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This paper extends Long and Staehler’s model and studies optimal export tax in the case of privatization. The authors find that optimal export tax increases with the degree of privatization if product differentiation exists. The authors provide a counterexample to Long and Staehler’s model and reach a different conclusion. This finding emphasizes that the relationship between the variables of optimal export tax and conditions of asymmetric cost and product differentiation is quite different from Long and Staehler’s model. Since optimal export tax is endogenous in the model, the authors also consider the potential endogeneity of privatization decision, which is an important issue in a traditional mixed duopoly analysis.

Since the 1980s, governments have begun to privatize state-owned enterprises. In keeping with this trend, many countries have changed the focus of their government policies towards international trade. Consequently, the relationship between privatization and strategic trade policies deserves further study.

Pal and White [

Most existing studies examine the relationship between import tariffs and privatization. However, the export tax is also an instrument of strategic trade policy. Although several papers, including Eaton and Grossman [

The innovation of this paper is as follows. First, Long and Staehler [

Thus, this paper aims to study the effects of privatization on the optimal export tax in the presence of a differentiated mixed duopoly with cost asymmetry. To do this, we use a quadratic utility function, an asymmetric cost, and a Cournot-Nash equilibrium game. Within this framework, we find that the relationship between the degree of product differentiation and the optimal export tax is non-monotonic, while the optimal export tax increases with the degree of privatization. Furthermore, we find that in the presence of a cost-symmetric duopoly, privatization is independent of the optimal export tax, while optimal export taxes increase as the degree of pro- duct differentiation decreases.

Our result demonstrates that cost asymmetry plays a crucial role in the relationship between privatization and optimal export taxes. This implies that with cost asymmetry, the government may encourage the low-cost firm to export its product more; therefore, privatization will affect optimal export taxes by altering production decisions. On the contrary, with cost symmetry, the government does not adjust the export policy according to the privatization policy.

This study contributes to the existing literature in two ways. First, our finding contrasts with the research of Long and Staehler [

The rest of the paper is organized as follows. Section 2 introduces our model, Section 3 solves the firm and government problems, and Section 4 concludes.

Our model is based on Long and Staehler’s [

where A is a constant and

To simplify the analysis, we assume that cost function is linear, i.e., firms have a constant marginal cost of production

As shown by Pal and White [

where w represents the level of social welfare. It should be noted that (2) does not include consumer surplus since both firms export their entire outputs. The mixed enterprise considers both the profit and welfare in (1) and (2). Hence, the objective function of the mixed firm is given by

where

The stages of the game involved proceed as follows. First, given

As is standard, we first solve the firm problem and then the government problem.

Firm 1 chooses

Next, turn to the choice of Firm 2’ s output,

Solving the simultaneous equations of (4) and (5) for

where

Equation (8) implies that increasing export taxes leads to a reduction in Firm 1’ s output if

From Equations (10)-(13), we find that comparative statics of the optimal level of production are uncertain. We will examine a numerical example to explain the possible effect more explicitly. First, we compute the optimal level of production with respect to the degree of product differentiation by setting

From

The following proposition summarizes what we have found:

Proposition 1: When production differentiation becomes larger, the output difference between two firms becomes smaller. On the contrary, when production differentiation becomes smaller, the output difference between two firms becomes larger.

Next, we compute the optimal level of production with respect to the degree of privatization by setting

From

The above allows the following result to be inferred:

Proposition 2: When the degree of privatization becomes larger, the output difference between two firms becomes smaller. On the contrary, when the degree of privatization becomes smaller, the output difference between two firms becomes larger.

The optimal export tax can be found by differentiating (2) with respect to t to yield:

Substituting (6), (7), (8), and (9) into (14) yields the following optimal export tax:^{1}

Equation (15) shows that the optimal export tax depends on a constant A, the degree of product differentiation

From (15), we cannot directly calculate the comparative statics of optimal export taxes; thus, simulations are needed. First, we analyze the effect of the degree of product differentiation on optimal export taxes.

we see that when

taxes leads to an increase in the high-cost firm’s output. Thus, in order to improve production efficiency, the government should impose higher export taxes on output if

Second, we analyze the effect of the degree of privatization on optimal export taxes.

The above allows the following result to be inferred:

Proposition 3: Consider an economy in which both mixed enterprises and private firms may export from the same country to another country. We find that the relationship between the degree of product differentiation and the optimal export tax is non-monotonic. In addition, the optimal export tax increases with the degree of privatization.

Note that it is also instructive to consider some special cases. First, with

Equation (16) means that the degree of privatization is independent of the optimal export tax in a homogeneous duopoly with cost symmetry. This result is consistent with that of Long and Staehler [

Next, with

Equation (17) means that the degree of privatization is also independent of the optimal export tax even in a differentiated duopoly with cost symmetry. To see the relationship between

Equation (18) means that if the degree of product differentiation decreases, optimal export taxes will become large. The reason is that with cost symmetry, as the degree of product differentiation decreases, both firms will reduce their output to pursue profits more aggressively. In addition, an increase in export taxes usually reduces the firms’ output. Therefore, export taxes and the degree of product differentiation are substitute relations. In

other words, optimal export taxes decrease with the degree of product differentiation.

From equations (16)-(18), we establish:

Proposition 4: Consider an economy in which both mixed enterprises and private firms may export from the same country to another country. We find that, in the presence of a cost symmetric duopoly, the degree of privatization is independent of the optimal export tax, while optimal export taxes increase as the degree of product differentiation decreases.

Finally, with

Equation (19) implies that the optimal export tax depends on

Equation (20) means that higher degree of privatization (higher value of

Proposition 5: Consider an economy in which both mixed enterprises and private firms may export from the same country to another country. We find that in a cost asymmetric duopoly, the optimal export tax rate monotonically increases as the degree of privatization increases.

Long and Staehler [

Our findings are as follows. First, we show that the relationship between the degree of product differentiation and the optimal export tax is non-monotonic, while the optimal export tax monotonically increases as the degree of privatization increases. Second, we find that in the presence of a cost symmetric duopoly, the degree of privatization is independent of the optimal export tax, while optimal export tax increases as the degree of product differentiation decreases. Following these arguments, an obvious policy implication is that the optimal export tax needs to be tailored to the cost asymmetry rather than product differentiation.

The limitations of this work are as follows. First, we do not consider how foreign competitors affect the relationship between privatization and optimal export taxes. Secondly, we ignore how increasing competitive firms in the home country affect the relationship between optimal export taxes. These issues, we believe, merit future research.