DBJ Discussion Paper Series, No.1103

The employment-isolation effect under a flexible exchange rate

Masayuki Otaki(Institute of Social Science, University of Tokyo)

December

2011

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings,
conclusions or recommendations expressed in these papers are those of the authors and do
not reflect the views of the Institute.

The employment-isolation eﬀect under a ﬂexible exchange rate

Masayuki Otaki
Institute of Social Science, University of Tokyo
Email: ohtaki@iss.u-tokyo.ac.jp
Abstract
This article considers the international diﬀusion of business cycle on the basisof a rigorous dynamic microeconomic foundation. The seminal work of Laursenand Metzler (1950) suggests that the employment-isolation eﬀect under the
ﬂexible exchange rate system is imperfect even if international capital mobility
is completely prohibited.
Assuming a small country model instead of the two country model by Laursenand Metzler (1950), we obtain the following results: (i) The business ﬂuctuationof the world economy diﬀuses to the small country through a change in the inﬂation rate resulting from the change in the real exchange rate. In this sense, theemployment isolation is imperfect. (ii) Domestic monetary expansion does notnecessarily improve the employment level. This is because the depreciation of
the real exchange rate (worsened terms of trade) should always be compensatedby the lowered inﬂation rate and thus reduces the consumption demand.
Keywords: Employment-Isolation Eﬀect, Laursen-Metzler Eﬀect, An
Open Macroeconomic Model with Analytical and Dynamic Microeconomic Foundation.
JEL Classﬁcations: F20, F41, E12, E24, E32.

1Introduction

The international transmission of business cycle is a serious problem under the
ﬂexible exchange rate system. We analytically (without using the numericalmethod adopted, for example, by Obstfeld and Rogoﬀ (1996)) consider thisproblem on the basis of an overlapping-generations model (OLG model) witha rigorous dynamic microeconomic foundation developed by Otaki (2007, 2009,2011a).
Generally, in two-period OLG models with no bequest motive, the balanceof trade must always equilibrate. This is because the supply of the foreign
currency by the old individuals in the home country should always be equal tothe demand for the domestic currency by the young individuals in the rest of
the world. That is, capital movement is substantially impossible because thediﬃculty of double coincidence of wants. This is a persuasive property of thelong-run structure of the foreign exchange market of a small open country thatcannot enjoy international seigniorage.1
The two-country model developed by Laursen and Metzler (1950) is a seminal work on the international diﬀusion of business cycle, which also assumes
that international capital movement is prohibited. Although their model is notbased on a neoclassical microeconomic foundation, it still has important implications. In particular, the model emphasizes the eﬀect of the terms of trade(the inverse of the real exchange rate) on the domestic consumption resulting
from the change in the ﬁscal expenditure.
Nevertheless, because of the lack of a microeconomic foundation, the obtained result is ambiguous and crucially depends on unknowable parameters.
Hence we resolve this problem by using some new methods. The most important factor in our theory is the manner in which the terms of trade aﬀects thereal reservation wage and the domestic inﬂation rate.
Whenever the real exchange rate appreciates by an exogenous increase inexport that is accompanied by the worldwide economic expansion, it is in favorof employees because it lessens the cost of living. However, as long as thedomestic economy is in imperfect unemployment equilibrium and employees
have no wage bargaining power, the current nominal (reservation) wages are
cut down and the price level falls down.
Nevertheless, if the purchasing power of money (the inverse of the future
price level) is kept constant (Otaki (2011a) deﬁnes such a situation as money iscredible), it implies that the equilibrium inﬂation is accelerated because the fu1 For the analysis concerning the key-currency country, see Otaki (2011b).

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ture good becomes more expensive compared to the current good. Thus, futurenominal wages simultaneously grow more rapidly. This movement of nominal
wages is consistent with that of the price level dominated by its marginal costs.
The accelerated inﬂation stimulates the consumption of the current goods
under some plausible assumption concerning the utility function, thereby increasing the employment. Consequently, the foreign business cycle diﬀuses thedomestic economy through the change of consumption caused by the terms oftrade eﬀect (i.e., the Laursen-Metzler eﬀect).
The important economic factor that our model has is money, which is notin Laursen and Metzler (1950). We can analyze how the domestic monetary
expansion aﬀects the economic activity in that country. A monetary expansion
brings about two eﬀects in the domestic economy. One is a direct eﬀect that
stimulates the economy through the multiplier eﬀect induced by Otaki (2007,2009).
The other is an indirect one that aﬀects the economy through the change
in the real exchange rate. A monetary expansion depreciates the real exchange
rate. This raises the current nominal wages because the depreciation is disadvantageous for employees. Hence the current price level also increases. However,if the purchasing power of money is kept constant (if money is credible), this also
lowers the equilibrium inﬂation rate and the increment of nominal wages. Thatis, the depreciation of the real exchange rate causes disinﬂation and reduces theconsumption demand.
Thus, the indirect eﬀect conversely reduces the economic activity. Accordingly, the power of monetary policy is weakened under the ﬂexible exchange
rate. This result contrasts that of the Mundell (1963)-Fleming (1962) model.
The remainder of this paper is organized as follows: In Section 2, the basic model is constructed. Section 3 deals with comparative statics. Section 4contains brief concluding remarks.

