Optimal Trade Policy in a Ricardian Model with Labor-Market Search-and-Matching Frictions

Wisarut Suwanprasert

doi:10.1515/bejte-2023-0120

Article

Optimal Trade Policy in a Ricardian Model with Labor-Market Search-and-Matching Frictions

Wisarut Suwanprasert

Published/Copyright: December 3, 2024

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From the journal The B.E. Journal of Theoretical Economics Volume 24 Issue 2

Abstract

I develop a dynamic general-equilibrium model that combines the Diamond–Mortensen–Pissarides labor market with the standard Ricardian model of international trade to investigate the potential role of unemployment as a justification for trade policy implementation. First, I compare a competitive equilibrium and a constrained-efficient equilibrium and then establish the condition in which the competitive equilibrium is constrained-efficient. Second, I show that free trade is optimal only when labor market inefficiency is absent. A small open economy may employ expansionary trade policies (such as export subsidies or reduced import tariffs) if it experiences inefficiently high unemployment. This study provides a rationale behind countries’ tendency to use export subsidies.

Keywords: optimal trade policy; unemployment; Ricardian model; labor market; search-and-matching frictions; export subsidy

JEL Classification: F13; F16; J64

Corresponding author: Wisarut Suwanprasert, Department of Economics and Finance, Middle Tennessee State University, MTSU Box 27, Murfreesboro, TN 37132, USA, E-mail: Wisarut.Suwanprasert@mtsu.edu

This paper is based on a chapter of my Ph.D. dissertation. I am deeply grateful to Robert Staiger for his invaluable guidance and constant support. I also thank Kamran Bilir, Charles Engel, John Kennan, Thomas Rutherford, Rasmus Lentz, Eric Bond, Kittichai Saelee, and Ohyun Kwon for insightful conversations. I would like to thank editor Daniela Puzzello and the anonymous reviewers for very useful and insightful comments. I have benefited from discussions with seminar participants at Vanderbilt University, Thammasat University, Puey Ungphakorn Institute for Economic Research (PIER), the American Economics Association conference (2019), the Eastern Economics Association conference (2018), the European Trade Study Group (ETSG 2017) conference, and the Midwest International Trade conference (2016). All remaining errors are mine.

A Appendix

A.1 Proof of Lemma 1

Lemma 1:

The elasticities of market tightness with respect to p _x and p _y are

d log θ x d log p x = 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ > 0 , d log θ x d log p y = − 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ < 0 .

Proof. First, I can rearrange the terms in equation (20) as follows:

(31) m θ i λ − 1 β S i + θ i p V ρ + δ + m θ i λ = p V m θ i λ − 1 β S i ρ + δ + m θ i λ = p V 1 − β m θ i λ ρ + δ + m θ i λ m θ i λ − 1 β S i p V = ρ + δ + 1 − β m θ i λ

Second, combining p V = χ 1 + τ x p x α 1 + τ y p y 1 − α in equation (4) and s _x = p _x h _x leads to

d log S x p V d log p x = 1 − α d log S x p V d log p y = − 1 − α .

Third, the derivative can be calculated as follows:

m θ x λ − 1 β S x p V = ρ + δ + 1 − β m θ x λ λ − 1 d log θ x d log p x + d log S x p V d log p x = 1 − β m θ x λ ρ + δ + 1 − β m θ x λ λ d log θ x d log p x 1 − α = 1 − ρ + δ ρ + δ + 1 − β m θ x λ λ d log θ x d log p x

Therefore,

d log θ x d log p x = 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ > 0 .

Similarly,

m θ x λ − 1 β S x p V = ρ + δ + 1 − β m θ x λ λ − 1 d log θ x d log p y + d log S x p V d log p y = 1 − β m θ x λ ρ + δ + 1 − β m θ x λ λ d log θ x d log p y − 1 − α = 1 − ρ + δ ρ + δ + 1 − β m θ x λ λ d log θ x d log p y

Therefore,

d log θ x d log p y = − 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ < 0 .

□

A.2 Social Planner’s Problem

In this perfect world, where consumers have access to borrowing and lending at risk-free interest rates, they can smooth consumption over time in accordance with their lifetime budget constraint. Therefore, the social planner’s utility maximization problem is equivalent to an income maximization problem.

