Parameter values.

## Abstract

A large body of literature in international economics has tried to explain the effect of asymmetric changes in trade barriers in welfare of the liberalizing country, however, there is no consensus on this issue. In this paper, I focus on the implications of a decline in import costs in welfare of the liberalizing country. I utilize a version of computational general equilibrium model of international trade (based on Armington assumption) where countries are potentially asymmetric in terms of labor endowment, productivity, trade barriers etc. under two different specifications of trade costs: (i) standard iceberg cost formulation and (ii) tariffs. The model numerically proves that unilateral trade liberalization is welfare improving for the liberalizing country in Armington setup with iceberg costs. However, when using tariffs, I numerically show that there exists a positive optimal tariff rate which maximizes welfare. This result indicates that a reduction in tariffs may either benefit or immiserize the liberalizing country depending on the pre-liberalization value of tariff. In the literature, a simple formula has been driven which shows the gains from trade for the case of iceberg costs. I generalize this formula in Armington setup with tariffs and highlight the importance of revenue generating tariffs.

### Keywords

- unilateral trade liberalization
- iceberg costs
- tariffs
- computational general equilibrium
- welfare

## 1. Introduction

In this paper, I focus on the implications of a decline in import costs (in terms of both iceberg costs and tariffs) in welfare[1] - of the liberalizing country. There is a vast literature on the effect of asymmetric changes in trade costs in welfare of the liberalizing country; however, there is no consensus on this issue. Moreover, Eaton and Kortum (2002) [1] derive a simple formula which shows the gains from trade and this formula is generalized by Arkolakis, Costinot, and Rodriguez-Clare (2012) [2] in the case of iceberg costs. I also generalize this formula in Armington setup with tariffs and highlight the importance of revenue generating tariffs.

In Melitz [3] setup with two large but possibly asymmetric economies, unilateral trade liberalization in terms of iceberg costs is welfare improving for the liberalizing country. Similarly, in a version of the Melitz [3] model for the case of a small economy, Demidova and Rodriguez-Clare [4] also establish that welfare increases for a country that unilaterally reduces importing trade barriers in terms of iceberg costs.

These results stand in sharp contrast to two different types of models. In the first category, Felbermayr and Jung [5] show that in a two-country Melitz [3] setup, unilateral liberalization of import tariffs lowers welfare of the liberalizing country. Demidova and Rodriguez-Clare [6] also show the existence of an optimal tariff in the small economy version of the Melitz [3] model suggesting that reduction in tariffs (compared to optimal level) lowers the welfare in the liberalizing country. As mentioned in [5], the reason behind this argument is that tariffs redistribute income across countries and this generates additional leverage to the selection effect in the models with firm-level heterogeneity.

In the second category, including [7–9], trade liberalization in home country results in a welfare loss. In this category, the difference arises from the presence of an outside sector that pins down the wages. However, these setups with outside sector ignore the general equilibrium forces that are crucial for the welfare analysis. Therefore, Demidova [7], Melitz and Ottaviano [8], Ossa [9] predict immiserization for the liberalizing country due to unilateral trade liberalization. Felbermayr and Jung [5] also point out that the assumption of a linear outside sector distorts the welfare predictions of the model: In a Melitz and Ottaviano [8] setup (due to a reduction in import costs), firms in liberalizing country relocate into the relatively more protected market (outside sector) from where they serve the liberalized economy. However, in Melitz [3] (without an outside sector) setup with Pareto assumption,[1] - the wage adjustment is exactly such that the relocation channel is compensated.

This paper utilizes a version of computational general equilibrium model of international trade (based on Armington assumption) where countries are possibly asymmetric in terms of labor endowment, productivity, trade costs, etc., under two different specifications: iceberg costs and tariffs. This paper aims to compute the effects of unilateral trade liberalization in welfare of the liberalizing country in both specifications. To achieve this goal, I follow two main steps for each version. I first define and characterize the general equilibrium. In other words, I obtain a system of nonlinear equations which should be solved numerically. Second, after determining the parameters, I compute the equilibrium with numerical methods (using MATLAB). The model numerically proves that unilateral trade liberalization is welfare improving for the liberalizing country in Armington setup with iceberg costs. However, with tariffs, I numerically show that there exists a positive optimal tariff rate which maximizes welfare suggesting that a reduction in tariffs may either increase or decrease welfare of the liberalizing country depending on the pre-liberalization value of tariff.

This paper also discusses the extensions of a simple formula which is first derived by Eaton and Kortum [1] and then generalized by Arkolakis et al. [2]. These papers focus on welfare gains from trade relative to autarky in the case of iceberg costs. I generalize this formula in Armington setup with tariffs and highlight the important difference between these two formulas.