2

The Model

2.1

The Structure of the Model

We consider a small open economy assuming that (i) the economy behaves
as if the international price of the foreign good is exogenously given, and (ii)the world inﬂation rate is not aﬀected by domestic aﬀairs such as a change inmonetary policy.
This economy specializes in single good production (good a). Since numerous
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ﬁrms produces goods, the market is under perfect competition. In addition,
there is the other good produced in foreign countries (good b). The economy
imports good b as a price taker. Furthermore, both goods are perishable.
At the beginning of each period, individuals are born with Lebesgue measure
1, and live in two periods. They can supply unit labor at their discretion only
when they are young. Unit labor produces unit good a.
There are two currency a (the domestic currency) and b (the world currency).
Exchanging the same type of currency is required for purchasing some type ofgood. Although it is not an unavoidable assumption, for simplicity, we assume
that the trade between young generations can be done by barter. The balanceof payment of this small economy B becomesB ≡ pa [E1a + E2a ] − πpb [M1b + M2b ],(1)where pa is the domestic price of good a. π and pb denote the nominal exchange
rate and the international price of good b respectively. Eia is the volume ofexport toward foreign i-th generation (i = 1(young), 2(old)). Mib is the volumeof i th generation’s import.
Since the loan within the same generation is infeasible, pa E1a = πpb M1b holds.
Thus, Equation (1) is transformed intoB ≡ pa E2a − πpb M2b .

(2)That is, the balance of payment is equal to the diﬀerence between the sumof the supply of currency b from the old generation in a foreign country andthe demand for the same currency of the young generation in this economy
preparing for his/her retirement. Since the latter generation can never tradehereafter, Equation (2) takes value zero.

2.2

Optimization Problem of Each Economic Agent

2.2.1

Individuals

Each individual has an identical utility function U :U ≡ u(c1 , c2 ) − δα,ci ≡ [ai ]β [bi ]1−β ,0 < β < 1.

(3)

ci is the aggregate consumption level during i th stage of life. ai and bi are theconsumption level of good a and b respectively. α denotes the disutility of labor.
δ is a deﬁnition function that takes value unity when employed and zero whenunemployed. u( · ) is a well behaved homothetic utility function concerning
consumption stream.
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Elementary calculation leads us to the corresponding expenditure functionΦ:()Φ ≡ ϕ [pa1 ]β [π1 pb1 ]1−β , [pa2 ]β [π2 pb2 ]1−β f (u),(4)

where u is a utility level. Since ϕ is a linear homogenous function, we cantransform (4) into()
Φ = pa1 ϕ e1−β, ρa · e2 1−β f (u) = pa1 [e∗ ]1−β ϕ(1, ρa )f (u),1(5)

where ρa is the equilibrium inﬂation rate. e∗ is the stationary equilibrium realexchange rate, where stationary means that the ﬂuctuation of the real exchange
rate e is converged, and hence e1 = e2 holds.
From Equations (3) and (5), we can obtain the nominal reservation wageWRas
W R = pa1 [e∗ ]1−β ϕ(1, ρa )f (α).

(6)

The equilibrium nominal wage is equal to W R as long as the economy is fallen
into underemployment equilibrium. It is the market clearing condition for thelabor market.
2.2.2

Firms

Since all ﬁrms are assumed to be price takers with the linear production function
and a unit productivity, the zero proﬁt condition corresponds to the solution of
the maximization problem. Thus, we obtain
pa1 = W R⇒

1 = [e∗ ]1−β ϕ(1, ρa )f (α).

(7)

Since ϕ is an increasing function of ρa , Equation (7) clearly shows that theinﬂation is accelerated whenever the real exchange rate e∗ appreciates.
2.2.3

The Government

In accordance with Otaki (2007, 2009, 2011a), the government keeps the realMicash mi ≡ a constant through time once it decides the initial value m1 . Hencepi
the budget constraint of the government becomesg = (1 −

1
)m1 ,
ρa

where g is the wasteful real government expenditure.

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(8)

2.3

Market Equilibrium

Our model contains four markets: the domestic good market; labor market,
domestic money market, and foreign exchange market. By Walras’ law, we
abbreviate the equilibrium condition for the domestic money market. The labormarket is in interior equilibrium iﬀ Equation (6) holds.
The foreign exchange market is cleared iﬀ B in Equation (2) is equal to zero.
Again, elementary calculation leads us toE2a = β[1 − cb (ρb )]e∗ y b ,e∗ M2b = [1 − β][1 − ca (ρa )]y a ,where cj (j = a, b) is the marginal propensity to consume of each economy. bj
is the real GDP in terms of each economy’s good. Accordingly, we obtain thefollowing equation as the equilibrium condition for the foreign exchange market:
β[1 − cb (ρb )]e∗ y b = [1 − β][1 − ca (ρa )]y a .

(9)Taking Equation (9) into consideration, the domestic good market is in equilibrium wheny a = ca (ρa )y a + m1

(10)

holds. ca (ρa ) is the marginal propensity to consume of the economy.
In sum, we have three endogenous variables: (y a , ρa , e∗ ). These variables
are determined by Equations (7), (9), and (10). Thus, the model is completely
closed.

