Discussion Paper No. 659

PROTECTIVE TRADE POLICIES‘REDUCE’ EMPLOYMENT:A DYNAMIC OPTIMIZATION APPROACH

Yoshiyasu Ono

April 2006

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

April 2006

Protective Trade Policies ‘Reduce’ Employment:
A Dynamic Optimization Approachby

Yoshiyasu Ono*
Osaka University

Abstract
Using a competitive two-country two-commodity monetary model with optimizing agentsin which persistent unemployment arises, this paper examines the effects of trade restrictions
on consumption and employment in the two countries. When facing unemployment, a country
tends to impose an import restriction so that domestic firms will increase production and raise
employment. However, this policy improves the current account and hence its currency
appreciates, causing its products to lose international competitiveness. Therefore, employment
and consumption eventually decrease in the country while in the foreign country its currency
depreciates and hence employment and consumption increase.
JEL classification: F13, F41, F42
Keywords: persistent unemployment,
dynamically optimizing agents.

trade

restrictions,exchange-rate

adjustment,

Address: Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka,
Ibaraki, Osaka, 567-0047, JAPANE-mail: ono@iser.osaka-u.ac.jp*

For useful comments I thank Y. Iida and participants in the Sophia Symposium 2005. This research isfinancially supported by the 21st Century COE Program of the Ministry of Education, Culture, Sports, Science,
and Technology.

1. Introduction
In the 1980s the USA was annoyed by a huge trade deficit against Japan. Various US
industries were threatened by massive Japanese exports and many employees were laid off.
Consequently, trade frictions arouse in various industries, such as steel, color TV, automobiles,
and microchips. As a new friction occurred, the US government imposed a trade restriction toprotect a threatened industry under the belief that such a protection would provide a larger
market to import-competing firms and hence increase employment. In reality, however,
employment did not recover as expected. The US dollar then continued to rise against theJapanese yen, causing the price competitiveness of US products to deteriorate, and new trade
frictions occurred one after another.
This paper examines the abovementioned process of unemployment and currency
appreciation due to a trade restriction. In doing so it introduces a tariff or a quota into a
two-country two-commodity continuous-time competitive model presented by Ono (2006) inwhich people rationally behave and wages and prices continue to adjust, albeit in a sluggish
manner, and yet a persistent demand shortage arises under a liquidity trap.1 In this framework it
is found that an import tariff/quota improves the current account and raises the value of thehome currency, which increases the relative price of the home products.2 Moreover, the pricerise is so high that employment eventually decreases in the home country. It in turn lowers therelative price of the foreign products and improves employment in the foreign country. Thus, a
trade restriction is found to generate currency appreciation and worsen unemployment, as
actually observed in the USA in the late 1980s and the early 1990s.
In the conventional analysis of optimal tariffs/quotas with full employment and perfectcompetition the optimal tariff for a small country is widely known to be zero. In a two-country
setting a positive tariff benefits the tariff-imposing country and harms the other through an
improvement in the terms of trade. Moreover, in the presence of unemployment, a positive
tariff may seem even more beneficial since it protects an import-competing industry and raises
employment. In fact, Choi and Beladi (1993, 1998) assume wage and interest-rate rigidities
and show that a positive tariff is beneficial even in a small economy.

1

It is an open-economy extention of Ono (1994, 2001), where persistent unemployment is found to arise
within a closed-economy framework.
2

In fact, a recent empirical research by Santos-Paulino and Thirlwall (2004) finds that a trade liberalization
worsens the current account.

1However, in a small country with Harris-Todaro-type urban unemployment caused by
fixed urban and flexible rural wages, Chen and Choi (1994) find that a negative tariff benefits
the country. It is because they assume the country to import a capital-intensive commodity andthus an import promotion lowers the capital rent and raises the rural wage, which causes urban
unemployment to decrease. Chao and Yip (2000) introduce a cash-in-advance constraint into amonetary economy with Harris-Todaro-type unemployment and find that a negative tariff canbenefit the country.3 All of these studies consider a static framework and hence ignore thecurrent-account adjustment that determines the exchange rate.
There are also some papers that analyze the effect of a tariff on the dynamic profile of thecurrent account in a continuous-time dynamic optimization setting. They are e.g. Roldos(1991) with capital accumulation, Mansoorian (1993) with habit formation, and Ikeda (2003,
2006) with weakly non-separable intertemporal preferences.4 However, none of them consider
the possibility of unemployment. Moreover, they consider a small country.5 Van Wijnbergen(1987) uses a two-period model with wage rigidity in the first period and analyzes the effect ofa tariff on the current account and employment. Unlike the present analysis, however, itregards unemployment as a short-run phenomenon that disappears in the second period.
When analyzing unemployment in an open-economy dynamic framework, the new open
economy macroeconomic models, e.g., Obstfeld and Rogoff (1995), Christiano, Eichenbaumand Evance (1997), Hau (2000), and Betts and Devereux (2000a, 2000b), are often utilized.6
They adopt a period analysis with monopolistic competition and nominal price/wage stickinessand assume that prices/wages can be modified only at the beginning of each period. In thissetup, if a government imposes a trade restriction in the middle of a period, disequilibrium
arises only in that period and full employment is achieved in the next period and thereafter.
Hence they cannot deal with persistent unemployment, which the present paper focuses on.
In the following section 2 presents a basic structure of the model. Section 3 obtains
conditions under which persistent unemployment arises. The effects of an import tariff on theexchange rate, the relative price, employment and consumption are examined in section 4. It is

