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Tariffs, quotas and the terms of trade.

The differences between tariffs and quotas in their economic effects have been extensively discussed in the literature. One of them is that tariffs could lower the domestic relative price of the importable good (This is known as the Metzler paradox(4)), whereas import quotas always increase the domestic relative price of the importable good(1).

It has been shown by Lerner(2) that a country's terms of trade could also deteriorate after it imposes a tariff. The purpose of this paper is to show that a country's terms of trade will always improve after it imposes an import quota or an export quota. The offer curve approach(3) will be used in this study. It is assumed that both the exportable good and the importable goods are normal goods.

In Figure 1, the vertical axis and horizontal axis measure the importable good Y and exportable good X of the home country A, respectively. (Assume that country A's elasticity of demand for imports is inelastic.) Draw any international price line Ot. Od will be the domestic price line after a given tariff rate (CG/GH or DC/CE) is imposed. If the home government spends the tariff revenue entirely on the exportable good X (GC of good X), then G will be the trading point for the country as a whole. The coordinates of point G would measure the quantities of good X and good Y which the home country would like to export and import, respectively. The welfare of the private sector will be represented by the trade indifference curve tangent to Od at C.

If the tariff revenue is spent by the home government entirely on the importable good Y (DC of good Y), then D will be the trading point for the country as a whole. The welfare of the private sector will be represented by the trade indifference curve tangent to Od at C.(1)

However, if the tariff revenue is spent by the private sector(2), then the trading point will be at F. (The slope of the trade indifference curve at F is equal to that at C.) The private sector spends the tariff revenue on IC of good X and IF of good Y. The welfare of the private sector is represented by the trade indifference curve passing through F. Point J is a point on OA. Point F will lie to the left of J because the slope of the trade indifference curve at F is equal to that at C, which in turn is smaller than that at J.

Repeating the same process for any other international price line, one can derive offer curves OA|prime~, OA|double prime~ and OA|triple prime~ in Figure 2. OA|prime~ is the tariff distorted offer curve derived under the assumption that the home government spends the tariff revenue entirely on the exportable good X. OA|double prime~ is the tariff distorted offer curve derived under the assumption that the tariff revenue is spent by the private sector. lastly, OA|triple prime~ is the tariff distorted offer curve derived under the assumption that the home government spends the tariff revenue entirely on the importable good Y.

OA|prime~ and OA|double prime~ will lie to the left of the free trade offer curve OA. However, OA|triple prime~ would intersect OA. OB in Figure 2 is the foreign offer curve. OA intersects OB at Q. OT will measure the terms of trade under free trade. The terms of trade will improve after the tariff, assuming that the tariff revenue is spent by the home government entirely on the exportable good X or by the private sector. However, the terms of trade will deteriorate after the tariff if the tariff revenue is spent by the home government entirely on the importable good Y. OA|triple prime~ intersects OB at Q|triple prime~. The terms of trade will be measured by OT|triple prime~, which is less steep than OT. Line OK will be the domestic price line and Q|triple prime~ K of good Y is the tariff revenue appropriated by the home government. The welfare of the private sector is represented by the trade indifference curve tangent to OK at K.

Next suppose that the home country A imposes the optimum import quota,(3) which is equal to OS of good Y(4). This is shown in Figure 3. The offer curve of the home country after the import quota is OVMRS, which intersects OB at |Mathematical Expression Omitted~. The terms of trade after the import quota will be measured by |Mathematical Expression Omitted~, which is steeper than OT. This means that the terms of trade will improve after the import quota. This is true whether the import quota revenue is spent by the private sector or the home government.(5) This can be explained as follows.

First, if the import quota revenue is spent by the private sector, |Mathematical Expression Omitted~ will measure the terms of trade. The domestic price ratio will be measured by the slope of the trade indifference curve at |Mathematical Expression Omitted~ or by the slope of OM. The private sector spends the import quota revenue on LM of good X and |Mathematical Expression Omitted~ of good Y. The welfare of the private sector is represented by the trade indifference curve passing through |Mathematical Expression Omitted~.

Second, if the import quota revenue is spent by the home government entirely on good X, the domestic price line will be OR. However, |Mathematical Expression Omitted~ still measures the terms of trade. The private sector uses ON of good X to exchange for RN of good Y, whereas in the international market, the home country uses only OU of good X to exchange for |Mathematical Expression Omitted~ of good Y. |Mathematical Expression Omitted~ of good X is the import quota revenue appropriated by the home government. The welfare of the private sector is represented by the trade indifference curve tangent to OR at R.

Lastly, if the import quota revenue is spent by the home government entirely on good Y, OT still measures the terms of trade. The domestic price line will be OV. The private sector uses OU of good X to exchange for UV of good Y, whereas in the international market, the home country uses OU of Good X to exchange for |Mathematical Expression Omitted~ of good Y. |Mathematical Expression Omitted~ of good Y is the import quota revenue appropriated by the home government. The welfare of the private sector is represented by the trade indifference curve tangent to OV at V.(6)

Under the import quota, the home country can not import more than the import quota, OS. This is true whether the import quota revenue is spent by the private sector or the home government. Therefore, after the import quota, the trading point will be always at |Mathematical Expression Omitted~ and the terms of trade will be always measured by |Mathematical Expression Omitted~.