The next section presents two specifications of the model and characterizes the equilibrium for each case. Section 3 discusses the results of the numerical computations. Section 4 analytically analyzes the welfare gains from trade. Finally, Section 5 concludes.

## 2. Model

I utilize a version of Armington model [11–13] with two different specifications. In the first specification, I assume that trade costs are in terms of standard iceberg formulation. However, in the second case, I assume that trade costs are in terms of tariffs and tariff revenue is redistributed to the consumers in a lump-sum fashion. In both versions, there are

### 2.1. Model with iceberg costs

#### 2.1.1. Demand

Country

where

where

The utility maximization subject to the budget constraint yields the following demand function of country *j* toward goods produced in *i*:

where

Using Eq. (4), I simply get

#### 2.1.2. Supply

Goods are produced in competitive markets. Labor is the only factor of production. In country

The profit maximization of a representative producer in country

The profit maximization in competitive markets yields the following price rule:

#### 2.1.3. Equilibrium conditions

In order to fully characterize the equilibrium, one needs two more conditions. I first consider the labor market clearing condition. This condition implies that labor supply has to be equal to the total labor demand in country *i*. Hence, labor market clearing condition for country *i* can be written as:

Second equilibrium condition is the balanced trade condition. This condition implies that the value of total imports has to be equal to the value of total exports of country

#### 2.1.4. Characterization of equilibrium

The equilibrium is characterized by

However, the given system has twelve unknown variables: eight prices (

Given the value of parameters and price normalization, one has to solve for three prices (

### 2.2. Model with tariffs

#### 2.2.1. Demand

Now, I assume that trade barriers are in terms of tariffs rather than iceberg trade costs. In this setup, tariff revenue from imports is redistributed to the consumers in a lump-sum fashion. The only change in country *j*’s utility maximization problem is the budget constraint:

where

The utility maximization subject to this new budget constraint yields the following demand equation:

where

#### 2.2.2. Supply

The only change in firm’s problem is that

#### 2.2.3. Equilibrium conditions

In order to fully characterize the equilibrium, one needs three conditions: labor market clearing condition, the balanced trade condition and the tariff revenue that has to be fully redistributed to the consumers.

Labor market clearing implies that labor supply in country has to be equal to the total labor demand in country

Note that in contrast to the iceberg formulation, there are no additional production and employment for tariffs. Second equilibrium condition is the balanced trade condition. This condition implies that the value of total imports has to be equal to the value of total exports of country

where dividing by

Finally, tariff revenue in country

#### 2.2.4. Characterization of equilibrium

Consider a two-country

Given the value of parameters and price normalization, one has to solve for three prices (

## 3. Numerical exercises: unilateral trade liberalization

### 3.1. Iceberg costs

Consider two symmetric countries: home (country 1) and foreign (country 2). Main goal of this section is to compute the effects of unilateral trade liberalization (at home) in welfare. In a benchmark model, I assume that

Benchmark model | Counterfactual analysis | |
---|---|---|

1 | 1 | |

1 | 1 | |

1 | 1 | |

1 | 1 | |

8 | 8 | |

0.6 | 0.6 | |

0.4 | 0.4 | |

0.4 | 0.4 | |

0.6 | 0.6 | |

1 | 1 | |

1.2 | 1.2 | |

1.2 | 1 | |

1 | 1 |

For the trade elasticity, I follow Anderson and Van Wincoop [14]. Anderson and Van Wincoop [14] suggest that the value for trade elasticity (

Table 2 presents the computation results of both exercises: benchmark model and counterfactual analysis.

Benchmark model (I) | Counterfactual analysis (II) | (II)/(I) | |
---|---|---|---|

1 | 0.9202 | 0.9202 | |

1.2 | 1.1043 | 0.9202 | |

1.2 | 1 | 0.8333 | |

1 | 1 | 1 | |

1 | 0.9202 | 0.9202 | |

1 | 1 | 1 | |

1.0498 | 0.9461 | 0.9012 | |

1.0498 | 1.0324 | 0.9834 | |

Welfare_{1} | 0.9526 | 0.9726 | 1.0210 |

Welfare_{2} | 0.9526 | 0.9686 | 1.0167 |

Exports/GDP_{1} | 15.69% | 27.14% | 1.7297 |

Imports/GDP_{1} | 15.69% | 27.14% | 1.7297 |

Exports/GDP_{2} | 15.69% | 24.98% | 1.5920 |

Imports/GDP_{2} | 15.69% | 24.98% | 1.5920 |

Computation results in Table 2 imply that unilateral reduction in iceberg costs in country 1 increases the welfare in country 1. The mechanism is as follows: A decrease in import trade barriers in country 1 reduces the price of the imported good in country 1 which yields an increase in imports from country 2. To restore trade balance nominal wages in country should fall and this causes a decline in the price of domestic goods. The reduction in both prices (domestic and import) yields a reduction in aggregate price index in country 1 as well. The decrease in price index dominates the decrease in nominal wages and therefore, real income (welfare) in country 1 is increasing. Moreover, the unilateral reduction in iceberg costs in country 1 causes an increase in real income of country 2. However, the increase in country 2 is smaller than the increase in country 1.