3Comparative Statics

3.1

The Diﬀusion of the World Economy’s Business Cycle

We consider the eﬀect of the world economy’s business cycle on the domestic
economy. The rigorous discussion is extended in the Mathematical Appendix.
Assume that the world economy is upturned and y b increases. It directly stimulates the export and results in the appreciation of the real exchange rate e∗ .
This is in favor of employees because the import price is lowered. However, in
the imperfect employment equilibrium, where some employees are unemployed,
there is a room for ﬁrms to cut down the nominal wage, and thus the price ofthe current domestic good pa1 is also lowered.
As long as money is credible and its purchasing power
inﬂation is accelerated. Hence, if

1
is kept intact, thepa2

dca
is positive, the real eﬀective demand y adρ5increases and the upturn of the world economy diﬀuses to the domestic economy.
In this sense, the employment-isolation eﬀect is certainly incomplete under the
ﬂexible exchange rate system.

3.2

The Monetary Expansion

Let us consider the eﬀect of the domestic monetary expansion (i.e., increasein m1 ). Contrary to the Mundell (1963)-Fleming (1962) model, our model
suggests that the eﬀect of the domestic monetary expansion becomes weaker, oreven ambiguous when the intertemporal substitution of the consumption stream
is adequately high.
Equation (10) clearly shows that ceteris paribus, a monetary expansion increases the real GDP y a through the multiplier eﬀect formulated by Otaki(2007). Nevertheless, it depreciates the real exchange rate and employees are ina disadvantageous position. Subsequently, ﬁrms are forced to raise the nominal
wage and, as a result, the current price pa1 becomes high.
When money is credible, it implies the reduction of the inﬂation rate ρa .
Thus, employees recover their lifetime utility. However, since lowered inﬂation
rate decreases the aggregate consumption, the contractive eﬀect appears in ourmodel. Accordingly, at least, an easy monetary policy has a weaker eﬀect thanthat in the case of a closed economy.

4

Concluding Remarks

In this paper, we construct a small open economy model on the basis of the twoperiod overlapping generation model developed by Otaki (2007, 2009, 2011a).
the results obtained are as follows:First, the employment-isolation eﬀect in the ﬂexible exchange rate system iscertainly imperfect, which is ambiguous in Laursen and Metzler (1950). This isbecause the appreciation of the real exchange rate accelerates domestic inﬂation.
Moreover, the accelerated inﬂation stimulates the aggregate consumption andthe real eﬀective demand.
Second, the power of monetary policy in open economy is weaker than ina closed economy. This is because the depreciation of the real exchange ratealways accompanies lower inﬂation. This theoretical causality does not exist ina closed economy model. Furthermore, such a proposition is counterintuitivefrom the perspective of the traditional Mundell (1963)-Fleming (1962) model.

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Mathematical Appendix
In this appendix, we show the mathematical results concerning propositionsin Section 3. We have three structural equations: (7), (9), (10). Since Roy’sϕ′identity induces us to= sa ≡ 1 − ca , Equation (7) is transformed intoϕ
[1 − β]dedρ+ ρsa (ρ)
= 0.
e
ρ

(11)

Diﬀerentiating both sides of Equations (9) and (10) and substituting (11), we
obtain1sa y a dy abρsa[] [ dy ]a−η +b
1−β  y
= y ,
dρ
a ′ a
dm
−ρ[c ] y
ρ

where
η≡−

(12)

ρ[sa ]′.
sa

Solving (12), we ﬁnally obtain
[


dy a
]
a ′ a
a
1  ρ[s ] yy=dρ∆−sa y a
ρ

where
∆≡−

η−

 dy bρsa][
1 − β  yb ,
dm
1

(13)

ρy a [sa ]2
< 0.
1−β

References[1] Fleming, J. M. (1962), ‘Domestic ﬁscal policies and ﬂoating exchange rates’
IMF Staﬀ Papers 9: 369-380.
[2] Laursen, S., and Metzler, L. (1950), ‘Flexible exchange rates and the theoryof employment,’Review of Economics and Statistics 32: 281-299.
[3] Mundell, R. A. (1963), ‘Capital mobility and stabilization policy underﬁxed and ﬂexible exchange rates,’ Canadian Journal of Economics andPolitical Science 29: 475-485.
[4] Obstfeld, M., and Rogoﬀ, K. (1996), Foundations of International Economics, MIT Press, Massachusetts.
[5] Otaki, M. (2007), ‘The dynamically extended Keynesian cross and thewelfare-improving ﬁscal policy,’ Economics Letters 96: 23-29.
7[6] Otaki, M. (2009), ‘A welfare economics foundation for the full-employment
policy,’ Economics Letters 102: 1-3.
[7] Otaki, M. (2011a), ‘A pure theory of aggregate price determination,’ Theoretical Economics Letters (forthcoming).
[8] Otaki, M. (2011b), ‘On the function of key currency,’ DBJ Discussion Paper
Series No. 1102, Research Institute of Capital Formation, Development
Bank of Japan.

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