Domestic product standards, harmonization, and free trade agreements

Abstract

This study considers endogenous domestic standards on products to control negative consumption externalities using a three-country model of international oligopoly with a possible free trade agreement (FTA). The authors examine how the level of product standards and welfare are affected under an FTA and how the harmonization of standards affects the impact of the FTA. They find that if asymmetries in preferences or transboundary externalities are not too strong, an FTA makes product standards more stringent. In such a case, the FTA may or may not make the member countries better off, but it does make the non-member country better off. They also demonstrate that harmonizing the standards across the FTA members makes an FTA more favorable.

Appendix A. Proofs

1.1 Proof of Lemma 4

Comparing the slopes at the origin, we have $d{\bar{\gamma }}_i^M(0)/d\beta _i=3/4<1=d{\bar{\gamma }}_i^F(0)/d\beta _i$. In addition, it holds that ${\bar{\gamma }}_i^F(\alpha _i/2)=(1-\sqrt{15}/30)\alpha _i\approx 0.8709\alpha _i>{\bar{\gamma }}_i^M(\alpha _i/2)$. Since both ${\bar{\gamma }}_i^M(\beta _i)$ and ${\bar{\gamma }}_i^F(\beta _i)$ are increasing and convex in $\beta _i$, the statement of the lemma holds. $\square$

1.2 Proof of Proposition 2

From (7), (8), (12), and (13), we have

$$\begin{aligned} W_i^M-W_i^F&=w_i^M(s_i)+\pi _{ji}^M(s_j)-[w_i^F(s_i)+\pi _{ji}^F(s_j)] \nonumber \\&=\frac{4a_i(s_i)^2-6a_i(s_i)b_i(s_i)+b_i(s_i)^2}{10}+\frac{[a_h(s_h)-2b_h(s_h)]^2}{100} \nonumber \\&\quad -\frac{15a_i(s_i)^2-30a_i(s_i)b_i(s_i)+b_i(s_i)^2}{42}-\frac{[6a_j(s_j)+b_j(s_j)]^2}{441}. \end{aligned}$$

(A1)

If the member countries are symmetric, only cases (i), (iv), and (ix) in Table 1 are possible. In case (i), (A1) can be rewritten as

$$\begin{aligned} W_i^M-W_i^F =-\frac{(423\alpha -1256\beta )(3\alpha +4\beta )}{44100}. \end{aligned}$$

(A2)

Then, $W_i^M>W_i^F$ ($W_i^M<W_i^F$) if and only if $\beta >(<) \;423\alpha /1256 \approx 0.3368\alpha$.³⁵ In case (iv), (A1) can be rewritten as

$$\begin{aligned} W_i^M-W_i^F =\frac{-141\alpha ^2-3136\alpha \beta +686\beta ^2+4300\alpha \gamma -2150\gamma ^2}{4900}. \end{aligned}$$

(A3)

Given the parameter restrictions $\alpha >\gamma$ and $\alpha >2\beta$, it can be verified that $W_i^M>W_i^F$ ($W_i^M<W_i^F$) holds if and only if

$$\begin{aligned} \gamma > (<) \; {\tilde{\gamma }}(\beta )\equiv \alpha -\frac{7}{5}\sqrt{\frac{41}{86}\alpha ^2-\frac{32}{43} \alpha \beta +\frac{7}{43}\beta ^2}. \end{aligned}$$

It also holds that ${\tilde{\gamma }}(0)\approx 0.0333\alpha$ and ${\tilde{\gamma }}(\alpha /2)\approx 0.4663\alpha \in \left( {\bar{\gamma }}^M(\alpha /2),{\bar{\gamma }}^F(\alpha /2)\right)$. Finally, in case (ix), (A1) can be rewritten as

$$\begin{aligned} W_i^M-W_i^F =-\frac{141(\alpha -\gamma )^2}{4900}<0. \end{aligned}$$

(A4)

Therefore, the FTA achieves higher welfare for the member countries than the MFN tariff does.$\square$

