in the output levels of the two sectors as (rx increases. output will increase directly through increases in the output level if (1 - q(“” -X)( . ) is positive. changes in K’ on the domestic price level depends on its influence

on the marginal cost curve of the firm. Thus, as c? increases, the price of home as follows. goods will increase if (yl”“‘+ yl”‘q”$“Y) > 0, which may be elaborated First, an increase in the aggregate output level, as the output of export goods increases, may raise the demand for inputs such as labour and place upward pressures on the input prices, and hence shifts the MCC for home goods of the firm. Secondly, an increase in Y may affect the demand for home goods and may generate an increase in the marginal costs of the firm through an increase in the production of home goods. The latter effect on the price of home goods is captured by the term (yl’h’l”yla”Y), while that of former is captured by Y]‘.~’in (55). An increase in (Y* may affect the domestic price of export goods in three ways as shown in equation (56). First, the changes in the slope of the marginal cost curve of export goods affect the domestic price of exports. The two expressions, $“‘!‘( 1 _shqa'Y)(l _$""?M) and y~'.'Q'($"d+ q"'Y)(l -q"'"'), explain the way that the slope of the MCC of export goods may be affected by the changes in the output level of the home goods sector.16 Secondly, if #‘I’>0 the shifts in the marginal cost curve of export goods will increase T[,‘, as shown by the expressions SxIJ”‘Y ( 1 _ $%” -M) and sX~c~y$‘liq’~(l- #@) in (56). Thirdly, as crX increases, if (vChY+ $h9”qa”Y)>0, the increase in the price level of home goods may raise the price level of export goods endogenously if $““’ >O. It is also worth noting here that the last two terms, (qChY+ $nq”@Y), in (56) are equal to the first two terms in (55), which explains the cause of the changes in the price of home goods as ax increases. It can be observed from equations (52) and (55) that the effects on the aggregate output level and the price level of the home goods of a change in cP are not independent of each other. We have already seen that as a” increases, the price of home goods will increase if (&‘+ yl’.“9”&Y ) > 0. Correspondingly, even if this expression (l-&n\

is positive, the price level of home goods ‘may not be affected unless we take -X)>O. Therefore the sufficient condition for an increase in the price of home goods is that both of these terms should have the same sign. On the other hand, as shown in equation (52), the aggregate output level will increase if we take SX(1 _ $‘” -X)> 0, provided that one of the expressions in [( 1- v’.~“’ -M) + ~““~“(1 - &‘““)] is positive. Thus, we may conclude that the price and output effects of a change in c? are not independent in our model.

” The changes

in the output

level of home goods

may occur through

changes

in the elasticity

of ag-

gregate demand for home goods with respect to Y and through changes in the elasticity of the marginal cost of/,home goods with respect to 4” and Y. Thus, we have the same expressions, #‘(I -r/“” -M) and ,,” ‘(, ~ rlCZ”,7” ), in both equations (53) and (56).

30

5. Effects

K. Abayasiri-silva

of exogenous

changes

/ Open-economy

mesoeconomics

in costs

The exogenous changes in cost (dr) may be caused by (instead of changes in T?‘, rrl, and Y) changes in government monetary or fiscal policy, captured by the variable 19, and in other exogenous variables such as trade union militancy and changes in technology, denoted by cc. For simplicity, we assume that the changes in government policy as well as other exogenous factors affect the production costs of home goods and export goods of the firm equi-proportionately, although there are two cost functions for two commodities in our model. Hence we have drh/ch = d?/c’. Moreover, to isolate the effects of changes in exogenous costs from other factors, we set dab = 0, da-‘= 0, dji”‘= 0, and dp”= 0. This corresponds to the mesoequilibrium analysis used in this study and takes into account the endogenous changes through #““, vu”‘, ylahY, $“‘, q(“‘, v”“~“, and 1;1(“q1.Imposing our restrictions into equations (41)-(45) and rearranging, we obtain: /1Y’=

-$i{s'~[(l-~'."~_x)+q';9~(1-rl"~~~)](l-~";i~)

+ $[( 1 _ p

*CJ”?_

;,

_&f)+

p(1

_ $"n")+

f'q(l_

p)S,

(57)

{s.\[rlah’((l_ul’.“~“_M)+ul(.‘~“)

(59)

(60)

(61) where

/+z

‘4

dQ” =~.dc _

Qtc_ dQ” =__.dr

C Q”’ c Q.”

