Silviase/jgov_v1.4_full_ann huggingface dataset:
$$ Q=W/\phi,\qquad Q^{*}=W^{*}/\phi^{*}, $$

#### 2.2. Households

We assume that the size of households in the home and foreign countries are L and $ L^{*} $ , respectively. In addition, each household is endowed with one unit of (inelastically supplied) labor. The households in each country consume both commodity 1 and 2, and obtain utility $ v(m) $ by holding real money balances m (i.e., a money-in-the-utility-function model). The consumption index c, defined below, is assumed to be symmetric both within and across countries. A home country’s household allocates total assets a between real money balances m and an international asset b. Hence, the intertemporal maximization problem is:

$$ U(c,m)=\int_{0}^{\infty}\bigl[u(c)+v(m)\bigr]\mathrm{e x p}(-\rho t)d t, $$

$$ u^{\prime}(\cdot)>0,u^{\prime \prime}(\cdot)<0;\nu^{\prime}(\cdot)>0,\nu^{\prime \prime}(\cdot)\leq0, $$

$$ \dot{a}=r a+w x-c-R m+\zeta, $$

$$ a=m+b, $$

$ x=\min\left(1,\ \frac{l_{z}}{L}\right) $ for the home country, $ x^{*}=\min\left(1,\ \frac{l_{z}^{*}+l_{y}^{*}}{L^{*}}\right) $ for the foreign country.

In (8), $ \rho $ is the subjective discount rate, assumed to be identical across both countries. Equation (9) is the flow budget equation, where $ w\ (\equiv W/P, $ where P is the price index in the home country) denotes the real wage rate, $ ^{4} $ x is the employment rate, and $ \zeta $ is lump-sum transfer from government. The nominal rate of return from holding home (foreign) assets is defined as $ R\ (R^{*}) $ . If the two assets are perfect substitutes, these assets must yield equal rates of return; i.e., $ R=\dot{\varepsilon}/\varepsilon+R^{*} $ . The real rates of return to home and foreign are defined, respectively, as $ r\equiv R-\pi $ and $ r^{*}\equiv R^{*}-\pi^{*} $ where $ \pi\ (\=\dot{P}/P) $ and $ \pi^{*}\ (\=\dot{P}^{*}/P^{*}) $ represent inflation rates. Equation (10) represents the stock constraint, we assume that the initial international asset holdings (that is initial debt) is zero, $ b_{0}=0 $ . Equation (11) implies that realized labor supply is determined on the short side either as the potential labor supply or as actual labor demand by the firm.
Before turning to the dynamic problem, we consider the composition of a given level of nominal expenditure, E, in each instant to maximize the consumption index c. The consumption index, aggregating across the consumption of two goods $ (c_{1}, c_{2}) $ , is given by

$$ c=\left(\kappa_{1}{c_{1}}^{\sigma}+\kappa_{2}{c_{2}}^{\sigma}\right)^{1/\sigma},1>\sigma>0, $$

where $ \kappa_{i} $ is the preference parameter for the good i (i = 1, 2) and $ \sigma $ is related to the elasticity of substitution, which is given by $ 1/(1 - \sigma) $ . We take a particular point in time and define E as $ E = P_{1}c_{1} + \varepsilon P_{2}^{*}c_{2} $ . Subject to this, the individual determines $ c_{1} $ and $ c_{2} $ to maximize (12). We obtain the following demand functions:

$$ P_{1}c_{1}=\delta(\omega)E\mathrm{a n d}\varepsilon P_{2}{}^{*}c_{2}=(1-\delta(\omega))E, $$

where the relative price $ \omega $ is represented by

$$ \omega=\varepsilon P_{2}^{*}/P_{1}, $$

and

$$ \delta(\omega)=\kappa_{1}^{1/(1-\sigma)}/\left[\kappa_{1}^{1/(1-\sigma)}+\kappa_{2}^{1/(1-\sigma)}\omega^{-\sigma/(1-\sigma)}\right], $$

$$ 1>\delta(\omega)>0,\delta^{\prime}(\omega)=[\sigma/(1-\sigma)][\delta(1-\delta)/\omega]>0. $$