3

There are also other types of distortions that cause a negative tariff to be beneficial. For example, under anoligopolistic vertical relationship Lahiri and Ono (1999) show a negative tariff to be beneficial. See also Larueand Gervais (2002) for the same possibility with oligopolistic distortions.
4

Inoue (2000) adopts a two-period trade model and finds that a negative tariff can benefit the country.

5

Ikeda (2006) analyzes a two-country case as well.

6

See Lane (2001) for an extensive survey on the new open economy macroeconomics.

2

shown that an import tariff that is aimed to raise employment in fact ‘lowers’ it by causing theexchange rate to appreciate. Section 5 proves the equivalence between a tariff and a quota inthe presence of unemployment. Thus, a quota is shown to generate the same controversial
effect as a tariff does. Finally, section 6 summarizes and concludes this paper.

2. The Model
Consider an economy with two countries, 1 and 2, in which the firm sector of country 1 (or2) specializes in commodity 1 (or 2) and inputs labor l (or l*) to produce y1 (or y2*). The
production functions are
y1 = θ1l,y2* = θ2l*,(1)

where input-output coefficients θ1 and θ2 are assumed to be constant. Given nominal
commodity price P1 (or P2*) and nominal wage W (or W*), each firm sector maximizes profits:(θ1P1 − W)l,(θ2P2* − W*)l*.

(2)

There are three kinds of assets, viz. an international interest-earning asset, the homecurrency and the foreign currency.7 Among the three the household sector of each country
chooses two assets, the home currency and the international asset, since the foreign currency
neither yields interest nor has liquidity. The nominal interest rates of the international asset incountries 1 and 2 are respectively R and R*. The no-arbitrage condition between the domestic
and foreign interest rates requires
R = ε& / ε + R*,(3)

where ε is the exchange rate of country 1’s currency against country 2’s one and a dot implies
a time derivative. Total asset a (or a*) consists of home currency m (or m*) and international
asset b (or b*), all measured in real term,8 and thus each country’s asset constraint is
a = b + m, a* = b* + m*.

(4)

Since the government of country 1 imposes tariff t on its import of commodity 2 while
country 2 imposes no tariff, the nominal consumer prices of the two commodities are
P1 and (1 + t)εP2* in country 1,
P1/ε and P2* in the international market and country 2.

(5)Given these prices the household sectors respectively maximize
7

Because of the production technology given by (1) the firm values are zero.

8

Note that the real values of nominal variables in the two countries have different units since a tariff makes the

3

∞

∞

0

0

U = ∫ (u (c1 , c 2 ) + v(m) ) exp(−ρs )ds , U* = ∫ (u * (c1 *, c 2 *) + v * (m*)) exp(−ρs )ds ,(6)

where they have the same subjective discount rate ρ. Utility from liquidity holding v(m) andv*(m*) satisfyv′(m) > 0, v″(m) < 0;v*′(m*) > 0, v*″(m*) < 0.

In order for the consumer price index to be a function of only the prices of the two
commodities, utility functions of consumption, u(c1, c2) and u*(c1*, c2*), are assumed to beu(c1, c2) = (1/σ)ln(κ1c1σ + κ2c2σ), u*(c1*, c2*) = (1/σ)ln(κ1c1*σ + κ2c2*σ),where 1 > σ > 0.
Under the utility functions given above and commodity prices given by (5), consumer
price index P* and real consumer prices of the two commodities p1* and p2* in theinternational market and country 2 are respectively
P* = 1/{κ11/(1−σ)(P1/ε)−σ/(1−σ) + κ21/(1−σ)P2*−σ/(1−σ)}(1−σ)/σ,p1* ≡ (P1/ε)/P* = p1(ω) = [κ11/(1−σ) + κ21/(1−σ)ω−σ/(1−σ)](1−σ)/σ,p2* ≡ P2*/P* = p2(ω) = ωp1(ω) = [κ11/(1−σ)ωσ/(1−σ) + κ21/(1−σ)](1−σ)/σ,(7)where ω is the international relative price of commodity 2:ω = εP2*/P1.