K. Abayasiri-silva

&g

/ Open-economy

mesoeconomics

31

.+,

and /&!$>.

Following

Ng (1982,

1986, ch. 3) to identify

the primary

effects

on the aggregate

output level and the price level of an exogenous change in cost as shown in equations (57), (60), and (61), we ignore the secondary cost and demand effects that will occur aiiKll , rl”‘7P, $“Y, through the influence of v~“‘~, #‘Ini‘, $““, $“‘, rl M, and X by setting their values to zero. Thus, we have Aye= _ [sh(l-~?c.‘iY”)+SX(l--~iql)] (1 _ &4”)( 1 _ $‘Y ‘) Sh s” = - (1 + $‘?“) - (1 + p) /1K”’

(62)

’

1 = (1 + yl(.“y’)’

‘4”“ =

(63)

1 (64)

(1 + yI(“@) . When

sx = 0 (or sh = l), equation /1YC=

(62) is reduced

to

1 (1 + #Jv) .

Thus, equations (62)-(64) show that the primary cost effects on the aggregate output level and the price level (of home goods and export goods) of an exogenous change in marginal cost in our open-economy model are the same as in the closed-economy model of Ng (1982, 1986, ch. 3). This shows that our result is a generalization of the Ng’s proposition 1 on the primary effects of an exogenous increase (decrease) in marginal cost on the level of aggregate output and the price level for an open economy.” Nevertheless, the secondary cost effects, which relate to the endogenous shifts in the MCC as rrh, rcx, and Y change, on the output and the price level are more complicated owing to the interdependency of the two sectors in our model. This can be seen by subtracting equations (62)-(64) from (57), (59), and (60), respectively. However, the final outcome of the total effects (primary and secondary) of exogenous changes in costs on the level of price and output depends on the respon” Proposition 1 of Ng (1982) says that ‘the primary effects of an exogenous increase/decrease in marginal costs are to increase/decrease prices and reduce/expand output by less than/exactly/more than proportionately if MCC (the marginal cost curve of the representative firm) is upward/horizontal/downward sloping’.

32

K. Abayasiri-silva

/ Open-economy

mesoeconomics

siveness of ah and c?, which may occur endogenously, to the changes in rc”, rcb, and Y. Correspondingly, if (l-~‘.‘“‘-X)+(l-~?a”“‘)s”$““‘(l-~a’n‘)>(lsIIqu”Y)(I _q7(“7’ -X) + ss$“(l - v”~“), the aggregate output effects dominate the effects on the price level of home goods and vice versa. On the other hand, if S.\-(1_ &‘_ M)(l _ #“““) +S.VyI’.‘~“(l _ rlU‘7‘) > (1 _ shvlu”Y)(l _ r?““K”_ M) +Sh(yl’.“Y_ $“)(l~“““l’), the effects on aggregate output will be greater than the effects on the price of export goods. The effects of an exogenous change in the marginal costs on the output levels of the home goods sector and the export goods sector are shown in detail in equations (58) and (59).

6. Effects

of changes in the price of imports

To isolate the effects of changes in the price of imports on the aggregate output and the price level of our economy, we ignore the effects of other factors, such as exogenous changes in aggregate demand, in costs, and in the price of foreign goods competing with domestic exports, but take into account the endogenous changes in 0” , in (Y’, and in costs. Thus, we have d&” = 0, do” = 0, dr = 0, and d$‘= 0. By imposing these restrictions on equations (41)-(45), after rearranging the terms we obtain: /1Y@” =$

{s”[rla”““‘(l

+ &ql

AQ”/7”

=$

_ Vm‘“‘)l

{ [rl”“ql

+

_ @“)

