Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
The Effect of Currency Devaluation and the Labor
Market with Monopolistic Competition
Hong-Yu Lin
The contractionary effect of currency devaluation has been
investigated in different directions. This paper examines the effect
of currency devaluation under the labor market with monopolistic
competition. A model is developed to provide an explanation for the
empirical findings of contractionary devaluation. The result shows
that currency devaluation leads to a contractionary effect on the
domestic output when the labor market with monopolistic
competition is introduced into the open economy model.
Keywords: currency devaluation; monopolistic competition; contractionary
effect
JEL classification: F41
I. Introduction
The expansionary effect of the currency devaluation on the domestic
output is first concluded by Meade (1951), Tsiang (1961), and Takayama
(1969). However, Cooper (1971, 1973), Solimano (1986), Edwards (1986),
Kamin and Rogers (2000), and Chou and Chao (2001) use empirical studies
and find that the devaluation has contractionary effect on the domestic output.
Therefore, lots of efforts are devoted in finding a new theory to support this
phenomenon. For example, Krugman and Taylor (1978), Hanson (1983), van
Wijnbergen (1986), Findlay and Rodriguez (1977), Buffie (1989), Taylor (1981),
Lai (1990), and Lai et. al (1996).1 Although many researches have examined
the empirical findings of contractionary devaluation, the market structure of
monopolistic competition has never been considered as this research is still in
its beginning stages.
_________________
Hong-Yu Lin, Department of Business Management, Ming Chi University of
Technology, Taiwan. Email: hylin@mail.mcut.edu.tw
1
Lizondo and Montiel (1989) provide a detailed overview.
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Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
The market structure with monopolistic competition was first
demonstrated as a mathematical model by Dixit and Stiglitz (1977). Their
model has been applied to examine different issues in macroeconomics. For
example, Kiyotaki (1985), Weitzman (1985), Blanchard and Kiyotaki (1987),
Startz (1989), Obstfeld and Rogoff (1995, 1996), Heijdra and van der Ploeg
(1996), Hau (2000), Bacchetta and van Wincoop (2000), and Benigno (2002).2
Nevertheless, none of these literatures have evaluated the influence of
currency devaluation on the domestic output under monopolistic competition.
Therefore, this paper considers the labor market with monopolistic competition
in the standard open economy model using the innovation of Blanchard and
Kiyotaki (1987) and Obstfeld and Rogoff (1996) to explain the contractionary
effect of currency devaluation.
This paper is divided into four sections. Section I is designated as
introduction, and the model in Section II will explain explicitly the aggregate
supply function of labor market with monopolistic competition. Section III will
investigate the effect of currency devaluation on domestic output while the
conclusion will be presented in Section IV.
II. The Model
We assume that this country is a small open economy with fixed
exchange rates. Domestic production is limited to a single final composite
commodity. The produced products will gratify the domestic and exported
demand. Both kinds of domestic and imported products are imperfect
substitutes and are consumed by the domestic consumers. The model is
demonstrated as followed.
(1)
Y  C(Y )  I (r )  G  T (q, Y )
L(Y , r )  M P
T (q, Y )  K (r )  F
(2)
(3)
Y  S ( P, E, P * )
(4)
where, Y: domestic output; C: consumption expenditure; I :investment
expenditure; r: domestic interest rate; G: government expenditure; T: balance
of trade; q  EP * P : terms of trade; E: exchange rate ( defined as domestic
2
To use it in closed economy is the important foundation of the New Keynesian Economics.
Introducing monopolistic competition into open economy is called the new open economy
macroeconomics.
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Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
currency price of foreign currency ); P * : foreign currency price of imports; P:
domestic currency price of domestic output; L: real money demand; M:
nominal money supply ; K: net capital inflow; F: balance of payments; r * :
foreign interest rate; S: aggregate supply function. According to the common
macroeconomics, the variables should be limited as followed. 0  CY  1 ,
I r  0 , Tq  0 3, TY  0 , LY  0 , Lr  0 , K i  0 .
Equation (1) represents the equilibrium condition of the commodity market
while equation (2) represents the equilibrium condition of the money market.
We assume that any balance-of-payments surplus or deficit will not feed into
the nominal money supply because of full sterilization. Equation (3) states that
the overall balance of payments is the sum of the current and capital accounts.
Equation (4) is the aggregate supply function of the labor market with
monopolistic competition and will be discussed further in this section.
To derive equation (4), we assume that the single final composite
commodity is supplied competitively. However, the representative firm must
employ different types of labor N ( j ) , where j  [0,1] . According to the
linear-homogeneous CES production function
1
Y  [ N ( j)
0
 1

dj ]