(8)

Since country 1 imposes a tariff on commodity 2, consumer price index P and real prices p1 andp2 in country 1 are
P = 1/{κ11/(1−σ)P1−σ/(1−σ) + κ21/(1−σ)[(1 + t)εP2*]−σ/(1−σ)}(1−σ)/σ,p1 ≡ P1/P = p1((1 + t)ω),p2 ≡ (1 + t)εP2*/P = p2((1 + t)ω),(9)

where the functional form of p1(⋅) and that of p2(⋅) are given in (7).
From (3), (7), (8) and (9) real interest rates r and r* satisfy& / ω = r* − δ(ω) ω& / ω,r − δ((1 + t)ω) ω

where function δ(⋅) implies
δ(ω) = κ11/(1−σ)/[κ11/(1−σ) + κ21/(1−σ)ω−σ/(1−σ)] = 1 + p1′(ω)ω/p1(ω) = p2′(ω)ω/p2(ω),
1 > δ(ω) > 0, δ′(ω) = [σ/(1 − σ)][δ(1 − δ)/ω] > 0.

(10)Note that real interest rates r and r* can be mutually unequal although international asset tradeis allowed since tariff t causes the consumer price index to differ between the two countries.

relative price differ in the two countries.

4

The flow budget equation of each household sector measured in real term is9

a& = ra + wx − c − Rm + z, a& * = r*a* + w*x* − c* − R*m* + z*,(11)where w and w* are real wages, x and x* actual labor supplies, z and z* real lump-sum transfers,
and c and c* real total consumption represented byc = p1c1 + p2c2 , c* = p1*c1* + p2*c2*.
Since each household’s labor endowment is normalized to unity, x and x* arex = min(1, l),x* = min(1, l*).

Each household sector maximizes life-time utility (6) subject to (4) and (11). The
intratemporal optimal conditions are

p1c1 = δ((1 + t)ω)c, p2c2 = [1 − δ((1 + t)ω)]c,
p1*c1* = δ(ω)c*, p2*c2* = [1 − δ(ω)]c*,(12)

where δ(⋅) is given by (10). The intertemporal optimal conditions areρ + c& / c + π = R = v′(m)c,

ρ + c& * / c * + π* = R* = v*′(m*)c*,(13)

where π (or π*) represents the inflation rate of P (or P*). The transversality conditions arelim λ(s)a(s)exp(− ρs) = 0,s →∞lim λ*(s)a*(s)exp(− ρs) = 0,

s →∞

(14)

where λ and λ* are co-state variables for a and a* respectively.
The equilibrium conditions of the two countries’ money markets and that of theinternational asset market are
the money markets:

M/P = m,the international asset market:10

M*/P* = m*,(15)

Pb + εP*b* = 0.

(16)

Commodity prices P1 and P2* are also assumed to adjust perfectly and hence at any point intimeθ1x = c1 + c1* = [δ((1 + t)ω)/p1]c + [δ(ω)/p1*]c*,θ2x* = c2 + c2* = {[1 − δ((1 + t)ω)]/p2}c + {[1 − δ(ω)]/p2*}c*.

(17)

The labor market is internationally segmented and the adjustments of nominal wages inboth countries are assumed to be sluggish.11 They move according to each unemployment rate:

9

The nominal flow budget equation is

A& = Wx + RPb − Pc + Pz,
where A (= Pa) represents total asset holdings measured in terms of yen. Equation (11) is derived from thisequation and (4).
10

Because of Walras’s law for stock variables, (16) is valid if (15) holds.

11

This assumption is imposed in order to allow disequilibrium to occur in the labor market; otherwise thepossibility of unemployment is avoided by definition. Note that even under this assumption the possibility of the5W& / W = α(l − 1),

W& * /W * = α*(l* − 1).

(18)

From (2), (18), and the perfect adjustment of P1, if θ1P1 > W, l = ∞, causing W to adjust
immediately. If θ1P1 < W, l = 0 and hence commodity supply is zero, causing P1 to jumpupward. Thus, θ1P1 always equals W. In this case l can take any finite value and thus equals theactual employment level. After all P1 and W move in parallel and follow (18) where l = x. The
movements of P2* and W* analogously obtain. In sum,p1θ1 = w (= W/P),

p2*θ2 = w* (= W*/P*),

P&1 / P1 = W& / W = α(x − 1), P&2 * / P2 * = W& * /W * = α*(x* − 1).
From these equations and the definition of δ(ω) given in (10), π and π* are& / ω , π* = α*(x* − 1) − δ(ω) ω& / ω.
π = α(x − 1) + [1 − δ((1 + t)ω)] ω(19)The government of country 1 transfers tariff revenue tεP2*c2/P to the household sector in a
lump-sum manner while that of country 2 imposes no tariff. Therefore, from (9) one derivesz = tp2c2/(1 + t), z* = 0.
Applying these equations and (15) to (11) yields the dynamics of the two countries’international asset holdings:
b& = rb + p1θ1x − p1c1 − p2c2/(1 + t),

b& * = r*b* + p2*θ2x* − p1*c1* − p2*c2*.