(pp

+ &f(l

_s.\.~1(.\~“(~?u”/)i”)?‘.“4”

_ $“““)

+ p$,‘~

_ @“”

Y

)(I

+ M(1

_

_ #“T”

_ ll”““q[(l

_ #‘d

_ &f)(l

_ @K’)},

_ r?“““J”),[(l

_ $‘”

_

;,

+ (1 -&~“Y)$\q(l_

_X)

(66)

{Vd”“J,(s”ll~‘Y(l

_ M[(shVC‘Y

(65)

+S”I;I’.‘~“(yla”P”‘yl’.‘iY

p7‘)]

+M@j(l-@nl)}, /lQ’p”’

_X)

_ ul”‘~‘J)

(1 _ @“7”

+ V?c’n”(~7(.“q”

+ sl~yl’.“Y ),

_ @P”‘) @‘Jq},

(67)

,l”‘~a.“,~([rl.“‘l~‘J(~~“~“+SI’~~”Y)_M(I_S6~.”Y),,(1_9C.I._X)

+Il’.‘q‘(l_~a’n\)l+Sb~(.~Y(~?C”q”yla”p~”_M)(1_~a~~‘)},

&T‘“”

= $

{@q&f’Y

(I _ r7(.V’)

+ )jl(.‘n~‘(Vc”q”

+M[(Shyl’.‘Y(1_yl”“~“__~“P’f’)_(1_Sh~a”Y)yl’.i~‘i’]),

(68) +Sh#J’Y

)]

(69)

K. Abayasiri-silva

/ Open-economy

mesoeconomics

33

where dY ji’” ‘4 Wf’= ~ ._ - djj”’ Y ’

Equation (65) shows that an increase in the price of imports may affect the aggregate output level of an open economy directly through changes in the output level of the home goods sector and indirectly through changes in the output of the export goods sector. The details of these sectorial changes in the output level are shown in equations (66) and (67). Conventionally, as the price of imports increases it is expected to raise the domestic output level” because of the rise in the relative price of imports in terms of home goods and ‘conversion’ of the household’s demand for import goods into home goods. This conventional theory is captured by the term a”P m . our model. Correspondingly, it indicates that the effects of an increase in 17 the price of imports on the output level of home goods depends on the value of the elasticity of aggregate demand for home goods with respect to the price of imports, 0“li”’ vl . The elasticity of aggregate demand for home goods with respect to the price of imports can be regarded as an indicator of the degree of substitutability between home goods and import goods. Thus, if yla”‘j”’= 00, we can deduce that home goods and import goods are perfect substitutes. On the other hand, if rl”l’““=O, they may be regarded as independent (different) goods. However, assuming that home goods are non-inferior to import goods, we treat the value of ylVilD”as positive. Thus, as IS” increases, we can expect a shift to the right in the demand curve for home goods since v~“~” >O. Yet, according to the traditional analysis, a rightward shift in the demand curve may not increase the output level of home goods if However, VCh’(ii=1, but may only increase the price level by the same proportion, our analysis contributes a more comprehensive picture to the traditional analysis by emphasizing the importance of the role of the elasticity of marginal revenue of the

” We assume that import goods and home goods are gross substitutes. Since there are only two goods in our model, they must be net substitutes. Hence, the assumption that home goods are noninferior is sufficient to ensure gross substitutability.

