Appendix: An Algebraic Model of the Price and Quantity Effects of Trade Preferences and MFN Tariff Reductions

The algebraic model presented here is a very simple static three-country model, very much along the lines of Viner’s (1950) theory of customs unions, though rather than a customs union it reflects a unilateral tariff preference. The three countries (or country groups) considered are an importing country granting a trade preference (country A), the group of exporting developing countries receiving the trade preference (country B), and other (developed) exporting countries (country C),which face the MFN tariff on their exports to country A. Only one product is considered. For simplicity, import demand and export supply curves are assumed to be linear, and both the MFN and the preferential tariff are assumed to be specific.

Import demand in country A (M_A) and export supply in countries B and C (X_B and X_C) depend on domestic prices (P_I).

(1) M_A = m_A - n_AP_A
(2) X_B = m_B + n_BP_B
(3) X_C = m_C + n_CP_C

Note that these equations are written such that all slope parameters n_i are positive.

Export prices received in countries B and C are the domestic market price in country A minus, respectively, the preferential tariff T_B and the MFN tariff T_MFN (transport costs and trading margins are neglected):

(4) P_B = P_A - T_B
(5) P_C = P_A - T_MFN

Equations (4) and (5) imply that the price received by preferred exporters from country B exceeds the world market price, i.e. the price received by MFN exporters from country A, by the preference margin T_MFN - T_B:

P_B = P_C + T_MFN - T_B.

In equilibrium, aggregate export supply equals import demand:

(6) X_B + X_C = M_A

This system of six equations can be solved for the six unknowns, i.e. three quantities and three prices.

If export supply of the non-preferred country C is assumed to be infinitely elastic, price in country C, equivalent to the world market price, is exogenously fixed (P_C^*). The price in importing country A is equally fixed:

P_A = P_C^* + T_MFN.

This is true at least as long as part of country A’s imports are sourced in country C, i.e. as long as the trade preference does not result in a situation where country B takes over the entire import market of country A. As long as that is so, price in country A is not affected by the trade preference.

The price received by the preferred exporters is determined by the fixed world market price plus the preference margin:

P_B = P_C^* + T_MFN - T_B.

In this simple case, it is clear that the price received by the preferred exporters responds inversely to the level of the preferential tariff. Hence introduction of a trade preference (i.e. a reduction of T_B from the original situation where T_B= T_MFN) raises the price received by the preferred exporters, and hence their export quantity and welfare. At the same time there is no doubt that complete liberalization, i.e. setting both T_MFN and T_B to zero, results in a price to preferred exporters which is lower than that received under a positive MFN tariff and a trade preference. In other words, the tariff-cum-preference scenario ‘sucks’ exports from the preferred exporters B in a direction which is not sustainable under free trade.

On the other hand, if the MFN tariff is reduced without being totally eliminated, the price received by the preferred exporters, the quantity exported by them, and their economic welfare directly depend on what happens to the preference margin. If the preferential tariff is defined as the MFN tariff minus a given number of monetary units per quantity (i.e. if the preference margin is kept constant), and if the reduced MFN tariff is still at least as high as the preferential tariff, then reduction of the MFN tariff has no effect on the price received by the preferred exporters, and hence on their export volume and welfare. Conversely, if the preference margin declines as a result of the reduction of the MFN tariff, the preferred exporters clearly lose on export price and volume and in terms of welfare.

In the more general case, where export supply of the MFN exporter C is less than infinitely elastic, prices in all three countries depend on the tariffs set. Solving the system of equations for the prices, it can easily be shown that price in country A then is:

P_A = [n_CT_MFN + n_BT_B + m]/n,

while the price received by preferred exporters is:

(7) P_B = [n_CT_MFN - (n_A + n_C)T_B + m]/n,

where m and n are defined as m º m_A - m_B - m_C and n º n_A + n_B + n_C.

In this case it is clear that, with a given MFN tariff, price in country A is the lower, the more generous is the trade preference (T_B). Conversely, the price received by preferred exporters is the higher, the lower is the preferential tariff. In this case it is not absolutely clear whether the trade preference has the effect of ‘sucking’ country B’s exports in a direction that is not sustainable under free trade. This depends on the sign of the term n_CT_MFN - (n_A + n_C)T_B. If that term is positive, then complete trade liberalization will bring about a decline of P_B, and vice versa. Which sign prevails depends on both tariff rates and response parameters. The larger the preference margin (i.e. the lower T_B with a given T_MFN), the more likely is it that the export structure resulting from the trade preference is not sustainable after complete trade liberalization. However, with a zero preferential tariff there is no doubt whatsoever that reduction of the MFN tariff to zero reduces the price received by preferred exporters, and hence triggers downward adjustment of the export volume.

What happens to the price received by preferred exporters (and hence to their export volume and welfare) if the MFN tariff is reduced again depends on how the preference margin behaves in this case. This is best seen if equation (7) is rewritten to bring out the preference margin (PM (T_MFN - T_B):

(7a) P_B = [(n_A + n_C)PM - n_AT_MFN + m]/n.

If the MFN tariff reduction does not affect the size of the preference margin, then P_B definitely rises and hence preferred exporters gain. If the preference margin is narrowed by the same amount of monetary units as the MFN tariff (i.e. the preferential tariff remains constant when the MFN tariff is reduced), then preferred exporters definitely lose. Between these two border cases, however, there are situations where the preference margin declines somewhat with the MFN tariff reduction, but the price received by preferred exporters still rises, and hence their exports grow and welfare improves.

TC/D/Y2732E/1/2.02/500