Figure 1 depicts the welfare changes associated with unilateral trade liberalization (in terms of iceberg costs) in country 1 keeping

In Figure 1, I conclude that trade liberalization (in the case of iceberg costs) monotonically increases the welfare of the liberalizing country.

### 3.2. Tariffs

Using the same parameters in Table 1 for the benchmark and counterfactual analyses, Table 3 presents the computation results of both exercises in the case of tariffs. Exports and imports values are presented in both ways (inclusive and exclusive in tariffs).

Benchmark model (I) | Counterfactual analysis (II) | (II)/(I) | |
---|---|---|---|

1 | 0.9092 | 0.9092 | |

1.2 | 1.0910 | 0.9091 | |

1.2 | 1 | 0.8333 | |

1 | 1 | 1 | |

1 | 0.9092 | 0.9092 | |

1 | 1 | 1 | |

1.0498 | 0.9377 | 0.8932 | |

1.0498 | 1.0292 | 0.9803 | |

Welfare_{1} | 0.9781 | 0.9696 | 0.9913 |

Welfare_{2} | 0.9781 | 1.0167 | 1.0394 |

Exports/GDP_{1} | 13.07% | 25.51% | 1.9517 |

Imports/GDP_{1} | 13.07% | 25.51% | 1.9517 |

Exports/GDP_{2} | 13.07% | 22.16% | 1.6954 |

Imports/GDP_{2} | 13.07% | 22.16% | 1.6954 |

Exports/GDP_{1}* | 15.68% | 25.51% | 1.6269 |

Imports/GDP_{1}* | 15.68% | 25.51% | 1.6269 |

Exports/GDP_{2}* | 15.68% | 22.16% | 1.4132 |

Imports/GDP_{2}* | 15.68% | 22.16% | 1.4132 |

Tariff revenue_{1} | 0.0268 | 0 | 0 |

Tariff revenue_{2} | 0.0268 | 0.0464 | 1.7313 |

Tariff revenue_{1}/GDP_{1} | 2.61% | 0% | 0 |

Tariff revenue_{2}/GDP_{2} | 2.61% | 4.43% | 1.6973 |

Tariff multiplier_{1} | 1.0268 | 1 | 0.9738 |

Tariff multiplier_{2} | 1.0268 | 1.0464 | 1.0190 |

In contrast to the iceberg cost formulation, unilateral trade liberalization causes a welfare loss in the liberalizing country 1. However, this result depends on pre-liberalization value of tariffs. Figure 2 shows the welfare changes associated with unilateral trade liberalization in country 1 (in terms of tariffs) keeping

Figure 2 also implies that there exists an optimal positive tariff rate (which maximizes welfare) which is around 20% in our case.

### 3.3. Discussion: iceberg costs versus tariffs

Numerical solutions suggest that in Armington setup, iceberg cost and tariff formulations give the different welfare implications. Therefore, the type of trade barrier plays a crucial role in computing the welfare gains due to trade liberalization. This result can be generalized (see [1, 3, 15, 16] for details).

Similar to my findings, Felbermayr and Jung [5] show that in a two-country Melitz [3] setup, unilateral liberalization of import tariffs lowers welfare of the liberalizing country. Demidova and Rodriguez-Clare [6] also show the existence of an optimal tariff in the small economy version of the Melitz [3] model, suggesting that reduction in tariffs (compared to optimal level) lowers the welfare in liberalizing country.

## 4. Gains from trade: welfare analysis

Eaton and Kortum [1] show that welfare gains from trade are function of only two elements in the case of iceberg costs: (i) the share of expenditure on domestic goods, which is equal to one minus the import penetration ratio and (ii) trade elasticity (an elasticity of imports with respect to variable iceberg trade costs). This result is generalized by Arkolakis et al. [2] for a large class of trade models, including the one used in this paper (version of Armington model), Eaton and Kortum [1], Krugman [15] and Melitzs [3] models in the case of iceberg costs.[1] - This generalized result implies that although recent quantitative trade models can explain a wider set of micro-level facts, all type of models mentioned above calculate the exact same amount of gains from trade in the case of iceberg costs. In summary, welfare gains from trade liberalization do not depend on the different models microstructure.[1] -

However, this paper argues that the result generalized by Arkolakis et al. [2] is only true in the case of iceberg costs, but not in the tariff formulation, since the formula generalized by Arkolakis et al. [2] ignores the tariff redistribution.

