# Terms of trade

In international economics and international trade, terms of trade are the ratio of the price of an export commodity(s) to the price of an import commodity(s). "Terms of trade" are sometimes used as a proxy for the relative social welfare of a country, but this heuristic is technically questionable and should be used with extreme caution. An improvement in a nation's terms of trade is good for that country in the sense that it has to pay less for the products it imports, that is, it has to give up less exports for the imports it receives.

## Two country model

In the simplified case of two countries and two commodities, terms of trade is defined as the ratio of the price a country must pay for its import commodity to the price it receives for its export commodity. In this simple case the imports of one country are the exports of the other country. For example, if a country exports 100 dollars worth of export product in exchange for 50 dollars worth of imported product, that country's terms of trade are 100/50 = 2. The terms of trade for the other country must be the reciprocal (50/100 = .5). When this number is falling, the country is said to have "deteriorating terms of trade". If multiplied by 100, these calculations can be expressed as a percent (200% and 50% respectively). If a country's terms of trade fall from say 100% to 70% (from 1.0 to .7), it has experienced a 30% deterioration in its terms of trade. When doing longitudinal (time series) calculations, it is common to set the base year to 100% to make interpretation of the results easier.

## Multi-commodity multi-country model

In the more realistic case of many products exchanged between many countries, terms of trade can be calculated using a Laspeyre's index. In this case, a nation's terms of trade is the ratio of the Laspeyre price index of exports to the Laspeyre price index of imports. The Laspeyre export index is the current value of the base period exports divided by the base period value of the base period exports. Similarly, the Laspeyres import index is the current value of the base period imports divided by the base period value of the base period imports.

[itex]{{p_x^c\, q_x^0}\over{p_x^0\, q_x^0}}

\left/ {{p_m^c\, q_m^0}\over{p_m^0\, q_m^0}}\right.[itex]

Where

[itex]p_x^c=\mbox{price}\ \mbox{of}\ \mbox{exports}\ \mbox{in}\ \mbox{the}\ \mbox{current}\ \mbox{period},[itex]
[itex]q_x^0=[itex] quantity of exports in the base period
[itex]p_x^0=[itex] price of exports in the base period
[itex]p_m^c=[itex] price of imports in the current period
[itex]q_m^0=[itex] quantity of imports in the base period
[itex]p_m^0=[itex] price of imports in the base period

## Other terms-of-trade calculations

1. The net barter terms of trade is the ratio (expressed as a percentage) of relative export and import prices when volume is held constant.
2. The gross barter terms of trade is the ratio (expressed as a percent) of a quantity index of exports to a quantity index of inputs.
3. The income terms of trade is the ratio (expressed as a percent) of the value of exports to the price of imports.
4. The single factorial terms of trade is the net barter terms of trade adjusted for changes in the productivity of exports.
5. The double factorial terms of trade adjusts for both the productivity of exports and the productivity of imports.

## Limitations

Terms of trade should not be used as synonymous with social welfare, or even Pareto economic welfare. Terms of trade calculations do not tell us about the volume of the countries' exports, only relative changes between countries. To understand a county's social utility changes, it is necessary to consider changes in the volume of trade, changes in productivity and resource allocation, and changes in capital flows.

In the real world of over 200 nations trading hundreds of thousands of products, terms of trade calculations can get very complex. The possibility of errors is significant.

## References

• Bhagwati, J. (1959) Growth terms of trade and comparative advantage, Economia Internazionale, 1959.
• Dorrance, J. (1948) The income terms of trade, Review of Economic Studies, 1948-49.
• Krueger, A. and Sonnenschein, H. (1967) The terms of trade, the gains from trade, and price divergence, International Economic Review, vol 8-1, February, 1967, pp. 121-127.de:Terms of Trade

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