The social planner’s income maximization problem can be written formally as follows:

(32) ρ G u x , u y , p x , p y = max L x , L y , θ x , θ y , x c , y c p x X s + p y Y s − χ p x x c + p y y c θ x u x L x + θ y u y L y p x α p y 1 − α + ∂ G ∂ u x u ̇ x + ∂ G ∂ u y u ̇ y

(33) s.t. u ̇ i = δ 1 − u i − m θ i λ u i X s = h x 1 − u x L x Y s = h y 1 − u y L y L = L x + L y 1 = x c α y c 1 − α α α 1 − α 1 − α θ i ≥ 0

The Lagrangian equation associated with the income maximization problem is

L = p x h x 1 − u x L x + p y h y 1 − u y L y − χ p x x c + p y y c θ x u x L x + θ y u y L y p x α p y 1 − α + ∂ G ∂ u x δ 1 − u x − m θ x λ u x + ∂ G ∂ u y δ 1 − u y − m θ y λ u y + μ 1 L − L x − L y + μ 2 x c α y c 1 − α α α 1 − α 1 − α − 1 + μ 3 θ x + μ 4 θ y .

The first-order conditions are

(34) L x p x h x 1 − u x − χ p x x c + p y y c θ x u x − μ 1 = 0

(35) L y p y h y 1 − u y − χ p x x c + p y y c θ y u y − μ 1 = 0

(36) θ x − χ p x x c + p y y c u x L x + ∂ G ∂ u x − λ m θ x λ − 1 u x + μ 3 = 0

(37) θ y − χ p x x c + p y y c u y L y + ∂ G ∂ u y − λ m θ y λ − 1 u y + μ 4 = 0

(38) x c − χ p x θ x u x L x + θ y u y L y + μ 2 α x c α − 1 y c 1 − α α α 1 − α 1 − α = 0

(39) y c − χ p y θ x u x L x + θ y u y L y + μ 2 x c α 1 − α y c − α α α 1 − α 1 − α = 0

The envelope theorem implies that

(40) ρ ∂ G ∂ u x = − p x h x L x − χ p x x c + p y y c θ x L x + ∂ G ∂ u x − δ − m θ x λ

(41) ρ ∂ G ∂ u y = − p y h y L y − χ p x x c + p y y c θ y L y + ∂ G ∂ u y − δ − m θ y λ

The constraints are

(42) x c α y c 1 − α α α 1 − α 1 − α = 1

(43) L x + L y = L

(44) μ 3 θ x = 0

(45) μ 4 θ y = 0

First, I use equations (38), (39) and (42) to solve for x ^c and y ^c as

x c = α p x α − 1 p y 1 − α y c = 1 − α p x α p y − α .

Let’s define p V = χ p x x c + p y y c as the vacancy cost. Thus, from x ^c and y ^c calculated above, p V = χ p x α p y 1 − α .

Substitute p V = χ p x x c + p y y c into equations (40) and (41),

(46) ρ ∂ G ∂ u x = − p x h x L x − p V θ x L x + ∂ G ∂ u x − δ − m θ x λ

(47) ρ ∂ G ∂ u y = − p y h y L y − p V θ y L y + ∂ G ∂ u y − δ − m θ y λ

To be consistent with the definitions in equations (1) and (2), in this social planner’s problem, I also define S _x = p _x h _x and S _y = p _y h _y as the match surpluses in sectors X and Y, respectively.

From equations (40) and (41),

(48) ∂ G ∂ u x = − S x L x − p V θ x L x ρ + δ + m θ x λ

(49) ∂ G ∂ u y = − S y L y − p V θ y L y ρ + δ + m θ y λ

Substituting equations (48) and (49) into equations (36) and (37) gives

(50) − p v u x L x + − S x L x − p V θ x L x ρ + δ + m θ x λ − λ m θ x λ − 1 u x + μ 3 = 0

(51) − p v u y L y + − S y L y − p V θ y L y ρ + δ + m θ y λ − λ m θ y λ − 1 u y + μ 4 = 0 .