(20)

From (3), (7)-(9), (16) and (17) it is found that one of the two equations in (20) implies theother.

3. The Steady State with Unemployment
This section explores the condition under which persistent unemployment arises. In thesteady state c stays constant, and thus from (13)r = ρ, r* = ρ.
Since b and b* then stay constant,12 from (12) and (20),b& = ρb + p1((1 + t)ω)θ1x − c[1 + tδ((1 + t)ω)]/(1 + t) = 0,b& * = ρb* + p2(ω)θ2x* − c* = 0.

(21)

If full employment obtains in this state,x = 1, x* = 1.

(22)

full employment steady state is not eliminated. In fact, the full employment steady state is presented in section 3.
See van der Ploeg (1993) for the same type of sluggish price adjustment.
12

Otherwise, the transversality condition is not satisfied.

6

Therefore, from (21),c = (p1θ1 + ρb)(1 + t)/[1 + tδ((1 + t)ω)],c* = p2*θ2 + ρb*.

(23)

Substituting (22) and (23) into the first equation of (17) gives the equation that ω has to satisfy.
It is{[1 − δ((1 + t)ω)]θ1 − ρb(1 + t)δ((1 + t)ω)/p1}/[1 + tδ((1 + t)ω)]= (p2*θ2 + ρb*)δ(ω)/p1*.

(24)Note that c, c* and ω are independent of m or m*. Once c and c* are determined by (23) and(24), from (13), (19) and (22) m and m* are obtained so that they satisfyv′(m)c = ρ, v*′(m*)c* = ρ.

(25)

Now suppose the possibility of a liquidity trap. Liquidity demand functions imply the
relationship between R and m for a given c and that between R* and m* for a given c* derived
from (16). They are
R = v′(m)c, R* = v*′(m*)c*.

(26)

Since v″(m) < 0 and v*″(m*) < 0, R (or R*) is negatively related to m (or m*). If v′(m) andv*′(m*) have positive lower bounds,13v′(∞) = β > 0,v*′(∞) = β* > 0,(27)

R (or R*) decreasingly approaches a constant level βc (or β*c*) as m (or m*) increases. It never
becomes lower than βc (or β*c*), implying a liquidity trap.
In the presence of the liquidity trap, the solutions of m and m* that satisfy (25) may notexist. In fact, from (26) and (27),βc ≥ ρ ⇔ the m does not exist.
β*c* ≥ ρ ⇔ the m* does not exist.

(28)

In the above inequalities c and c* take the values derived from (23) and (24). From (27) and(28) it is evident that, if the m that satisfies the first equation of (25) does not exist, the left-handside of the equation exceeds the right-hand side for any m, implying that the desire for saving
exceeds that for consumption if the consumption level is so high as to attain full employment.
Therefore, a demand shortage arises. The appendix exhibits the range of b in which the two
13
Keynes (1936, Ch.17) mentions that this is an essential property of money and that under this property ashortage of effective demand obtains. See Ono (1994, pp.31-33; 2001) for the implication of this property on theeffective-demand shortage caused by a liquidity trap. This property is empirically shown by Ono (1994, chap.3)
using the GMM (Generalized Method of Moments), and more extensively by Ono, Ogawa, and Yoshida (2004)
using both a parametric and a non-parametric approach.

7

inequalities in (28) are vaild.
Let us next obtain the steady state when both conditions in (28) hold and hence the twocountries face a shortage of demand. In this state prices and wages continue to decline andv′(m) and v*′(m*) converge to β and β* respectively.14 Therefore, from (13) and (19) in whichc, c*, and ω stay constant, one finds
βc = ρ + α(x − 1), β*c* = ρ + α*(x* − 1),(29)

where x and x* are given as functions of ω, c and c* in (17). From (17) and (29), c and c* arec = f(c*, ω; t) = [(ρ − α)/β + c*δ(ω)α/(βp1*θ1)]/[1 − δ((1 + t)ω)α/(βp1θ1)],
c* = f*(c, ω; t)= {(ρ − α*)/β* + c[1 − δ((1 + t)ω)]α*/(β*p2θ2)}/[1 − (1 − δ(ω))α*/(β*p2*θ2)].

(30)

These two curves are shown by figure 1. Note that the figure is illustrated so that for a given ω
c is positive even if c* is zero, that an increase in c* raises c, and that the intersection point
exists. These properties are satisfied under the following conditions:A ≡ [1 − δ((1 + t)ω)α/(βp1θ1)][1 − (1 − δ(ω))α*/(β*p2*θ2)]− {δ(ω)α/(βp1*θ1)}{[1 − δ((1 + t)ω)]α*/(β*p2θ2)} > 0,
ρ > α, ρ > α*.