Similarly, we obtain the following demand functions for a foreign household:

$$ (P_{1}/\varepsilon)c_{1}^{*}=\delta(\omega)E^{*}\mathrm{a n d}P_{2}^{*}\;c_{2}^{*}=(1-\delta(\omega))E^{*}, $$

where $ E^{*} = (P_{1}/\varepsilon)c_{1}^{*} + P_{2}^{*}c_{2}^{*} $ . In this case, the general price levels P and $ P^{*} $ and real prices $ p_{1}(\omega) $ and $ p_{2}(\omega) $ are respectively

$$ P=\left[\kappa_{1}^{1/(1-\sigma)}P_{1}^{-\sigma/(1-\sigma)}+\kappa_{2}^{1/(1-\sigma)}(\varepsilon P_{2}^{*})^{-\sigma/(1-\sigma)}\right]^{-(1-\sigma)/\sigma}, $$

$$ \boldsymbol{P}^{*}=\left[\kappa_{1}^{1/(1-\sigma)}(P_{1}/\varepsilon)^{-\sigma/(1-\sigma)}+\kappa_{2}^{1/(1-\sigma)}P_{2}^{*-\sigma/(1-\sigma)}\right]^{-(1-\sigma)/\sigma}, $$

$$ p_{1}(\omega)\left(\equiv P_{1}/P\right)=\left[\kappa_{1}^{1/(1-\sigma)}+\kappa_{2}^{1/(1-\sigma)}\omega^{-\sigma/(1-\sigma)}\right]^{(1-\sigma)/\sigma}, $$

$$ p_{2}(\omega)\left(\equiv P_{2}^{*}/P^{*}\right)=\omega\left[\kappa_{1}^{1/(1-\sigma)}+\kappa_{2}^{1/(1-\sigma)}\omega^{-\sigma/(1-\sigma)}\right]^{(1-\sigma)/\sigma}. $$

From the first two equations of (17), P and $ P^{*} $ satisfy

$$ P=\varepsilon P^{*}, $$

and thus inflation rates $ \pi\left(=\dot{P}/P\right) $ and $ \pi^{*}\left(=\dot{P}^{*}/P^{*}\right) $ satisfy
$$ \pi=\dot{\varepsilon}/\varepsilon+\pi^{*}. $$

Moreover, using $ R = \dot{\varepsilon}/\varepsilon + R^{*} $ and the definition of the real rates of return, we obtain $ r = r^{*} $ . From (12), (13), and (17), we obtain

$$ c=e,\quad where e=E/P. $$

In real terms, (13) and (16) can be rewritten as

$$ p_{1}c_{1}=\delta(\omega)e,\quad p_{2}c_{2}=(1-\delta(\omega))e, $$

$$ p_{1}c_{_{1}}^{*}=\delta(\omega)e^{*},\quad p_{2}c_{_{2}}^{*}=(1-\delta(\omega))e^{*}. $$

We now turn to the dynamic optimization problem. Because each household maximizes (8) subject to (9), (10), and (19), the current value Hamiltonian is given by $ H = u(e) + v(m) + \lambda [ra + wx - e - Rm] $ , where $ \lambda $ is the costate variable for a. The first-order optimality conditions for this problem reduce to

$$ \uprho+\upeta\frac{\dot{e}}{e}+\pi=R=v^{\prime}(m)/u^{\prime}(e), $$

where $ \eta \equiv -u''(e)e/u'(e) $ is the elasticity of marginal utility with respect to consumption. Similarly, from the first-order conditions for a foreign household, we have

$$ \rho+\eta\frac{\dot{e}^{*}}{e^{*}}+\pi^{*}=R^{*}=v^{\prime}(m^{*})/u^{\prime}(e^{*}). $$

The transversality conditions are

$$ \lim_{t\to\infty}\lambda_{t} a_{t}\exp(-\rho t)=0,\quad\lim_{t\to\infty}\lambda_{t}^{*}\overset{*}{a_{t}}\exp(-\rho t)=0. $$