34

K. Abuyasiri-silva

/ Open-economy

mesoeconomics

representative firm with respect to the relative price of imports at a given p’ and rrh (i.e. the value of M), in determining the output level. In Section 3 we showed that the marginal revenue of the firm increases (decreases) at a given p’ as the (absolute) demand elasticity (-qqi’“‘) of the representative firm increases (decreases), and the sign of A4 may be positive (negative) if the increase (decrease) in $‘l/rr/l increases (decreases) the absolute demand elasticity. In other words, the sign of A4 indicates the relationship between the direction of changes in j)“‘/,r 11and _ ,.,&J”. In equations (65)-(67) A4 appears with a plus as well as a minus sign.‘” This indicates that the elasticity of marginal revenue of the representative firm with respect to the relative price of imports could affect the output level of an open economy in two ways, depending on whether M is positive or negative. This can be explained as follows. First, as p”’ increases, the relative price of imports in terms of home goods will increase, and will shift the demand curve for home goods to the right. In this case there will be positive (negative) effects on the output level of home goods if M appears with a plus (minus) sign and an increase in ,Y’/rc’ increases (decreases) the absolute demand elasticity of the firm at a given p”, since we have a positive (negative) sign for M. Secondly, with a given initial increase in p”!, as the demand for home goods and hence the output of home goods increases (through through the primary and seconrl“i”““>O), the rr” may also increase endogenously dary cost effects. The increase in rclr will decrease the relative price of imports in terms of home goods ($“/Tc”) endogenously, and may generate secondary shifts in the demand curve for home goods towards the left. However, even for this case there will be positive (negative) effects on the output level of home goods if M appears with a minus sign in the equation and the decrease in $“/rr” increases (decreases) the absolute demand elasticity of the firm, since we have a negative sign for M indicating a negative relationship between the direction of change in $“/rc’ and the -yl’li”“‘. Correspondingly, in contrast to the traditional analysis, the emphasis on the importance of the role of the elasticity of marginal revenue of the representative firm with respect to the relative price of imports in determining the output level of our model, makes two contributions to the theory of output fluctuations. First, it says that since Y]““~“’is positive, even if the marginal cost of home goods is fully responsive to the endogenous increase in R’, that is #‘i’i[i’= 1, there may still be output effects through the role of M. Secondly, for the extreme case, even if a”P”‘= 0, since the role of M is predominant in equations (65) and (66), the output V level of home goods will be increased as jY’/rc” increases, since (1 - q’l’““) > 0. This latter point has strong implications for the results of the traditional analysis, which is solely based on the non-zero value of @@“. ” It should

be noted that whether

A4 will be positive

or negative

the direction of changes in p”‘/zh and the Pv qhnh. This should sign that appears before M in equations (65)-(69).

depends

on the relationship

not be confused

between

with the plus or minus

K. Abayasiri-silva

/ Open-economy

35

mesoeconomics

The expansionary effects on the aggregate output level that may occur owing to increases in the output level of home goods may be offset by the decrease in the output level of export goods if r~“‘~ >O, as indicated by the negative sign of the second expression in equation (65). On the other hand, the negative sign for the output equation of export goods (equation (67)), indicates that the output of export goods will fall as p”’ increases if q”‘(. ) and u”“~(. ) are positive, since we have (1 - qa‘“‘) > 0. This confirms the correctness of the negative sign of the second expression in (65). It is interesting to note here that, except for the additional term (1 - qaiA’), all the terms in the output equation of export goods (equation (67)), are equal to the price equation of export goods (equation (69)). This reveals that the effect of an exogenous increase in the price of imports on the output of the export goods sector and on the price level of export goods is determined by the same set of conditions. As shown in equation (69), the effects of an increase in the price of imports on the domestic price level of export goods depend on the elasticity of the marginal cost of export goods with respect to the aggregate output and the price level of home goods. Thus, if QJ’~(. ) >O and (or) $‘I”’ (. ) > 0, the price of export goods will increase. The expressions in the two square brackets in (69) intuitively explain that, since ~~“3” >O and (or) if M>O, the increase in the output level of home goods may shift the MCC of export goods and increases the p”( = xx) if $“’ and q“lni’ are positive. Equation (68) shows the effects on the price level of home goods of an increase in the price of imports. Accordingly, the price level of home goods may increase if the elasticity of the marginal cost of home goods with respect to the output of home goods ($‘4”) and the aggregate output ($‘l”) and (or) the elasticity of domestic aggregate demand for home goods with respect to the aggregate output level (v~“~) are positive. It can be observed that the two expressions in the first square bracket in the aggregate output equation, (65), i.e. [qahD”‘(l-II’“““) +M(l - qahkh - $‘hp’“)], appear in the price equation of export goods (equation (69)). Similarly, the two expressions in the second square bracket in (63, (1 - qclzi‘ -X) + &4‘(1 - qaliI’), are included in the price equation of home goods (equation (68)). This shows that the output effects and the price effects of an increase in the price of imports are not independent. On the one hand, this may be due to the interdependency between the two sectors of our economy. On the other hand, an increase in the price of imports may not necessarily lead to an increase in the aggregate output level, since the expansionary effects that may occur through the increase in the output level of home goods may be offset by the contractionary effects that may emerge through the decrease in the output of export goods.