(31)

From the two equations in (30), c and c* are determined as functions of ω and t.
c = {[(ρ − α)/β][1 − (1 − δ(ω))α*/(β*p2*θ2)] + [(ρ − α*)/β*]δ(ω)α/(βp1*θ1)}/A,
c* = {[(ρ − α*)/β*][1 − δ((1 + t)ω)α/(βp1θ1)]+ [(ρ − α)/β][1 − δ((1 + t)ω)]α*/(β*p2θ2)}/A,(32)

where A is given by (31). In figure 1 point E represents c and c* that satisfy (32). By applying
these functions and (29) to the first equation in (21) and equalizing it to zero one finds ω thatbalances the current account. We here assume the current account function to satisfy the
Marshall-Lerner condition (∂ b& /∂ω > 0). Since from (9), (10), (21), (29), (31) and (32),ω∂ b&(ω, t ) /∂ω⏐t = 0= [δ(1 − δ)/(1 − σ)](c + c*){[1 − α/(βp1θ1)][1 − α*/(β*p2*θ2)]/A − (1 − σ)},(33)

the Marshall-Lerner condition is rewritten as15
∂ b&(ω, t ) /∂ω > 0 ⇔ [1 − α/(βp1θ1)][1 − α*/(β*p2*θ2)]/A − (1 − σ) > 0.

14

(34)

See Ono (2006) for the stability of the present dynamics when t = 0.

It is valid when σ is close to 1 and hence the two commodities are close substitutes to each other. See Ono(2006) for this property.
15

8

Once ω is thus determined, from (32) c and c* obtain. From (13) the steady-state levels of
R and R* are
R = βc,R* = β*c*.

Therefore, from (3) ε& / ε is
ε& / ε = βc − β*c*.

(35)

From (28) and (29) x and x* are smaller than 1 in this state, and thus all nominal prices andwages continue to decline and m and m* continue to expand. Nevertheless, the twotransversality conditions in (14) hold since from (13) and (15)m& / m = − π = ρ − βc < ρ,m& * / m * = − π* = ρ − β*c* < ρ.

4. An Import Tariff
This section focuses on the case where both countries face unemployment, and examines
the effect of country 1’s import tariff on the exchange rate and the two countries’ consumption
and employment. The effect of the tariff is examined in the neighborhood wheret = 0.
In this case (34) reduces to
A ≡ δ[1 − α/(βp1θ1)] + (1 − δ)[1 − α*/(β*p2*θ2)] > 0.
Since [1 − α/(βp1*θ1)][1 − α*/(β*p2*θ2)] is positive under the Marshall-Lerner condition givenby (34), the above property implies
1 − α/(βp1θ1) > 0, 1 − α*/(β*p2*θ2) > 0.

(36)

From (7), (9) and (16), country 1’s real asset holding b is
b = − b*{κ11/(1−σ) + κ21/(1−σ)[(1 + t)ω]−σ/(1−σ)}(1−σ)/σ/{κ11/(1−σ) + κ21/(1−σ)ω−σ/(1−σ)}(1−σ)/σ.
For simplicity, the international asset is assumed to be a real bond measured in terms ofinternational prices and thus b* does not change when tariff t is imposed. Thus, partiallydifferentiating the above equation with respect to t or ω and using (10) yields∂b/∂t⏐t = 0 = − (1 − δ)b, ∂b/∂ω⏐t = 0 = 0.

(37)

By applying (7), (9), (10), (29) and (37) to the total differentiations of the two equations in (21)
it is found that, if relative price ω responds to tariff t so that the current-account balance canrecover, thendb& = (βp1θ1/α − 1)dc − (1 − δ) p1θ1xdω/ω = 0,

db&* = (β*p2*θ2/α* − 1)dc* + δp2*θ2x*dω/ω = 0.

9

(38)

By substituting the partial derivative of c given in (32) with respect to t:∂c(ω, t)/∂t = {αδ(1 − δ)[1 − α*/(β*p2θ2)]/[βp1θ1(1 − σ)]}c/A,(39)

to the first equation of (38), it is obtained that under (36)
∂ b&(ω, t ) /∂t = [δ(1 − δ)/(1 − σ)][1 − α/(βp1θ1)][1 − α*/(β*p2θ2)]c/A > 0.

(40)

From (34) and (40), dω/dt satisfies
dω/dt = − [∂ b&(ω, t ) /∂t]/[∂ b&(ω, t ) /∂ω] < 0.