These equations are simplified to

λ m θ x λ − 1 S x + θ x p V ρ + δ + m θ x λ + μ 3 = p V λ m θ y λ − 1 S y + θ y p V ρ + δ + m θ y λ + μ 4 = p V

which lead to equation (27) in the main text. They can be re-arranged as

λ m θ x λ S x = θ x p V ρ + δ + 1 − λ m θ x λ − μ 3 ρ + δ + m θ x λ λ m θ y λ S y = θ y p V ρ + δ + 1 − λ m θ y λ − μ 4 ρ + δ + m θ y λ

Next, I use the definitions of S _i and p _V to simplify equations (34) and (35):

(52) S i 1 − u i − p V θ i u i = μ 1 .

We substitute the steady state level of unemployment u i = δ δ + m θ i λ in equation (52) and get

(53) S i m θ i λ δ + m θ i λ − p V θ i δ δ + m θ i λ = μ 1 .

We substitute S _i in equations (50) and (51) into equation (53) and simplify the terms to

p V θ x λ δ + m θ x λ ρ + 1 − λ δ + m θ x λ − μ 3 ρ + δ + m θ x λ = μ 1 p V θ y λ δ + m θ y i λ ρ + 1 − λ δ + m θ y λ − μ 4 ρ + δ + m θ y λ = μ 1

We will consider three possible cases: (i) both cases are active, (ii) only sector x is active, and (iii) only sector y is active.

Both sectors are active.

In this case, we have that θ _x > 0 and θ _y > 0 which conclude that μ ₃ = 0 and μ ₄ = 0. Since this expression holds for both i = x, y, we have that

p V θ x λ δ + m θ x λ ρ + 1 − λ δ + m θ x λ = p V θ y λ δ + m θ y λ ρ + 1 − λ δ + m θ y λ .

Consider the function

h z = p V z λ δ + m z λ ρ + 1 − λ δ + m z λ .

We can show that h z is strictly increasing and, hence, is one-to-one. Therefore, h θ x = h θ y implies θ _x = θ _y = θ.

Given that θ _x = θ _y = θ, equation (53) leads to

m θ λ δ + m θ λ S x − p V θ δ δ + m θ λ = μ 1 = m θ λ δ + m θ λ S y − p V θ δ δ + m θ λ .

This implies that S _x = S _y = S or, equivalently,

(54) p x h x = p y h y .

Only sector x is active

When only sector x is active, we have that θ _x > 0 and L _x > 0. Because sector y is inactive, then θ _y = 0 and L _y = 0. This implies that S _x > S _y or, equivalently, p _x h _x > p _y h _y.

Only sector y is active

A similar argument to that of the previous case shows that the parameters must satisfy S _x > S _y or p _x h _x < p _y h _y.

A.3 Proof of Lemma 2

Lemma 2:

A competitive equilibrium coincides with a constrained-efficient equilibrium if and only if λ = β and τ = 0.

Proof. First, when we compare the constraints of the competitive equilibrium in Section 3.1 and the constraints of a constrained-efficient equilibrium in Appendix A.2, we can conclude that τ must be zero. That is, price distortions must not exist. Second, the two equilibria are identical only if equations (20) and (27) are equivalent. This implies λ = β. □

A.4 Proof of Lemma 3

Lemma 3:

The derivative d W / d log τ x is

d W d log τ x = 1 − α 1 + τ x − 1 − α 1 − α 1 + τ x + α 1 + τ x 1 − α 1 − α 1 + τ x + α × p x p y 1 − α h x 1 − u x L x τ x + − u x L x + 1 + τ x 1 − α 1 − α 1 + τ x + α p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ λ m θ x λ − 1 u x × d θ x d log τ x .

Proof. From equation (24), the Bellman equation for social welfare is

ρ W = p X s + Y s − p V V P p x , p y , τ x , τ y + ∂ W ∂ u x u ̇ x + ∂ W ∂ u y u ̇ y , s.t. u ̇ i = δ 1 − u i + m θ λ u i

where P p x , p y , τ x , 0 = α + 1 − α 1 + τ x 1 + τ x 1 − α p x α p y 1 − α . From the fact that p V = χ 1 − α 1 + τ x + α 1 + τ x 1 − α p x α p y 1 − α and Y ^S = 0, the Bellman equation is modified to