1.3 Proof of Proposition 3

If the pair of parameters $(\beta _i,\gamma )$ for each member country is in either region I or region III in Fig. 1, $W_C^M<W_C^F$ holds because $\pi _{iC}^M(s_L)-\pi _{iC}^F(s_L)=-(17\alpha _i-24\beta _i)(3\alpha _i+4\beta _i)/4900<0$ and $\pi _{iC}^M(s_H)-\pi _{iC}^F(s_H)=-51(\alpha _i-\gamma )^2/4900<0$. If $(\beta _i,\gamma )$ is in region II, where member country i chooses $s_L$ under the MFN regime and $s_H$ under the FTA, it holds that

$$\begin{aligned} \pi _{iC}^M(s_L)-\pi _{iC}^F(s_H) =-\frac{(17\alpha _i-14\beta _i-10\gamma )(3\alpha _i+14\beta _i-10\gamma )}{4900}. \end{aligned}$$

Since $\alpha _i>2\beta _i$, it holds that $17\alpha _i-14\beta _i-10\gamma>10(\alpha _i-\gamma )>0$. Therefore, the sign of the above expression is positive (negative) if and only if $\gamma >(<)\;(3\alpha _i+14\beta _i)/10$ holds. Since Region II is contained in the set $\left\{ (\beta _i,\gamma )\in \mathbb {R}_+^2 \mid \gamma <(3\alpha _i+14\beta _i)/10, \; \alpha _i>2\beta _i\right\}$, $\pi _{iC}^M(s_L)<\pi _{iC}^F(s_H)$ holds, which means that $W_C^M<W_C^F$ holds as well. $\square$

1.4 Proof of Lemma 5

Since the countries are assumed to be symmetric, either $(s_A^F,s_B^F)=(s_L,s_L)$ or $(s_A^F,s_B^F)=(s_H,s_H)$ holds under national standards. Suppose that $(\beta ,\gamma )$ is in region I in Fig. 1. In this case, the threat point in the bargaining problem is $(s_A^F,s_B^F)=(s_L,s_L)$. In light of (11), (12), and (13), it follows that the member countries jointly choose $s=s_H$ if

$$\begin{aligned} \omega _i(s_H)- \omega _i(s_L)= \frac{387\gamma ^2-774\alpha \gamma +606\alpha \beta -23\beta ^2}{882} \end{aligned}$$

(A5)

is positive for $i=A,B$.³⁶ We can verify that $\omega (s_H)>\omega (s_L)$ holds if and only if $387\gamma ^2-774\alpha \gamma +606\alpha \beta -23\beta ^2>0$, or equivalently, $\gamma <\bar{{\bar{\gamma }}}^F(\beta )$. However, this contradicts the assumption that $(\beta ,\gamma )$ is in region I, which satisfies $\gamma >{\bar{\gamma }}^F(\beta )$. This is because $d\bar{{\bar{\gamma }}}^F(0)/d\beta =101\alpha /129\approx 0.7829\alpha$ and $\bar{{\bar{\gamma }}}^F(\alpha /2)=(1-\sqrt{359}/6\sqrt{43})\alpha \approx 0.5184\alpha$, and thus, it follows that $\bar{{\bar{\gamma }}}^F(\beta )<{\bar{\gamma }}^F(\beta )$ for all $\beta \in (0,\alpha /2)$. Therefore, the member countries must jointly choose $s_L$ if $(\beta ,\gamma )$ is in region I. Suppose next that $(\beta ,\gamma )$ is in region II or III. In this case, the threat point is $(s_A^F,s_B^F)=(s_H,s_H)$, and the member countries jointly choose $s=s_L$ if $\omega (s_H)<\omega (s_L)$. In light of (A5), the condition is satisfied if and only if $\gamma \in \left( \bar{{\bar{\gamma }}}^F(\beta ), {\bar{\gamma }}^F(\beta )\right)$. If $\gamma <\bar{{\bar{\gamma }}}^F(\beta )$, by contrast, the member countries jointly choose $s=s_H$. $\square$