(41)

From (26), (29), (35), (38) and (41), the effects of country 1’s import tariff are
dc/dt < 0, dx/dt < 0, dR/dt < 0, dπ/dt < 0,dc*/dt > 0, dx*/dt > 0, dR*/dt > 0, dπ*/dt > 0,dω/dt < 0, d( ε& / ε )/dt < 0.
Since neither W nor W* can jump and P1 and P2* are always set equal to W/θ1 and W*/θ2
respectively under production technology (1), neither P1 nor P2* can jump. Therefore, (8) and(41) imply exchange rate ε to jump downward when tariff t is imposed. Thereafter, exchange
rate ε moves along with P1 and P2* so that ω stays constant over time. These properties are
summarized as follows:

Proposition 1: An increase in a country’s import tariff raises the value of its own currency

against the other’s and thus raises the relative price of its products (1/ω). Consequently, its
own employment and consumption decline whereas those of the other country expand. The
appreciation speed of its own currency increases.

Intuitively, a rise in t potentially improves the current account of the tariff-imposing
country, causing the value of its currency to appreciate. Therefore, the other country’s demandfor its own commodity increases and eventually improves its employment and consumption. In
turn, the other country’s demand for the tariff-imposing country’s product decreases so muchthat employment and consumption decrease in the tariff-imposing country.
The abovementioned mechanism seems quite opposite to what policy makers usually havein mind.16 It may be because they ignore the adjustment of the exchange rate. In fact, from (7),(9), (10) and (30), if the exchange rate is unchanged and thus relative price ω is invariant, a rise16

It is also different from the result of the conventional Mundell-Fleming with flexible exchange rates. An
import tariff can either reduce or increase the tariff-imposing country’s effective demand. See the appendix for
this property.

10

in the tariff rate shifts the f curve in figure 1 upward and the f* curve leftward, as illustrated infigure 2. It implies that an import tariff raises employment and hence stimulates consumption
in the tariff-imposing country while in the other country it reduces employment andconsumption. Consequently, the intersection point of the two curves moves in the north-west
direction, implying the tariff-imposing country’s consumption to increase and the other’s
consumption to decrease. The former property is valid since ∂c(ω, t)/∂t given by (39) is
positive under (36) while the latter is derived from (32) and (36) as follows:∂c*/∂t = − [δ(1 − δ)/(1 − σ)][1 − α/(βp1θ1)][α*/(β*p2θ2)]c/A < 0.
Thus, if relative price ω is fixed, a tariff protection raises consumption in the tariff-imposing
country and lowers it in the other country, as is usually expected. However, this processaccompanies an improvement in the current account. Thus, under the flexible exchange-rate
regime the exchange rate appreciates, which harms the competitiveness of the tariff-imposing
country’s product. Proposition 1 implies that the harmful effect is so strong that the
tariff-imposing country’s employment and consumption decrease while the other country’s
employment and consumption increase.

5. Tariff-Quota Equivalence
If country 1 imposes quota q, instead of tariff t, on the import of commodity 2, thecommodity market equilibrium conditions areθ1x = [δ(ωq)/p1(ωq)]c + [δ(ω)/p1*]c*,θ2x* = q + {[1 − δ(ω)]/p2*}c*, q = {[1 − δ(ωq)]/p2(ωq)}c,(42)

where ωq is the relative price in country 1 under quota q. Since transfer z equals the quota
revenue and the nominal price of commodity 2 in country 1 is p2(ωq)P, from (42) z is
z = (p2(ωq)P − εP2*)q/P = [1 − δ(ωq)](1 − ω/ωq)c.
Substituting this equation into (11) yields country 1’s current account under quota q:
b& = ρb + p1θ1x − c[1 + γδ((1 + γ)ω)]/(1 + γ) = 0,(43)where γ is the mark-up ratio of the relative price of commodity 2 under quota q:
ωq = (1 + γ)ω.
Since the relationship between c and x and that between c* and x* given in (29) still hold in
the present case, from (29) and (42) c and c* are determined as functions of ω and q.

11

Substituting those functions into (43) gives the equilibrium level of ω and hence all variables
are determined.
By replacing mark-up ratio γ by tariff rate t, one finds that (42) and (43) are equivalent to(17) and the first equation of (21), respectively. Therefore, the equilibrium levels of all
variables under tariff t are the same as those under quota q that makes the mark-up ratio of theprice of commodity 2 equal t. This property is restated as follows:

Proposition 2: The equivalence between tariffs and quotas is valid in the stagnation steadystate.