#### 2.3. Governments

Suppose that the government of home country imposes a tariff on imported outsourced goods while that of country 2 imposes no tariff and that all tax revenue is shared home households in a lump sum. Then the government budget equation is given by $ \tau\varepsilon Q^{*}z^{*}/L=P\zeta $ . Using $ P=\varepsilon P^{*} $ , it can be rewritten in real terms:

$$ \tau q^{*}z^{*}/L=\zeta. $$
#### 2.4. Market adjustments

Given the household, firm and government behavior discussed above, the money and equity markets perfectly adjust, so that at any point in time: $ ^{6} $

$$ the money markets:mL=M/P,m^{*}L^{*}=M^{*}/P^{*}, $$

$$ the international asset market:bL+b^{*}L^{*}=0. $$

The commodity market adjustment is also assumed to be perfect, and hence:

$$ \mathrm{C o m m o d i t y}1\colon y_{1}=c_{1}L+\ c_{1}^{*}L^{*}=(e L+e^{*}L^{*})\delta(\omega)/p_{1}(\omega), $$

$$ \mathrm{C o m m o d i t y}2\colon y_{2}=c_{2}L+\ c_{2}^{*}L^{*}=(e L+e^{*}L^{*})(1-\delta(\omega))/p_{2}(\omega). $$

In contrast, the labor market is segmented internationally and the nominal wage adjustment is sluggish, so we can consider the possibility of unemployment. $ ^{7} $ This is simply represented by:

$$ \frac{\dot{W}}{W}=\alpha(x-1),\quad\frac{\dot{W}^{*}}{W^{*}}=\alpha^{*}(x^{*}-1), $$

where $ \alpha\left(\alpha^{*}\right) $ represents the adjustment speed of the nominal wage $ W\left(W^{*}\right) $ , and the employment rate $ x\left(x^{*}\right) $ of each country in (11) can be defined as:

$$ x=\frac{l_{_{z}}}{L},\boldsymbol{x}^{*}=\frac{l_{_{z}}^{*}+l_{_{y}}^{*}}{L^{*}}. $$

Expression (28) implies that the instant rate of nominal wage rates W (respectively $ W^{*} $ ) are positively related to the excess labor demand $ (l_{z}-L) $ (respectively $ l_{z}^{*}+l_{y}^{*}-L^{*} $ ).

From (3), (5), (7) and (17), the relationships between the real price of good and wage rate can be rewritten as,

$$ \theta p_{1}=\Omega w^{1-\gamma}((1+\tau)w^{*})^{\gamma}, $$

$$ \boldsymbol{\theta}^{*}\boldsymbol{p}_{2}=\boldsymbol{w}^{*}. $$

and then the relative wage is given by

$$ w^{*}\mid w\equiv f(\omega;\tau)=[\Omega(\theta^{*}\mid\theta)]^{1/(1-\gamma)}(1+\tau)^{\gamma/(1-\gamma)}\omega^{1/(1-\gamma)} $$
where $ \Omega\equiv\Gamma/\phi^{1-\gamma}(\phi^{*})^{\gamma} $ . Using Shephard's lemma $ ^{8} $ , we obtain $ l_{z}(=z/\phi) $ and $ l_{z}^{*}(=z^{*}/\phi^{*}) $ from (2) and (26) as:

$$ l_{z}=(1-\gamma)\frac{1}{\theta}\Omega\big((1+\tau)f(\omega)\big)^{\gamma}y_{1}=(1-\gamma)\frac{1}{\theta}\Omega\big((1+\tau)f(\omega)\big)^{\gamma}\frac{\delta(\omega)}{p_{1}(\omega)}(e L+e^{*}L^{*}) $$

$$ l_{z}^{*}=\gamma\frac{1}{\theta}\Omega\frac{1}{\left((1+\tau)f(\omega)\right)^{1-\gamma}}y_{1}=\gamma\frac{1}{\theta}\Omega\frac{1}{\left((1+\tau)f(\omega)\right)^{1-\gamma}}\frac{\delta(\omega)}{p_{1}(\omega)}\left(eL+e^{*}L^{*}\right) $$