Section 4.1 derives the simple formula which is generalized by Arkolakis et al. [2] in the case of iceberg costs. Section 4.2 extends the simple formula in the case of tariffs and highlights the important difference between two formulas.

### 4.1. Simple formula for the gains from trade: iceberg cost formulation

Arkolakis et al. [2] generalized a simple formula for the gains from trade for a large set of trade models including Armington [11], Krugman [15], Eaton and Kortum [1] and Melitz [3] models in the case of iceberg costs. In order to compute the gains from trade by this simple formula, one only needs two elements: (i) the share of expenditure on domestic goods (

Using our model in Section 3, let’s first show that trade elasticity (elasticity of imports with respect to iceberg costs) which is defined as

For the first step, let’s write the equation for imports of country

Let’s multiply both sides by

Let’s derive

Taking the natural logarithm of both sides of Eq. (40), I obtain:

By using Eq. (41), after the simple math, I get:

Hence, the trade elasticity (elasticity of imports with respect to iceberg costs) is equal to one minus elasticity of substitution across good varieties.

For the second step, I use the definition

After solving for

For the final step, let’s define welfare in country j,

Finally, by substituting

Welfare gains from trade can be shown as the change in welfare before and after trade:

where

Let’s apply our formula to the numerical exercise in Section 3.1 for country 1. 0.1569 and 0.2714 are the share of imports to GDP before and after unilateral trade liberalization (reduction in

National income in country 1 increased by 2.1% due to unilateral trade liberalization which is the same result I obtain in Table 2.

### 4.2. Simple formula for the gains from trade: tariff formulation

This section extends the simple formula derived by Arkolakis et al. [2]. In this section, I assume that trade barriers are in the form of tariffs rather than iceberg costs. In order to compute the gains from trade by the extended formula, one needs three elements rather than two: (i) the share of expenditure on domestic goods (

Applying the similar steps with the previous section (the case of iceberg costs), I obtain the same equation for

However, in the case of tariff, total income in country j is *j*. By definition, I have:

Multiplying RHS by

Since I know that

Hence, I have:

where

Finally, by substituting

Welfare gains from trade can be shown as the change in welfare before and after trade:

where

Let’s apply our formula to the numerical exercise in Section 3.2 for country 1. 0.1568 and 0.2551 are the share of imports to GDP (inclusive of tariffs) before and after unilateral trade liberalization (reduction in

National income in country 1 decreased due to unilateral trade liberalization which is the same result I obtain in Table 3.

## 5. Conclusion

Although there is a fairly sizable literature in international trade, there is no general agreement on the implications of unilateral trade liberalization in welfare of the liberalizing country. This paper studies the effects of a decline in import costs (in terms of both iceberg cost and tariffs) in welfare of the liberalizing country. Based on Armington model, I numerically show that unilateral trade liberalization is welfare improving for the liberalizing country in the case of iceberg costs. However, in the tariff case, I numerically show that there exists a positive optimal tariff rate which maximizes welfare, suggesting that a reduction in tariffs may either increases or decreases welfare of liberalizing country depending on the pre-liberalization value of tariff.

Moreover, this paper also discusses the welfare gains from trade with a simple equation which is derived by Eaton and Kortum [1] and generalized by Arkolakis et al. [2] in the case of iceberg costs. I generalize this formula in Armington setup with tariffs and highlight the importance of revenue-generating tariffs.

## Notes

- Given the class of models considered in this study, I use the terms welfare and real income interchangeably throughout the paper.
- This distributional assumption is widely used in the literature. Besides the analytical convenience of this distribution, Eaton et al. [10], among others, document that this distribution provides a reasonable approximation for the observed distribution of firm sizes.
- This result is proven in Section 4.
- The Frechet and the Parteo distributions are considered for productivities in Eaton and Kortum [1] and Melitz [3] frameworks, respectively.
- Arkolakis et al. [2] discuss some extensions of their result. Adding multiple sectors, tradable intermediate goods or multiple factors of production into the model can change the validity of their result. In particular, Balistreri et al. [17] add a second non-tradable sector and they show that models with perfect and monopolistic competition no longer have the same welfare implications.