ρ W = 1 + τ x 1 − α 1 − α 1 + τ x + α p x p y 1 − α h x 1 − u x L x − χ V + ∂ W ∂ u x u ̇ x + ∂ W ∂ u y u ̇ y , s.t. u ̇ x = δ 1 − u x + m θ x λ u x

The envelope theorem implies that

d W d τ x = 1 − α 1 + τ x − 1 − α 1 − α 1 + τ x + α 1 + τ x 1 − α 1 − α 1 + τ x + α × p x p y 1 − α h x 1 − u x L x + − u x L x + ∂ W ∂ u x − λ m θ x λ − 1 u x d θ x d τ x + ∂ W ∂ u y − λ m θ y λ − 1 u y d θ y d τ x + ∂ 2 W ∂ u x ∂ τ u ̇ x τ x + ∂ 2 W ∂ u y ∂ τ u ̇ y τ x , ρ ∂ W ∂ u x = − 1 + τ x 1 − α 1 − α 1 + τ x + α p x p y 1 − α h x L x − θ x L x + ∂ W ∂ u x − δ − m θ x λ ,

which lead to

(55) ∂ W ∂ u x = − 1 + τ x 1 − α 1 − α 1 + τ x + α p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ ,

In the steady state, we have u _x = u, θ _x = θ, S _x = S, u ̇ x = u ̇ y = 0 . Substituting ∂W/∂u _x in equations (55) into dW/dτ _x gives

d W d log τ x = 1 − α 1 + τ x − 1 − α 1 − α 1 + τ x + α 1 + τ x 1 − α 1 − α 1 + τ x + α × p x p y 1 − α h x 1 − u x L x τ x + − u x L x + 1 + τ x 1 − α 1 − α 1 + τ x + α p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ λ m θ x λ − 1 u x × d θ x d log τ x

□

A.5 Proof of Proposition 1.

Proposition 1:

The derivative of welfare with respect to τ _x evaluated at τ _x = 0 is

d W d log τ x τ x = 0 = λ − β β u x L x θ x χ 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ .

Proof. The value of the derivative d W d log τ x at τ _x = 0 is

d W d log τ x τ x = 0 = − u x L x + p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ λ m θ x λ − 1 u x d θ x d log τ x

Using the free-entry condition p V = m θ x λ − 1 β S x + θ x p V ρ + δ + m θ x λ in equation (20) to simplify the equation to

d W d log τ x τ x = 0 = u x L x χ λ β − 1 d θ x d log τ x = λ − β β u x L x θ x χ 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ ,

where the last step uses

d θ x d log τ x = 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ θ x .

□

A.6 Proof of Corollary 1.

Corollary 1:

Beginning at free trade, an export policy can improve a country’s welfare if λ ≠ β , and free trade is the optimal trade policy if λ = β.

Proof. When λ = β, d W / d log τ x τ x = 0 = 0 . Since the welfare function is strictly concave in τ _x, it follows that τ _x = 0 is a global maximum; free trade is the optimal trade policy. When λ ≠ β, we have that d W / d log τ x τ x = 0 ≠ 0 . Therefore, the government can improve the welfare of the country by slightly increasing τ _x if d W / d log τ x τ x = 0 > 0 or slightly decreasing τ _x if d W / d log τ x τ x = 0 < 0 . □

A.7 Proof of Proposition 2

Proposition 2:

In the Ricardian model, the optimal export subsidy τ x * has the same sign as the sign of λ − β.

Proof. Because the welfare function is strictly concave, dW/dτ _x is strictly decreasing in τ _x. When λ − β > 0, we have d W / d log τ x τ x = 0 > 0 = d W / d log τ x τ x = τ * , implying that the optimal export subsidy is positive, τ x * > 0 . In contrast, when λ − β < 0, we have d W / d log τ x τ x = 0 < 0 = d W / d log τ x τ x = τ * , leading to the conclusion that the optimal export subsidy is negative, τ x * < 0 . □

A.8 Proof of Lemma 4.

Lemma 4:

The derivative d W / d log τ y is

d W d log τ y = α 1 + τ y − α 1 − α + α 1 + τ y 1 + τ y α 1 − α + α 1 + τ y × p x p y 1 − α h x 1 − u x L x τ y + − u x L x + 1 + τ y α 1 − α + α 1 + τ y p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ λ m θ x λ − 1 u x d θ x d log τ y .