Furthermore, from (4) and (27), $ l_{y}^{*} $ is given by:

$$ {l_{y}}^{*}=\frac{1}{\theta^{*}}y_{2}=\frac{1-\delta(\omega)}{\theta^{*}p_{2}(\omega)}(e L+e^{*}L^{*}). $$

Since the money supply in each country is constant, from (24), the dynamics of m and $ m^{*} $ are represented by $ \dot{m}/m = -\pi $ , and $ \dot{m}^{*} / m^{*} = -\pi^{*} $ . Then, the foreign asset dynamics are obtained by substituting the dynamics of money into budget equations (9)-(10):

$$ \dot{b}=r b+w x+\zeta-e,\quad\dot{b}^{*}=r b^{*}+w^{*}x^{*}-e^{*}. $$

Expression (36) implies that total income (interest receipts, wage income and home government transfer) is devoted to expenditure and international assets holding.

### 3. Steady state with stagnation

We consider the case of persistent unemployment. Persistent stagnation that arises under a liquidity trap is analyzed by Ono (2001). $ ^{9} $ This section applies the models therein to the present setting.

Money demand is given by the second equality of (21):

$$ R=v^{\prime}(m)/u^{\prime}(c). $$

Along this curve, a liquidity trap arises if the desire for money holding is insatiable:
$$ \lim_{m\rightarrow\infty}\nu^{\prime}(m)=\beta>0, $$

where $ \beta $ is a positive constant. $ ^{10} $ Figure 1 illustrates the money demand curve in this case.

Now we present the steady-state conditions required for both the home and foreign countries to be in stagnation. The steady state with stagnation is fivefold $ (\omega, x, x^{*}, e, e^{*}) $ ^{[11]} The above definition means not only that the real and nominal rates of interest and the real exchange rate are fixed but also that e and $ e^{*} $ remain constant. In addition, the steady state with stagnation requires involuntary unemployment to exist, consequently causing nominal wages, nominal prices and the price level to continue to decline, and hence real balances to continue to increase. This is because

$$ \pi=\frac{\dot{P}_{1}}{P_{1}}=\frac{\dot{W}}{W}=\alpha(x-1),\quad\pi^{*}=\frac{\dot{P}_{2}^{*}}{P_{2}^{*}}=\frac{\dot{W}^{*}}{W^{*}}=\alpha^{*}(x^{*}-1) $$

hold in the steady state from (17), (30), and (31). $ ^{12} $ Hence the employment rate must satisfy 0 < x < 1 and $ 0 < x^{*} < 1 $ in the stagnation steady state, then $ v'(m) = \beta $ and $ v'(m^{*}) = \beta^{*} $ hold.

Moreover, because these remain constant, from (21) and (22), we obtain

$$ \boldsymbol{r}=\boldsymbol{r}^{*}=\boldsymbol{\uprho}. $$

Here, for simplicity, we specify the utility function for consumption as $ u(e) = \ln e $ . Then (21) and (22) are reduced to

$$ \beta e=\rho+\alpha(x-1),\quad\beta^{*}e^{*}=\rho+\alpha^{*}(x^{*}-1). $$

From (29), (32) and (33), x is given by

$$ x=\frac{1}{L}(1-\gamma)f(\omega;\tau)\frac{\delta(\omega)}{\theta^{*}p_{2}(\omega)}(e L+e^{*}L^{*}). $$

From (29), (32), (34) and (35), $ x^{*} $ is given by

$$ \boldsymbol{x}^{*}=\frac{1}{L^{*}}\bigg[\gamma\frac{\delta(\omega)}{1+\tau}+(1-\delta(\omega))\bigg]\frac{1}{\theta^{*}p_{2}(\omega)}(e L+e^{*}L^{*}). $$
Then, from the four equations in (40)-(42), e and $ e^{*} $ are determined as functions of $ \omega $ and $ \tau $ . The functions are implicitly derived in Appendix C.

