Effects of Tariffication: Tariffs and Quotas under Monopolistic Competition

Abstract

Recent rounds of GATT and later WTO have advocated widespread tariffication, meaning that existing non-tariff barriers be converted into import equivalent tariffs. From an economic point of view, the effects of such tariffication are not entirely clear. The paper presents a trade model with monopolistic competition to examine the welfare effects of tariffication. The ranking of pre- and post-tariffication welfare crucially depends on the nature of the initial trade barrier and the tariff tool applied. Tariffication using a specific (ad valorem) tariff results in the same (reduced) welfare level compared to an initial sold quota, whereas welfare is increased (the same) compared to an initial shared quota.

Appendix

1.1 A.1 Impact on the non-traded industry

Both labour and spending power (including redistributed funds from quota rents and tariff revenue), stemming from the constrained export industry will move to the non-traded industry. Formally, the labour supply for the non-traded industries, $\ifmmode\expandafter\hat\else\expandafter\^\fi{L}^{s}$, can be written as:

$$\ifmmode\expandafter\hat\else\expandafter\^\fi{L}^{s} = \frac{1}{2}L + \Delta L^{s} \,\,\,\,\,\,s = q,v,\tau ,t$$

(18)

The increase in available labour does not influence the equilibrium output and price of the individual firm in the non-traded industry and hence output and price is equal to ${\ifmmode\expandafter\hat\else\expandafter\^\fi{p}}$ and ${\ifmmode\expandafter\hat\else\expandafter\^\fi{x}}$ given implicitly in Eqs. 4a and 4b. This reallocation of labour is identical to an increase in market size, and thus only influences the equilibrium number of variants, and hence also total industry output. The equilibrium number of variants, $\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{s}$, is found by using the labour market clearing condition for the non-traded industry given by:

$$\ifmmode\expandafter\hat\else\expandafter\^\fi{L}^{s} = {\left( {\alpha + \beta \ifmmode\expandafter\hat\else\expandafter\^\fi{x}} \right)}\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{s} \,\,\,\,\,\,s = q,v,\tau ,t$$

(19)

Combining Eqs. 18 and 19 and inserting ΔL ^s found in Eqs. 8, 10 and 14, we find the equilibrium number of variants in the non-traded industry under the different trade policies:

$$\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{q} = \ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{\tau } = \frac{{2 - \theta \gamma }}{{2 - \theta }}n$$

(20)

$$\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{v} = \ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{t} = {\left( {2 - \gamma } \right)}n$$

(21)

From Eqs. 20 and 21 it immediately follows that $\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{q} ,\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{v} ,\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{t} ,\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{\tau } > n$ and $\ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{q} = \ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{\tau } < \ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{v} = \ifmmode\expandafter\hat\else\expandafter\^\fi{n}^{t}$.

1.2 A.2 Proof that U ^q, U ^v, U ^τ, U ^t < U

Consumer utility under trade protection, but with full reallocation of tariff revenues and quota rents, is less than utility under free trade. Recall from Proposition 1 that U ^τ = U ^q and U ^t = U ^v.

Proof

U^t < U. From Eq. 17c it follows that U^t = U + ln(2 − γ) + ln γ. Hence, one has to show that:

$$K^{t} = \ln {\left( {2 - \gamma } \right)} + \ln \gamma < 0.$$

(22)

It follows from Eq. 22 that lim_γ→0K^t = −∞ and lim_γ→1K^t = 0. Since $\frac{{\partial K^{t} }}{{\partial \gamma }} = \frac{{2 - 2\gamma }}{{{\left( {2 - \gamma } \right)}\gamma }} > 0,\,K^{t}$ is monotone increasing in γ for all 0 < γ < 1, Eq. 22 is fulfilled.□

Proof

U^τ < U. From Eq. 17d it follows that $U^{\tau } = U + {\left( {2 - \theta } \right)}\ln {\left( {\frac{{2 - \theta \gamma }}{{2 - \theta }}} \right)} + \theta \ln \gamma$. Hence, one has to show that:

$$K^{\tau } = {\left( {2 - \theta } \right)}\ln {\left( {\frac{{2 - \theta \gamma }}{{2 - \theta }}} \right)} + \theta \ln \gamma < 0$$

(23)

It follows from Eq. 23 that lim_γ→0K^τ = −∞and lim_γ→1K^τ = 0. Since $\frac{{\partial K^{\tau } }}{{\partial \gamma }} = \theta \frac{{2{\left( {1 - \gamma } \right)}}}{{{\left( {2 - \theta \gamma } \right)}\gamma }} > 0,\,\,K^{\tau }$ is monotone increasing in γ for all 0 < γ < 1, Eq. 23 is fulfilled.□

1.3 A.3 Proof that U ^τ > U ^t

Tariffication with a specific tariff and complete reallocation of all tariff revenues gives higher consumer utility than tariffication with an ad valorem tariff.

Proof

U^τ > U^t. FromEqs. 17c and 17d it follows that:

$$U^{\tau } > U^{t} \Leftrightarrow {\left( {2 - \theta } \right)}\ln {\left( {\frac{{2 - \theta \gamma }}{{2 - \theta }}} \right)} + \theta \ln \gamma > \ln {\left( {2 - \gamma } \right)} + \ln \gamma $$

(24)

Define the function:

$$F{\left( z \right)} = {\left( {2 - z} \right)}\ln {\left( {\frac{{2 - z\gamma }}{{2 - z}}} \right)} + z\ln \gamma $$

(25)

If F(z) is monotone decreasing in z, then b > a implies F(a) > F(b), and hence Eq. 24 is fulfilled as 1 > θ. From Eq. 25 it follows that

$$\frac{{\partial F}}{{\partial z}} = \ln {\left( {\frac{{{\left( {2 - z} \right)}\gamma }}{{2 - z\gamma }}} \right)} + \frac{{2{\left( {1 - \gamma } \right)}}}{{2 - z\gamma }}$$

(26)

One has to show that for a given z Eq. 26 is negative for all γ, 0 < γ < 1. It follows from Eq. 26 that

$${\mathop {\lim }\limits_{\gamma \to 0} }\frac{{\partial F}}{{\partial z}} = - \infty \,\,\,{\text{and}}\,\,\,{\mathop {\lim }\limits_{\gamma \to 1} }\frac{{\partial F}}{{\partial z}} = 0$$

(27)

and since

$$\frac{{\partial \frac{{\partial F}}{{\partial z}}}}{{\partial \gamma }} = \frac{{4\left( {1 - \gamma } \right)}}{{\gamma \left( {2 - z\gamma } \right)^2 }} > 0$$

(28)

Eq. 26 is monotone increasing in γ for all z and thus negative in the relevant parameter intervals, such that Eq. 25 is monotone decreasing and hence U^τ > U^t holds.