Proof. From equation (24), the Bellman equation for social welfare is

ρ W = p X s + Y s − p V V P p , τ + ∂ W ∂ u x u ̇ x + ∂ W ∂ u y u ̇ y , s.t. u ̇ i = δ 1 − u i + m θ λ u i

where P p x , p y , 0 , τ y = α 1 + τ y + 1 − α 1 + τ y α p x α p y 1 − α . From the fact that p V = χ 1 − α + α 1 + τ y 1 + τ y α p x α p y 1 − α and Y ^S = 0, the Bellman equation is modified to

ρ W = 1 + τ y α 1 − α + α 1 + τ y p x p y 1 − α h x 1 − u x L x − χ V + ∂ W ∂ u x u ̇ x + ∂ W ∂ u y u ̇ y , s.t. u ̇ x = δ 1 − u x + m θ x λ u x

The envelope theorem implies that

d W d τ y = α 1 + τ y − α 1 − α + α 1 + τ y 1 + τ y α 1 − α + α 1 + τ y × p x p y 1 − α h x 1 − u x L x + − u x L x + ∂ W ∂ u x − λ m θ x λ − 1 u x d θ x d τ y + ∂ W ∂ u y − λ m θ y λ − 1 u y d θ y d τ y + ∂ 2 W ∂ u x ∂ τ u ̇ x τ x + ∂ 2 W ∂ u y ∂ τ u ̇ y τ x , ρ ∂ W ∂ u x = − 1 + τ y α 1 − α + α 1 + τ y p x p y 1 − α h x L x − θ x L x + ∂ W ∂ u x − δ − m θ x λ ,

which lead to

(56) ∂ W ∂ u x = − 1 + τ y α 1 − α + α 1 + τ y p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ ,

In the steady state, we have u _x = u, θ _x = θ, S _x = S, u ̇ x = u ̇ y = 0 . Substituting ∂W/∂u _x in equations (56) into dW/dτ _x gives

d W d log τ y = α 1 + τ y − α 1 − α + α 1 + τ y 1 + τ y α 1 − α + α 1 + τ y × p x p y 1 − α h x 1 − u x L x τ y + − u x L x + 1 + τ y α 1 − α + α 1 + τ y p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ λ m θ x λ − 1 u x × d θ x d log τ y

□

A.9 Proof of Proposition 3.

Proposition 3:

The derivative of welfare with respect to τ _y evaluated at τ _y = 0 is

d W d log τ y τ y = 0 = − λ − β β u x L x θ x χ 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ .

Proof. The value of the derivative d W d log τ y at τ _y = 0 is

d W d log τ y τ y = 0 = − u x L x + p x p y 1 − α h x L x + θ x L x ρ + δ + m θ x λ λ m θ x λ − 1 u x d θ x d log τ y

Using the free-entry condition p V = m θ x λ − 1 β S x + θ x p V ρ + δ + m θ x λ in equation (20) to simplify the equation to

d W d log τ y τ y = 0 = u x L x χ λ β − 1 d θ x d log τ y = − λ − β β u x L x θ x χ 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ ,

where the last step uses

d θ x d log τ y = − 1 − α ρ + δ + 1 − β m θ x λ 1 − λ ρ + δ + 1 − β m θ x λ θ x .

□

A.10 Proof of Corollary 2.

Corollary 2:

Beginning at free trade, an import policy can improve a country’s welfare if λ ≠ β , and free trade is the optimal trade policy if λ = β.

Proof. When λ = β, d W / d log τ y τ y = 0 = 0 . Since the welfare function is strictly concave in τ _y, it follows that τ _y = 0 is a global maximum; free trade is the optimal trade policy. When λ ≠ β, we have that d W / d log τ y τ y = 0 ≠ 0 . Therefore, the government can improve the welfare of the country by slightly increasing τ _y if d W / d log τ y τ y = 0 > 0 or slightly decreasing τ _y if d W / d log τ y τ y = 0 < 0 . □

A.11 Proof of Proposition 4

Proposition 4:

In the Ricardian model, the sign of the optimal import tariff τ y * is the opposite of the sign of λ − β.