Applying (23), (29) and (39) to the first equation of (36) yields the balance of payments condition as follows (see Appendix B):

$$ \dot{b}\;L=\rho b L+\delta e^{*}\boldsymbol{L}^{*}-(1-\delta)e\boldsymbol{L}-\boldsymbol{q}^{*}\boldsymbol{z}^{*}. $$

On the right-hand side of this equation, the first term denotes the return of holding international assets (the income account), the second term denotes real exports and the third term denotes real imports. $ ^{13} $ Finally, the last term represents real imports of intermediate goods for home goods production. Then, from (31), (34) and (40) – (42), $ \dot{b}L $ in (43) is rewritten as

$$ \dot{b}\;L=\;\rho bL\;-\frac{1}{\Psi}\frac{1}{\beta\beta^{*}}\Bigg[(\rho-\alpha)\Bigg(\beta^{*}-\alpha^{*}\Bigg\{\frac{\gamma\delta}{1+\tau}+1-\delta\Bigg\}\frac{1}{\theta^{*}p_{2}}\Bigg)L+(\rho-\alpha^{*})\alpha(1-\gamma)f(\omega;\tau)\frac{\delta}{\theta^{*}p_{2}}L^{*}\Bigg] $$

$$ +\left(1-\frac{\gamma}{1+\tau}\right)\delta\frac{1}{\Psi\beta\beta^{*}}\Big[(\rho-\alpha)\beta^{*}L+(\rho-\alpha^{*})\beta L^{*}\Big], $$

$$ where\Psi\equiv1-\frac{\alpha}{\beta}(1-\gamma)f(\omega;\tau)\frac{\delta}{\theta^{*}p_{2}}-\frac{\alpha^{*}}{\beta^{*}}\left\{\frac{\gamma\delta}{1+\tau}+1-\delta\right\}\frac{1}{\theta^{*}p_{2}}>0,\quad\rho>\alpha,\quad\rho>\alpha^{*}.^{14} $$

This function is assumed to satisfy

$$ \mathrm{Marshall--Lerner\ condition:}^{15}\ \partial(\dot{b}L)/\partial\omega\left(\equiv\Theta\right)>0. $$

where $ \Theta\left(>\;0\right) $ is defined as the coefficient of current account derivative by $ \omega $ . The relative price $ \omega $ takes the value at which $ \dot{b}L $ is zero, otherwise, the transversality condition is not satisfied. $ ^{16} $ Then the steady state obtains

$$ \dot{b}L=0. $$

Once $ \omega $ is thus determined, $ e, e^{*}, x $ and $ x^{*} $ are obtained from (40)–(42).
### 4. Tariffs, consumption and employment

In this section, we examine how an increase in the tariff on imported intermediate goods affects consumption and employment in both countries. The purpose of this paper is not to determine the desirable tariff level but to show how tariffs affect macroeconomic variables.

In the neighborhood of the steady state, the partial derivatives of the current account (44) satisfy the following relationship: $ ^{17} $

$$ \partial(\dot{b}L)/\partial\tau>0. $$

Thus, (45) and (46) imply

$$ \tau\uparrow\Rightarrow\omega\downarrow. $$

Figure 2 illustrates this property. The intuition is as follows. From the second term on the right-hand side of (44), given the steady-state level real relative price $ \omega $ , an increase in the tariff $ \tau $ decreases employment and consumption in the foreign country, whereas it increases employment and consumption in the home country. These effects cause the home country's current account to deteriorate. Conversely, from the last term on the right-hand side of (44), an increase in the tariff $ \tau $ directly lowers imports of intermediate goods from the foreign country, and this improves the current account of the home country. Although these are opposing effects on the current account, in Appendix E, we show that the latter effect exceeds the former. Hence, given $ \omega $ , an increase in $ \tau $ improves the home country's current account. $ ^{18} $ Then, from the Marshall–Lerner condition, real relative prices fall to cause a deterioration in the current account.

