Privatization in the presence of foreign competition and strategic policies

Abstract

Recent evidence shows that developing and transition economies are increasingly privatizing their public firms and also experiencing rapid growth of inward foreign direct investment (FDI). In an international mixed oligopoly with strategic tax/subsidy policies, we analyze the interaction between privatization and FDI. We find that the incentive for FDI increases with privatization. However, the possibility of FDI reduces the degree of privatization. Our paper shows that FDI policies reducing the fixed-cost of undertaking FDI may need to complement the privatization policies to attract FDI and to improve domestic welfare.

Appendix

1.1 Appendix A: maximum value of $c$:

We see from (14) and (24) that $q_{p}^{x}$ and $q_{p}^{R}$ are positive respectively for:

$$\begin{aligned} c&< \bar{c}(\alpha ,s)\equiv \frac{1}{2\alpha +4}\left( s+\alpha +s\alpha +3\right) , \end{aligned}$$

(39)

$$\begin{aligned} c&< \hat{c}(\alpha )\equiv \frac{3-\alpha }{\alpha +\alpha ^{2}+3}. \end{aligned}$$

(40)

We further see that:

$$\begin{aligned} \frac{\partial \bar{c}(\alpha ,s)}{\partial \alpha }<0\quad \text { and }\quad \frac{d \hat{c}(\alpha )}{d\alpha }<0. \end{aligned}$$

(41)

Following (41), the least possible values of (39) and (40) are respectively:

$$\begin{aligned} c&< \bar{c}_{\min }\equiv \bar{c}(1,s)=\frac{s+2}{3} \end{aligned}$$

(42)

$$\begin{aligned} c&< \hat{c}_{\min }\equiv \hat{c}(1)=\frac{2}{5}. \end{aligned}$$

(43)

Comparing (42) and (43), we see that $\hat{c}(1)<\bar{c} (1,s).$ Hence, the relevant constraint is (3).

1.2 Appendix B: $W_{h}^{R}$ as a function of $\alpha$:

Differentiating domestic welfare $W_{h}^{R}\$under FDI in (35) partially with respect to $\alpha ,$ we see that there are two solutions to $\partial W_{h}^{R}/\partial \alpha =0,$ which we call $\underline{\alpha }$ and $\alpha _{R}^{*}$:

$$\begin{aligned} \underline{\alpha }=c-3,\, \, \, \,\, \, \, \alpha _{R}^{*}=\frac{c}{2-c}. \end{aligned}$$

(44)

We see that $0<\alpha _{R}^{*}<1$ and $\underline{\alpha }$ is negative.

In order to determine whether these two stationary points are maxima or minima, we differentiate partially with respect to $\alpha$ again:

$$\begin{aligned} \left. \frac{d^{2}\left( W_{h}^{R}\right) }{d\alpha ^{2}}\right| _{\alpha =\underline{\alpha }}&= \frac{1}{-4c+c^{2}+6}>0, \\ \left. \frac{d^{2}\left( W_{h}^{R}\right) }{d\alpha ^{2}}\right| _{\alpha =\alpha _{R}^{*}}&= -\frac{1}{4}\frac{\left( c-2\right) ^{4}}{ c^{2}-4c+6}<0. \end{aligned}$$

Hence, domestic welfare reaches a global maximum for $\alpha \in \left[ 0,1 \right]$ at $\alpha =\alpha _{R}^{*}$ as given by (44) .

1.3 Appendix C: $W_{h}^{R}$ is not higher than $W_{h}^{x}$ for $\alpha =1$:

Setting $\alpha =1$ in (35) we get the domestic welfare under FDI at $\alpha =1$ as:

$$\begin{aligned} W_{h\left| \alpha =1\right| }^{R}=\frac{7c^{2}-8c+4}{12}. \end{aligned}$$

(45)

Similarly setting $\alpha =1$ in (33), we get domestic welfare under export at $\alpha =1$ as:

$$\begin{aligned} W_{h_{|\alpha =1|}}^{x\max }=\frac{\left( 7c^{2}-8c+4\right) -s\left( 3\right) \left( 2c-s\right) }{8}. \end{aligned}$$

(46)

From (45) and (46), we see that:

$$\begin{aligned} \frac{d\left( W_{h}^{x}-W_{h}^{R}\right) _{\left| \alpha =1\right| }}{dc}=-\frac{1}{12}\left( 7c+9s-4\right) <0. \end{aligned}$$

The minimum value of $\left( W_{h}^{x}-W_{h}^{R}\right) _{\left| \alpha =1\right| }$ is at the maximum value that $c$ can take. From (45), (46) and the maximum value of $c$ given by (3), we see that:

$$\begin{aligned} \left( W_{h}^{x}-W_{h}^{R}\right) _{\left| \alpha =1\right| _{c_{\max }}}=\frac{1}{200}\left( -60s+75s^{2}+16\right) >0. \end{aligned}$$

Thus, we see that

$$\begin{aligned} W_{h\left| \alpha =1\right| }^{x}>W_{h\left| \alpha =1\right| }^{R} \end{aligned}$$

at $\alpha =1.$ Also, setting $\alpha =0,$in (33) and (35) we see that:

$$\begin{aligned} \left[ W_{h}^{R}-W_{h}^{x}\right] _{\alpha =0}=\frac{1}{6}s\left( 2c-s\right) >0. \end{aligned}$$

1.4 Appendix D: $\hat{F}$ could be negative at $\alpha =0$:

Substituting $\alpha =0$ into (31), we see that $\hat{F}>0$ at $\alpha =0$ for:

$$\begin{aligned} c>\check{c}\equiv 2s. \end{aligned}$$

(47)

Thus, we see that when $c<\check{c}$, $\hat{F}$ is negative at $\alpha =0$.

1.5 Appendix E: $\alpha _{R}^{*}<a_{F1}$:

If $\alpha _{R}^{*}>a_{F1},$ it implies from (29) that $\hat{F}$ should be positive at $\alpha =\alpha _{R}^{*}\equiv \frac{c}{2-c}.$

We see from (29) that $\hat{F}_{\alpha =\alpha _{R}^{*}}>0$ for:

$$\begin{aligned} c>\mathring{c}\equiv \frac{1}{2}\sqrt{16s+1}-\frac{1}{2}. \end{aligned}$$

(48)

However, for this to be consistent with the model setting, $\mathring{c}$ should be less than $\hat{c}$ in (3). On comparison from (48) and (3), we see that $\mathring{c}<\hat{c}$ for $s<0.14.$ Thus, for cases where $s<0.14,$ we see that $\alpha _{R}^{*}>a_{F1}.$