 1
,
(5)
where   1, each agent j in the economy is a monopoly supplier of N ( j )
and his market power is considered as deciding the amount of labor to supply. 4
In addition, we define w as the nominal wage index, and the pattern is,
1
1
w  [  w( j )1 dj ]1
0
Therefore, the decision behavior of the representative firm is to maximize
the profit within the limitation of equation (5) under the discussed conditions.
The objection function can be formulated as
1
max PY   w( j ) N ( j )dj
0
and the optimal condition is
N ( j)  (
w( j ) 
) N,
w
(6)
where N is the aggregate labor demand of the representative firm. Equation (6)
3
Tq  0 denotes that Marshall-Lerner condition is valid.
4
It also might think of each worker as the representative of a monopolistic union.
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Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
shows that the representative firm faces the downward-sloping labor demand
curves.
Besides, we adapt the concept from Blanchard and Kiyotaki (1987) and
assume the utility function of each labor as
w( j )
(
) N ( j)  N ( j)  ,
  1,
g
where  denotes the constant marginal utility of real wealth. Since the labors
consume both domestic and imported products, we use the general price index,
g  EP *  (1   ) P , to define the real wage. Note that  represents the
fraction of expenditure spent on imports and   1 denotes the elasticity of
marginal disutility of labor.
Hence, under the limitation of equation (6), the utility maximization for the
labors can be demonstrated as5
w( j ) 


gN ( j )  1
 1 
(7)
Equation (7) implies that the real wage equals “the mark-up”(  [ (  1)] )
times marginal disutility.
To derive the market equilibrium of the labor market, we focus on the
symmetric equilibrium. Symmetry implies that all labors ask for the same wage
and the representative firm will hire each type of labor in equal quantities.
The demand for the labor is consistent with the product level. Because of
the symmetric inputs, the representative firm‟s production function becomes a
simple linear form,
(8)
YN
Since the representative firm acts competitively, workers must be paid of their
marginal products. Therefore,
(9)
wP
If we apply the symmetric condition and equation (9) into equation (7), we can
develop the aggregate labor supply as
  1  P  1
N (
)
  g
1
(10)
Then, the labor market equilibrium condition can be derived using equations (8)
and (10). The developed labor market equilibrium condition is shown as
5
We make the usual “large numbers”assumption that each labor regards the wages of other labors
and aggregate labor demand as exogenous with respect to its own actions.
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Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
equation (11).
  1  P  1
Y (
)
  g
1
(11)
To simplify the notation, P  P*  E  1 is assumed to be the initial
condition through the whole paper. Then, totally differentiating equation (11)
yields
dY 

 1
1 
[(1  ) ]  1 (dP  dE  dP  ) .
1
(12)
 
Equation (12) demonstrates clearly that a devaluation of the domestic currency
or an increase in foreign prices will depress the domestic output while an
increase in the domestic price will enhance the domestic output. Moreover,
Figure 1 demonstrates the mathematical results of equation (12) with the
presence of equations (8) – (10).
P
w=P
AS’
AS
w
Y
labor supply function
Y=N
N
Figure 1
In Figure 1, the interspace between Y and N describes the production
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Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
function (equation (8)). The interspace between w and N describes the labor
supply function (equation (10)) and the interspace between w and P describes
the zero-profit condition, equation (9). We can obtain the labor market
equilibrium locus in the interspace between P and Y using these three graphs
above. We present the labor market equilibrium locus using the AS curve, and
find that the domestic product price and output share a positive relationship.
Also, when domestic currency devaluates because of the deflated real wage
and fixed“the mark-up”, the labor supply curve shifts leftward. This result
means that the AS curve shift leftward to the AS‟ curve and domestic output
decreases. The same analysis is also suitable for P * and will not be discussed
further in this paper. Furthermore, if the labor market tends towards perfect
competition (    ), both E and P  have greater effect on Y than the E and
P  of the labor market with monopolistic competition ( 0     ). This
phenomenon indicates that changing E or P  will result in larger shifting
distant (rightward or leftward) for the AS curve when the labor market tending
towards perfect competition than the labor market with monopolistic
competition.
Equation (12) can also be demonstrated as a function.
(4)
Y  S ( P, E, P * )
S P   S E   S P* 