We now examine the impact of increased tariff on the consumption levels of both countries. From (40)–(42) (see Appendix C), we obtain consumption levels of $ e = e(\omega, \tau) $ and $ e^{*} = e^{*}(\omega, \tau) $ . Thus, the impact on consumption is

$$ d e(\omega,\tau)/d\tau=\underset{p r o t e c t i v e_{-}e f f e c t}{\partial e/\partial\tau}+(\underset{r e l a t i v e_{-}p r i c e_{-}e f f e c t}{/\partial e/\partial\omega})(d\omega/d\tau), $$

$$ d e^{*}(\omega,\tau)/d\tau=\underset{p r o t e c t i v e_{-}e f f e c t}{\partial e^{*}/\partial\tau}+(\underset{r e l a t i v e_{-}p r i c e_{-}e f f e c t}{\partial e^{*}/\partial\omega})(d\omega/d\tau). $$

In (48), because $ (\partial e/\partial\tau)>0 $ , the first effect, which is the ‘protective effect’, represents the increase in consumption following an increase in home employment that operates through
shifting production to the home country. In addition, because $ (\partial e/\partial \omega)(\mathrm{d}\omega/\mathrm{d}\tau)<0 $ , the second effect, the ‘relative price effect’, represents the decrease in consumption following the appreciation of the real exchange rate. The real exchange rate appreciates because of reduced outsourcing—which happens for the reason stated in the mechanism for (47)—and this causes the international relative price of the home commodity to rise. In turn, this decreases world demand for the production of home goods, and domestic employment and consumption decrease. Conversely, from (49), the direct effect decreases consumption, whereas the relative price effect increases it in the foreign country.

From (A8) and (A9) in Appendix C, the impact on e and $ e^{*} $ of an increase in the tariff evaluated at $ \tau=0 $ is explicitly given by

$$ d e/d\tau=-\gamma\alpha(\rho-\alpha^{*})(e L+e^{*}L^{*})(e/e^{*})\delta\Delta_{1}/[w\Theta(\Psi\beta\beta^{*})^{2}L]<0, $$

$$ d e^{*}/d\tau=\gamma\alpha^{*}(\rho-\alpha)(e L+e^{*}L^{*})\delta\Delta_{2}/(1-\gamma)[w^{*}\Theta(\Psi\beta\beta^{*})^{2}L^{*}]>0, $$

where $ \Delta_{1}\equiv(\gamma/(1-\gamma))/\omega+(-p_{1}')/p_{1}>0 $ and $ \Delta_{2}\equiv[(1-\delta(1-\gamma))/\delta]p_{2}'/p_{2}>0. $ ^{[19, 20]}

Furthermore, (40) shows that de/dx > 0 and de^{*}/dx^{*} > 0 in the steady state with stagnation. Therefore, the impact of an increase in $ \tau $ on the steady-state employment rate is as follows:

$$ \mathrm{sgn}\;dx/d\tau=\mathrm{sgn}\;de/d\tau,\quad\mathrm{sgn}\;dx^{*}/d\tau=\mathrm{sgn}\;de^{*}/d\tau. $$

This is formally stated in the following proposition.

PROPOSITION 1: When unemployment arises in the steady state, an increased tariff on imported outsourced goods in the home country causes an appreciation of the real exchange rate and lowers both employment and consumption in the home country. Conversely, an increased tariff raises both employment and consumption in the foreign country.

Thus, if the relative price $ \omega $ is fixed, an increased tariff on imported outsourced goods raises employment and effective demand in the home country and lowers these variables in the foreign country, as expected. However, because reduced imports, through an increased tariff, improve the current account, the real relative price falls, and this lowers the competitiveness of home products. Proposition 1 implies that the relative price effect is so strong that an increased
tariff in the home country decreases effective demand and employment at home, whereas an increased tariff raises effective demand and employment in the foreign country. Thus, a decrease in the tariff, which promotes outsourcing activity, boosts home employment and consumption.

### 5. Comparison with full employment

In this section, we analyze the case of full employment when there is no liquidity trap (because the demand for money holdings is satiable). We then compare the effect on consumption of an outsourcing shift caused by tariff imposition under full employment with the corresponding effect from the previous section under stagnation. We find that the effect under full employment is the opposite of that under stagnation.