7. Effects of changes in the price of foreign goods competing To isolate

the effects

of changes

in the price of foreign

with domestic exports goods

competing

with

36

K. Abayasiri-silva

/ Open-economy

mesoeconomics

domestic exports on domestic output and the price level, we set dab, da”, dCh, and dp”’ equal to zero and obtain, after rearranging the terms:

x [( 1 - qChXh-M) /~Q”P’+

+ f?@( 1 - $“““)I},

(70)

{s.~[rla’~‘(l_yl”‘~‘)+~(l__yl”‘~“__~’p’)l [#‘Y

x

(1

ulM

_

_M)-)?(.“y(l-yla’~~‘~)J),

(71)

(72)

(73)

/,@D’+ + +

((~n'P'yl'.'q'_X)[(~c"q"+Shyl"'Y)(l_yla"n") (1

&

_

Y

)p”

_

((

p

1 _

_shva"Y

j/f)(l

-

M)

+

)]

vw’(

+S"~a'P'[YI"Kli(l;l'.'iY 1 -

f”““))]}

)

+

fyy"Y) (74)

where /1YP=

dY*” dP\’

AQ,ap,

=

dQh

Y’

P”

-S’Qh9

AQ',y' = dQX _-.-

W

P” Q"

’

An increase in the price of foreign goods competing with domestic exports directly affects the domestic output Ievel of our economy through the decrease in the relative price level of domestic exports and hence increase the foreign demand for domestic export goods. These direct effects are captured by the expressions a”‘“‘(. ) and X(. ) in equation (70). On the other hand, the indirect effects of an increase in p”

K. Abayasiri-silva

/ Open-econ0m.y

mesoeconomics

37

on the aggregate output level may occur through changes in the output level of home goods. The two expressions in the second square bracket [(l - vchni’-M) + ~l“~~~(l- v”~“~)] in (70), show the effect of changes in the output level of home goods on the aggregate output level. The details of these sectorial changes in the output levels are given in equations (71) and (72). The elasticity of foreign demand for domestic export goods with respect to the price of foreign goods competing with domestic exports (q”‘“‘) in our model tells us the well-known traditional theory. Accordingly, since $‘“‘ can be taken as positive, an increase in the domestic output of export goods is expected as the price of foreign goods competing with domestic exports increases, provided (lin addition to this traditional theory our analysis emP‘) > 0.20 Nevertheless, phasizes the importance of the role of the elasticity of marginal revenue of the representative firm with respect to the relative price of foreign goods competing with domestic exports in terms of domestic export goods (X) in determining the output effects. Thus, an increase in the price of foreign goods competing with domestic exports may affect the aggregate domestic output level in two ways, even if (for the extreme case) (1 - qcl“) = 0 and qn‘“‘ = 0, since a plus sign appears before X in equations (70)-(72). First, X may have positive (negative) effects on the output level of domestic export goods since the increase in p” increases p-‘/zry and increases (decreases) the absolute demand elasticity (-v~‘~’ ) of the firm. Secondly, X may have negative (positive) effects on the output level of domestic export goods since the output level of domestic export goods increases the endogenous increase in the domestic price level of export goods through the secondary cost effects, and will decrease px/zcy and lower (raise) -@‘p‘ of the representative firm. For the former case, X is positive, and in the latter case, X is negative in equations (70)-(72). Thus, the emphasis on X in evaluating the performance of our economy in response to changes in the price of foreign goods competing with domestic exports is similar to the role of M which we highlighted in the analysis of the effects of changes in price of imports in the previous section. Yet it is not repetitive to note here that our non-traditional results, which show the possibility of having output effects even if $‘“‘= 0, have strong implications for the traditional theory, the sole analysis of which is based on the non-zero value of ylaip’. The changes in the price of foreign goods competing with domestic exports (p”) may affect the domestic price of home goods through the primary and secondary cost effects on the home goods sector, as a result of changes in the aggregate output level. Equation (73) shows very clearly the cause and effect of changes in the slope of, and the shifts in, the MCC of home goods. The expression (~~~~“q~“~+ ylci”) in (73) refers to the primary and secondary cost effects on the price level of home goods, while the second expression [$‘“‘( 1 - QJ““) +X( 1 - qa“‘ - ~“o’)] explains the causes of these cost effects, which may be explained as follows. An increase in I0 In our economy taken