Proof. Because the welfare function is strictly concave, dW/dτ _y is strictly decreasing in τ _y. When λ − β > 0, we have d W / d log τ y τ y = 0 < 0 = d W / d log τ x τ x = τ y * , implying that the optimal import tariff is negative, τ y * < 0 . In contrast, when λ − β < 0, we have d W / d log τ y τ y = 0 > 0 = d W / d log τ y τ y = τ y * , leading to the conclusion that the optimal import tariff is positive, τ y * > 0 . □

A.12 Proof of Corollary 3

Corollary 3:

A small open economy that is concerned about inefficiently high unemployment can improve its welfare by using trade policies that expand the size of international trade.

Proof. From Propositions 1 and 3, a country with inefficiently high unemployment has λ > β, which implies that τ x * > 0 and τ y * < 0 . In this case, the optimal trade policies are export subsidies or reduced import tariffs. □

A.13 Discussion on Trade Policy and Pattern of Trade

This appendix explains why it is never optimal for the government to set trade policies that reverse the pattern of trade, and how this assumption simplifies the analysis without affecting the overall conclusions of the paper. Without loss of generality, the focus is on trade policy concerning exports, though an analogous argument can be made for import tariffs.

Mathematical Justification

It is never optimal to reverse the pattern of trade (i.e., switch from exporting good X and importing good Y to exporting good Y and importing good X). To illustrate this, suppose the government implements an export tax τ x 1 that leads to the country exporting good Y. The claim is that there is a preferable export tax τ x 2 that allows the country to reach the same or higher income while continuing to export good X.

In the case of an efficient labor market, a standard conclusion is that the country’s welfare reaches its minimum at the autarky price ratio and its welfare increases as the world price ratio moves further away from the autarky price ratio.

In the case of an inefficient labor market, the country’s welfare no longer reaches its minimum at the autarky price ratio. Suppose that welfare reaches its minimum at the price ratio p _minW. By the continuity of the welfare function and the fact that welfare approaches infinity as the price ratio increases to infinity or decreases to zero, there exists a price ratio, denoted by p equiv ≠ p x / p y A such that welfare at this price p _equiv is equal to welfare at autarky.

Consider two cases of labor market inefficiency:
1. Inefficiently high unemployment: λ > β
  
  In this case, the optimal trade policy is export subsidy or τ _x > 0. The trade pattern will remain unchanged, with the country continuing to export good X.
2. Inefficiently low unemployment: λ < β
  
  In this case, the optimal trade policy is an export tax τ _x < 0, and the derivative of income function with respect to price ratio, evaluating at the autarky price ratio, is negative. This implies p minW ≥ p x / p y A . Therefore, for any 1 + τ x p x / p y < p x / p y A , the income must have a value between the minimum and infinity. By continuity of the income function with respect to p _x/p _y in the range of p x / p y A , ∞ , there is a trade policy τ x 2 such that the country has the same nominal income as under export tax τ x 1 . By construction, it implies τ x 2 < τ x 1 leading to greater price distortion under τ x 1 compared to τ x 2 . Therefore, export tax τ x 2 , which does not alter the pattern of trade, gives the country the same nominal income while causing smaller price distortions. Therefore, it is never optimal for the government to use an export tax that reverses the trade pattern.
  
  A similar conclusion holds for import policies: it is never optimal to set tariffs high enough to reverse the trade pattern.
Practical Justification

From a practical perspective, reversing the trade pattern through trade policy would not be considered as a conventional “export” tax. Instead, it would effectively function as imposing a prohibitive export tax on good X and further providing an import subsidy for good X. While these two policies are theoretically equivalent within the model, their practical implementations differ significantly, with the latter being highly impractical.

Conclusion

Assuming that the government does not alter the trade pattern allows us to avoid complex and uninteresting proofs that do not contribute meaningful insights to the core findings. This assumption keeps the analysis focused on meaningful scenarios where trade policies enhance welfare without unnecessary complications and allows for more straightforward and concise mathematical derivations and discussions.

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Received: 2023-11-14

Accepted: 2024-09-10

Published Online: 2024-12-03

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Articles in the same Issue

https://doi.org/10.1515/bejte-2023-0120

Keywords for this article

optimal trade policy; unemployment; Ricardian model; labor market; search-and-matching frictions; export subsidy