Under full employment, x and $ x^{*} $ are unity, and hence, from (17), (23), (25), (29)–(33), (36) and (39), we obtain the following conditions in the steady state:

$$ \begin{aligned}e_{f}=[w(\omega;\tau)+(\tau/(1+\tau))\gamma\delta(\omega)(L^{*}/L)(w^{*}(\omega)+\rho b^{*})+\rho b]/[1-\gamma\delta(\omega)\tau/(1+\tau)]\\e_{f}^{*}=w^{*}(\omega)+\rho b^{*},\\\omega=\omega(\tau)\quad\Leftrightarrow(1-\gamma)\delta(\omega)(L+f(\omega;\tau)L^{*})/[1-\gamma\delta(\omega)\tau/(1+\tau)]=L,\end{aligned} $$

where $ e_{f} $ and $ e_{f}^{*} $ are the full-employment consumption levels of each country. $ ^{21} $ From the last of these equations, the impact of an increase in $ \tau $ on $ \omega $ evaluated at $ \tau=0 $ is given by

$$ \mathbf{d}\omega/\mathbf{d}\tau=-\gamma[(1-\gamma)\delta^{\prime}/\delta+(1-\delta(1-\gamma))/\omega]^{-1}<0. $$

From (17), the impact of an increased tariff on $ e_{f} $ and $ e_{f}^{*} $ evaluated at $ \tau=0 $ is as follows: $ ^{22} $

$$ \begin{align*}de_{f}/d\tau=&-w[(\gamma/(1-\gamma))/\omega+(-p_{1}^{\prime})/p_{1}](\mathrm{d}\omega/\mathrm{d}\tau)>0,\\&de_{f}^{*}/d\tau=w^{*}[p_{2}^{\prime}/p_{2}](\mathrm{d}\omega/\mathrm{d}\tau)<0,\end{align*} $$

Thus, when there is full employment in the steady state, an increased tariff on imported outsourced goods in the home country causes an appreciation of the real exchange rate and raises consumption in the home country. By contrast, such a tariff increase lowers consumption in the foreign country. Hence, we can state the following proposition.
PROPOSITION 2: When there is full employment in the steady state, the effect on consumption per capita of an increased tariff on imported outsourced goods is the exact opposite of the corresponding effect when there is unemployment in the steady state.

Intuitively, an increased tariff does not influence the employment rate because there is full employment. The effect of the tariff (shifting production from abroad to home) is to increase labor demand in the home market and reduce labor demand in the foreign market. Then, in the home market, an increase in labor demand leads to a rise in the wage rate through an appreciation of the real exchange rate. As a result of these effects, home country consumption increases. By contrast, in the foreign market, because a decrease in labor demand leads to a reduction in the wage rate, consumption decreases. Therefore, the effect of an increased tariff under full employment is the exact opposite of the corresponding effect when there is unemployment.

We can also interpret these results through the terms of trade. An appreciation of the real exchange rate following an increased tariff represents an improvement in the terms of trade $ (1/\omega) $ . Thus, in the full-employment case, the effect of an increased tariff is to increase the consumption per capita of the home country. This is equivalent to the standard optimal tariff result. On the other hand, because effective demand determines production under stagnation, an appreciation of the real exchange rate has a negative effect on the demand for home goods, which lowers the consumption per capita of the home country.

### 6. Conclusion

In this paper, we developed a two-country model of international trade incorporating outsourcing opportunities in which persistent unemployment arises. We then analyzed the effects of tariffs on employment and effective demand in both the home and foreign countries. We found that a production shift from the foreign to the home country following the imposition of an increased tariff on imported outsourced goods lowers home-country employment and consumption. However, the two countries respond in opposite ways to the production shift caused by outsourcing and to real exchange rate adjustment. Consequently, a tariff increase raises employment and consumption in the foreign country.

The mechanism is as follows. A tariff increase raises employment in the home country but also causes an appreciation of the real exchange rate. The latter effect occurs because a tariff increase lowers imports of intermediate goods from the foreign country and thus improves the current account. So that current account balance is restored, the home currency
appreciates against the foreign currency, which raises the international relative price of the home commodity. This price increase lowers world demand for domestic production. Because the latter effect, which operates through the appreciation of the real exchange rate, outweighs the former effect, both employment and effective demand in the home country decrease. By contrast, because the foreign country’s international relative price falls, world demand for foreign production rises. Therefore, an increased tariff in the home country increases both employment and effective demand in the foreign country.