Since the terms of trade and the amount of imports remain constant under the import quota, the domestic relative price of the importable good will depend on how the home government spends the import quota revenue. When the home government spends more of its import quota revenue on the importable good, less of the importable good will be available for the private consumption in the domestic market. Therefore, the domestic relative price of the importable good will be higher. This explains why the domestic price line changes from OR to OV as the home government spends successively more of its import quota revenue on the importable good.

Using the same analysis as above, it can be shown that the terms of trade will always improve for the home country when it imposes an export quota. Suppose that OW(7) in Figure 4 is the export quota imposed by the home country. The home offer curve after the export quota becomes OZP, which intersects the foreign offer curve OB at Q. Since OT is steeper than OT, the home country's terms of trade improve after it imposes the export quota. This is true whether the export quota revenue is spent by the private sector or the home government. This can be explained as follows.

First, if the export quota revenue is spent by the private sector, OT will measure the terms of trade. The domestic price ratio will be measured by the slope of the trade indifference curve at Q or by the slope of Ob. The private sector spends the export quota revenue on bd of good X and Qd of good Y. The welfare of the private sector is represented by the trade indifference curve passing through Q.

Second, if the export quota revenue is spent by the home government entirely on good X, the private sector will reach point a and the domestic price will be Oa. However, OT still measures the terms of trade. Although the home offer curve becomes OZP after the export quota, section ZA of the free trade offer curve OA still describes how the private sector would behave under different relative prices. The private sector will pay Oa|prime~ of good X for aa|prime~ of good Y. Out of Oa|prime~ of good X, OW (which is the export quota) is exported to the foreign country in exchange of WQ of good Y. Qa of good X is the export quota revenue appropriated by the home government.

Lastly, if the home government spends the export quota revenue entirely on good Y, OT still measures the terms of trade. The private sector will reach point Z and the domestic price line will be OZ. The private sector pays OW of good X for ZW of good Y. OW of good X (which is the export quota) is exported to the foreign country in exchange for WQ of good Y. QZ of good Y is the export quota revenue appropriated by the home government.(8)

Under the export quota, the home country can not export more than OW. This is true whether the export quota revenue is spent by the private sector or the home government. Therefore, after the export quota, the trading point will be always at Q and the terms of trade will be always measured by OT.

Since the terms of trade and the amount of exports (or the amount of imports) remain constant under the export quota, the domestic relative price of the importable good will depend on how the home government spends the export quota revenue. When the home government spends more of its export quota revenue on the importable good, less of the importable good will be available for the private consumption in the domestic market. Therefore, the domestic relative price of the importable food will be higher. This explains why the domestic price line changes from Oa and OZ as the home government spends successively more of its export quota revenue on the importable good.

In conclusion, it has been shown above that there is another difference between tariffs and quotas in their economic effects. The terms of trade could deteriorate for a country when it imposes a tariff. However, the terms of trade will always improve for a country when it imposes an import quota or an export quota.

Professor of Economics, University of Hawaii at Manoa. The author is grateful to an anonymous referee for valuable comments, but is responsible for any error which remains.

Notes

1. The trading point will be somewhere between G and D on the international price line Ot in case that the home government wants to spend the tariff revenue on both goods X and Y. The welfare of the private sector also will be measured by the trade indifference curve tangent to Od at C.

2. It is assumed that tariff revenues are redistributed to the private sector in the form of lump-sum transfers.

3. It is assumed that an import quota or an export quota is always binding and fully utilized.

4. The conclusion will not be affected if any non-optimum import quota is imposed instead.

5. It is assumed that the home government raises import quota or export quota revenues by selling import or export licenses through competitive auctions. When import quota or export quota revenues are redistributed to the private sector, it is done in the form of lump-sum transfers.

6. When the home government wants to spend the import quota revenue on both goods X and Y, the domestic price line will lie between lines OR and OV. However |Mathematical Expression Omitted~ still measures the terms of trade.

7. The conclusion will not be affected if any other export quota is imposed instead.

8. In case that the home government wants to spend the export quota revenue on both good X and good Y, OT still measures the terms of trade. However, the domestic price line will lie between OZ and Oa. For example, the domestic price line will coincide with OT if the home government spends the export quota revenue on Qe of good X and eQ of good Y.

References

(1) Falvey, Rodney, "A Note on the Distinction between Tariffs and Quotas," Economica, August 1975, pp. 319-326.

(2) Lerner, A.P., "The symmetry between Import and Export Taxes," Economica, August 1936, pp. 306-313; reprinted in Johnson, Harry G. and Caves, Richard E., eds., Readings in International Economics (Richard D. Irwin, 1968), pp. 197-203.

(3) Meade, James E., A Geometry of International Trade, (1952, George Allen and Unwin), Chapter 6.

(4) Metzler. Lloyd A., "Tariffs, the Terms of Trade, and the Distribution of National Income," Journal of Political Economy, February 1949, 1-29.
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Author:Yeong-Her Yeh
Publication:American Economist
Date:Sep 22, 1992
Words:2283
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