 1
1 
[(1  ) ]  1  0
1
 
The discussion in this section concludes that equation (4) is the aggregate
supply function of the labor market with monopolistic competition.
III. The Effect of Devaluation
Under fixed exchange rates, equations (1)-(4) can be simultaneously
solved to determine Y, r, P, and F. Totally differentiating equations (1)-(4) and
using Cramer‟s rule, we can the derive equation (13).
Ir M
Y

0
E  [(1  CY  TY ) Lr  I r LY ]  (Tq Lr  I r M ) S E
(13)
Equation (13) obviously shows that currency devaluation will definitely
depress the domestic output when the labor market with monopolistic
competition is considered.6 To show the effect of currency devaluation onto a
6
From equation (13), we can find that currency devaluation will depress the domestic output if the
labor market tends toward perfect competition ( 
  ).
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Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
diagram, equations (14) and (15) must be developed.
Equation (14) represents the P and Y combinations that gratify
equilibriums of both goods market and money market. Furthermore, equation
(14) is obtained by totally differentiating the equations (1) and (2), and
combining these two equations with the replacement of r. Note that the
replacement of r is achieved using the differentiated equations (1) and (2).
[(1  CY  TY ) Lr  I r LY ]dY  [ I r M  Tq Lr ]dP 
Lr dG  I r dM  Tq Lr (dE  dP  )
(14)
The locus formed by P and Y combinations is the aggregate demand
curve and will be represented as AD curve. From the equation (14), we know
that the slope of the AD curve is
 [(1  CY  TY ) Lr  I r LY ]
P

 0.
Y AD
I r M  Tq Lr
From equation (4), the locus for the equilibrium of labor market formed by
P and Y combinations can be achieved and is represented as the AS curve.
P
1
The slope of the locus is
(15)

0
Y AS S P
We draw the AD and AS curves on Figure 2 and assume that the
economic system is on the position Q0 at the beginning stage and the
reflected domestic price and domestic output are P0 and Y0 , respectively.
P
AS’
AS
P1
Q1
P0
Q0
AD’
AD
0
Y1 Y0
Figure 2
6
Y
Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
Figure 2 shows that the AD and AS curves shift upward when the currency
devaluates. The upwards shifting distant of the AS curve is larger than the AD
curve.7 This observation implies that the domestic output decreases and
domestic price rises when economic system reaches the new equilibrium
point Q1 . Moreover, this result indicates that currency devaluation definitely
results in stagflation.
The analysis of the equation (13) shows that the currency change has
more significant effect on the domestic output when labor market tends toward
perfect competition (    ) than the labor market with monopolistic
competition ( 0     ). This conclusion shows that when labor market
tends toward perfect competition, the leftward shifting distant of the AS curve
causing by currency devaluation is larger than that under labor market with
monopolistic competition. Therefore, when labor market tends toward perfect
competition, the contractionary effect of devaluation is more drastic than that
under labor market with monopolistic competition.8
IV. Conclusion
Using a standard open economy model, this paper examines the effect of
currency devaluation by considering the labor market with monopolistic
competition. It shows that currency devaluation will definitely depress the
domestic output. This conclusion provides an explanation for the empirical
findings of contractionary devaluation.
In addition, we also compare the effect of currency devaluation on the
domestic output under different market structures. The results show that when
labor market tends toward perfect competition, the contractionary effect of
currency devaluation on the domestic output is more drastic than that under
the labor market with monopolistic competition.
7
From the equation (4), we know:
know: 0 
8
P
E

AD
P
E
Tq L r
I r M  Tq L r
 1 ; from the equation (14), we
AS
 1.
From equations (4) and (15), we can find that the AS curve is flatter if σis larger. Therefore, when
domestic currency devaluates, the upward shifting distance for the AS curve is the same. However,
from the aspect of Y / E , the more flatter AS curve, the more negative effect will be on domestic
output.
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Proceedings of Global Business and Finance Research Conference
5-6 May, 2014, Marriott Hotel, Melbourne, Australia, ISBN: 978-1-922069-50-4
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