since the export

sector is not using export

as less than unity and hence we have (I - $ ‘“‘)>O.

goods as its sole inputs,

rf’“’

should

be

38

K. Abayasiri-silva

the price of foreign

goods competing

/ Open-economy

with domestic

mesoecononiics

exports will raise the foreign

de-

mand for domestic exports, and hence the output of export goods, if qaVP’>O and (or) X>O. If the economy is not at full employment, the increase in the output of export goods will raise the aggregate output level (Y). As Y increases, the demand for home goods, and hence the output level of home goods, will increase if quit’ is positive. The primary cost effects of these incidences are captured by the term ($l’q”$“Y) in (73). On the other hand, the increase in the aggregate output level will induce firms to raise their bids for input prices such as wages, and hence generate secondary cost effects on the price level of home goods if qciiy is positive. Thus, an increase in the price of foreign goods competing with domestic exports may have positive (negative or zero) effects on the price level of home goods if @/(.“y”&‘)l+ #“Y ) is positive (negative or zero). The effects on the domestic price of export goods of an increase in a” are captured by three expressions (~“‘“‘v]“‘~‘)(. ), (f‘D‘#“y)(. ), and (v?“‘~‘$““)(. ) in equation (74). The first expression explains the effect on the price of domestic exports of changes in the slope of the MCC of export goods that may occur through changes in the output level of home goods. It should be noted here that the bracketed expression of q”‘“‘@‘(. ), i.e. ~‘~“(1 - v”‘~” -M) + $““( 1 - u”“““), which appears in the output equation for home goods (equation (71)), elaborates the changes that may occur in the output level of home goods. The second expression, (q”‘“‘$“)(. ), indicates that the price level of the domestic exports may increase through shifts in t,he MCC of export goods as Y increases. Thus, the bracketed expressions of qa‘” q”‘( . ), i.e. (1 - $b”h -M) + v“*~~(1 - q”“““), rationalizes the increase in Y through changes in Qh. Finally, the last expression shows the potential effects on 7cXthrough the endogenous shift in the MCC of export goods as the price level of home goods increases. If these three expressions are positive, the domestic price of export goods will increase through the primary and secondary cost effects on the export goods sector until the new equilibrium price is reached at a point where px = xx =px.

8. Summary

of the results

In this paper we develop an open-economy mesoeconomic model, based on the work of Ng (1982, 1986, ch. 3), analysing the effects of exogenous changes in aggregate demand, in costs, in the price of imports, and in the price of foreign goods competing with domestic exports, on aggregate output and the general price level of an open economy having a fixed exchange rate regime. Despite the rather complicated analysis, the major contribution of the paper can be summarized in the following propositions. Proposition 1. An exogenous increase (decrease) in the domestic aggregate demand for home goods (ah) will have (a) direct positive (negative) effects on the output