Since (7), (9) and (16) giveb = − [p1(ω)/p1(ωq)]b*,
country 1’s current account (43) reduces to[p1(ω)/p1(ωq)] b& = − ρb* + δ(ω)c* − p2(ω)q = 0,
where p2(ω) and δ(ω) are respectively given by (7) and (10) and c* is derived as a function of ωand q from (29) and (42). Therefore, the Marshall-Lerner condition under quota q is{(1 − σ)/[δ(1 − δ)]}ω (∂ b& /∂ω⏐ω = ωq)= {[1 − α*/(β*p2*θ2)]/[1 − (1 − δ)α*/(β*p2*θ2)]}c* − (1 − σ)(c + c*) > 0,(44)

Note that this value is estimated when quota q is just non-binding and hence ω = ωq.
Under (44) a negative relationship between tariff t and equivalent quota qe obtains asfollows. Equations (33) and (40) give(1/ω)dω/dt = − {c[1 − α/(βp1θ1)][1 − α*/(β*p2θ2)]/A}/{[(1 − α/(βp1θ1))(1 − α*/(β*p2*θ2))/A − (1 − σ)](c + c*)} < 0,(45)

Totally differentiating c2 derived from the second equation of (12) and applying (10), the firstequation of (37) and (45) to the result yields[− ω/(dω/dt)]{p2(1 − σ)/[δ(1 − δ)]}dc2/dt= − c* + (1 − σ)(c + c*)[1 − (1 − δ)α*/(β*p2*θ2)]/[1 − α*/(β*p2*θ2)],
where the coefficient of dc2/dt in the left-hand side is shown to be positive by (45). Therefore,
under the Marshall-Lerner condition under quota q given by (44) one naturally finds
dc2/dt < 0,i.e., imposing an import tariff lowers the amount of import. It also implies the negative
relationship between tariff t and equivalent quota qe.
12dqe/dt < 0.
From this property and propositions 1 and 2 one finds the effect of an import restriction in
general. An import tariff or quota first raises the domestic price of the foreign commodity anddecreases its import, improving the restriction-imposing country’s current account. It raises thevalue of its currency so that the current account recovers the equilibrium level and thus lowers
the international (and foreign) relative price of the foreign commodity. Consequently, theforeign country’s demand for its own commodity increases. Moreover, the magnitude of theincrease is so large that it dominates the decrease in the restriction-imposing country’s demand
due to the restriction, and hence employment and consumption increase in the foreign country.
The appreciation of the restriction-imposing country’s currency also raises theinternational relative price of its product, causing foreign demand for it to decrease. The
magnitude of the decrease is so large that the world demand for it declines, and hence
employment and consumption decrease in the restriction-imposing country.
Finally, from (33) and (45) the effect of a tariff (or an equivalent quota) on the
restriction-imposing country’s domestic price, (1 + t)ω = ωq, is derived. It satisfies{(1 − σ)/[δ(1 − δ)]}(∂ b& /∂ω⏐t = 0)d[(1 + t)ω]/dt= {[1 − α/(βp1θ1)][1 − α*/(β*p2*θ2)]/A − (1 − σ)}c* − (1 − σ)c,where the coefficient of c* in the right-hand side is positive because of the Marshall-Lernercondition under tariff t given by (34). Thus, d[(1 + t)ω]/dt and dωq/dq can either be positive or
negative depending on c*/c, the relative size of the two countries’ consumption. Proposition 1
implies that import tariff t raises the value of its own currency and thus reduces ω, theinternational relative price of the import commodity. If c* is much smaller than c, the reductionin ω is so much that it dominates the increase in the tariff and decreases the domestic relative
price of the import commodity, (1 + t)ω = ωq. Otherwise, the domestic relative price naturally
rises.
Surprisingly, if the former is the case, which occurs when the restriction-imposing country
is much larger than the other, its demand for the home product decreases more than that for theforeign product does although an import restriction is imposed on the foreign product.

6. Conclusions
An import restriction, viz. a tariff or a quota, is broadly believed to raise domestic
employment and thus it tends to be imposed especially when a country faces serious
13unemployment. When such a policy is considered, the exchange rate adjustment is often
ignored. If the exchange-rate adjustment is taken into account, however, the result is quite
different from such a belief. Using a dynamic optimization model with a liquidity trap andpersistent stagnation, this paper finds that an import tariff/quota reduces employment andconsumption in the restriction-imposing country and increases them in the other country as aresult of the exchange-rate adjustment.
The mechanism is the following. An import tariff reduces import and thus improves thecurrent account. It leads the home currency to appreciate against the foreign currency so thatthe current account recovers the equilibrium level, causing the international relative price ofthe home commodity to rise. If the economy is under a liquidity trap and a shortage of effective
demand occurs, the appreciation of the home currency is so high that the amount of home
production decreases. Consequently, unemployment becomes worse and consumption
decreases. The appreciation of the home currency also implies a reduction in the price of theforeign commodity. The reduction is so large that the world demand for the foreign productexpands and hence both employment and consumption increase in the foreign country although
its export is restricted by the importing country. Since the equivalence of a tariff and a quota
still holds in the stagnation steady state, the same argument applies to the case of an importquota.

14

Appendix
Conditions for the stagnation steady state to obtain:

In the text I examine the effects of trade restrictions in the neighborhood where t = 0. Thus,
I assume t = 0 and obtain the region of b in which the two inequalities of (28) are both valid.
From (7), (8), (23) and (24), c and c* arec = κ1θ1σ(κ1θ1σ + κ2θ2σ)(1−σ)/σ + ρb,c* = κ2θ2σ(κ1θ1σ + κ2θ2σ)(1−σ)/σ − ρb.

(A1)Therefore, conditions (28) reduce toρ/β − κ1θ1σ(κ1θ1σ + κ2θ2σ)(1−σ)/σ ≤ ρb ≤ κ2θ2σ(κ1θ1σ + κ2θ2σ)(1−σ)/σ − ρ/β*,(A2)where the first inequality is the condition under which the full-employment level of m does notexist whereas the second one is the condition under which the full-employment level of m*does not exist.
Note that there is a region in which ρb that satisfies (A2) exists if both β and β* are large
enough or if θ1 and/or θ2 are large enough. For example, in a fully symmetric world, whereβ = β*, θ1 = θ2 = θ, κ1= κ2 = κ, b = b* (= 0),(A2) is valid if either β (= β*) or θ is so large thatρ/β ≤ 2(1−σ)/σκ1/σθ.
This condition is essentially the same as that for the stagnation steady state to obtain in Ono(2001, 2006).

Tariff Protections in the Mundell-Fleming Model:

Since investment is ignored in the present setting, the IS and LM curves in the twocountries are
y = c(y) + ex(y*, ω) − im(y, (1+t)ω),y* = c*(y*) − ex(y*, ω) + im(y, (1+t)ω),M/P = L(R, y),
M*/P* = L*(R, y*),(A3)

where ex is country 1’s export, im is its import, and y and L (or y* and L*) are respectively
country 1’s (or country 2’s) effective demand and money demand. They naturally satisfy∂ex/∂y* > 0, ∂ex/∂ω > 0,∂im/∂y > 0, ∂im/∂ω < 0,15

∂L/∂R < 0, ∂L/∂y > 0,
∂L*/∂R < 0, ∂L*/∂y* > 0.

(A4)

Note that under free international asset trade both countries face the same interest rate R.
General price indices P and P* are respectively given in (7) and (9) in which P1 and P2* are
fixed in the Mundell-Fleming setting.
By totally differentiating the four equations in (A3) and using (7) and (9) one obtains
Kdy/dt =Kdω/dt =(1 − δ)m∂e x / ∂ω δm* ∂im / ∂ω+,∂L / ∂R∂L*/ ∂R∂i∂i ⎛ ∂L / ∂y 1 − c ′ ∂L * / ∂y * ⎞(1 − δ)m ⎛1 − c ′ ∂e x ⎞⎜⎜1 − c ′ + m +⎟⎟ − ω m ⎜⎜⎟ , (A5)+∂L / ∂R ⎝∂y 1 − c*′ ∂y * ⎠∂ω ⎝ ∂L / ∂R 1 − c*′ ∂L * / ∂R ⎟⎠where from (7), (9), (A4) and (A5) K is∂i
δm* ⎞⎛
1 − c ′ ∂e x ⎞⎛ 1 ⎞⎛ (1 − δ)m⎟⎟⎜⎜1 − c ′ + m +⎟K = − ⎜ ⎟⎜⎜+∂y 1 − c*′ ∂y * ⎟⎠⎝ ω ⎠⎝ ∂L / ∂R ∂L */ ∂R ⎠⎝∂i ⎞⎛ ∂L / ∂y 1 − c ′ ∂L * / ∂y * ⎞⎛ ∂e⎟⎟ > 0.
− ⎜ x − m ⎟⎜⎜+⎝ ∂ω ∂ω ⎠⎝ ∂L / ∂R 1 − c*′ ∂L * / ∂R ⎠(A4) and (A5) imply
dy/dt > or < 0,dω/dt < 0,i.e., in the Mundell-Fleming setting an import tariff may or may not raise the tariff-imposing
country’s effective demand, as stated in footnote 16, while ω inevitably declines. Moreover,since totally differentiating the sum of the first two equations in (A3) gives the following
property:<>
dy/dt = 0 ⇔ dy*/dt = 0,<>
the effect on the other country’s effective demand is also indeterminate.

16

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18

f*(c, ω; t)cf(c*, ω; t)E
f(0, ω; t)O

c*f*(0, ω; t)Figure 1: Interdependence of Consumption

19

c
f*(c, ω; t)t↑f(c*, ω; t)
t↑
E′
E

c*

O

Figure 2: The Effect of a Tariff under Fixed Prices

20