K. Abayasiri-silva

/ Open-economy

mesoeconomics

39

level of home goods, in contrast to the traditional analysis, even if the marginal cost of home goods is fully responsive to the endogenous increase (decrease) in the price = I), provided the elasticity of marginal revenue of level of home goods (i.e. nCiiKit the representative firm with respect to the relative price of imports, at a given p”( = zh), i.e. M, is positive (negative); (b) indirect negative (positive) effects on the output level of export goods if the marginal cost of export goods is positively (negatively) responsive to the endogenous increase in the price of home goods and the level of aggregate output, i.e. n (.‘# >0 and n“‘Y>O; and (c) net positive (negative) effects on the aggregate output level if the expansionary (contractionary) effects on the output level of home goods is greater than the contractionary (expansionary) effects on the output level of export goods. Proposition 2. An increase in the price of imports will have positive (negative) effects on the aggregate domestic output level through the increase (decrease) in the output level of home goods as follows. (a) Traditional effect: if the elasticity of aggregate demand for home goods with respect to the price of imports is positive >O), as in the traditional analysis, provided the marginal cost of home (n?a”p”’ goods is less responsive to the endogenous increase in the price level of home goods (i.e. n(“‘“” < 1). (b) Non-traditional effect: even if the marginal cost of home goods is fully responsive to the endogenous increase in zh, provided the elasticity of marginal revenue of the representative firm with respect to the relative price of imports (M) is positive (negative). (c) Ultra non-traditional effect: for the extreme case, even if the responsiveness of domestic aggregate demand for home goods to the increase in the price of imports is zero (Y]““~” = 0), provided M is positive (negative). The new equilibrium level of aggregate domestic output will be higher (lower) than the initial output level or remain unchanged if the decrease (increase) in the output level of export goods is less (more) than or equal to the proportional increase in the output level of home goods, depending on the degree of responsiveness of the marginal cost of export goods to the endogenous increase in the price level of home goods, and to the initial increase in the aggregate output level (i.e. rl‘.‘““>O and (or) rf‘yzO). Proposition 3. An increase (decrease) in the price of foreign goods competing with domestic exports will have positive (negative) effects on the aggregate domestic output level through the increase (decrease) in the output level of export goods as in the case of increase in the price of imports mentioned in Proposition 2. Proposition

4. The price effects and the aggregate output effects of an exogenous

increase (decrease) in the domestic aggregate demand for home goods, in the price of imports, and in the price of foreign goods competing with domestic exports, are not independent of each other. An exogenous increase (decrease) in the domestic aggregate demand for home goods, and in the price of imports will have (a> positive (negative) effects on the average price level of home goods if the marginal cost of

40

K. Abayasiri-silva

/ Open-economy

mesoeconomies

home goods is positively (negatively) responsive to its own output and the aggregate output level of the economy (ylChqii •t shylChy>O); (b) positive (negative) effects on the average price level of export goods if the marginal cost of export goods is positively (negatively) responsive to the aggregate output and the (endogenous) increase in the price of home goods (v?“‘“” + q“” > 0). The larger the positive responsiveness of the marginal cost of export goods to the increase in the price of home goods, and in the aggregate output, the higher will be the price level and the lower will be the output level of the export goods sector, and the higher will be the degree of interdependency between the price effects (on export goods) and the effects on aggregate domestic output. The interdependency between the price effects and the aggregate output effects of an increase in the price of foreign goods competing with domestic exports will emerge through increases in the price level and decreases in the output level of home goods if the marginal cost of home goods is positively responsive to the changes in the level of aggregate output.

Appendix

Writing

(marginal

revenue),

we may derive and define &J+“/a

lpi?, X/q -3.

!$

lp’T,7[q

(A.11 i.e. price of imports where @z=$“/z~, Similarly, for export goods we have

in terms of home goods.

K. Abqvasiri-silva / Open-economy mesoeconomics

41

(A.21 where R=pX/7rX, i.e. price of foreign goods competing with domestic exports in terms of domestic export goods. Dividing (29) and (30) by $‘=,IJ’ and c’=,u’ (marginal cost is equal to the marginal revenue, which is the equilibrium condition) and substituting

from (A.l)

from

and

(A.2) we have equations

Acknowledgments I am indebted

(31) and (32) in the text.

42

K. Ahayasiri-silva

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