A refinement in the concept of net barter terms of trade was made by G.S. Dorrance by introducing the concept of income terms of trade. Dorrance defined income terms of trade as the index of the value of exports divided by the price index for imports. Thus:
Where, T stands for the income terms of trade,
P denotes prices, and
Q denotes quantity,
x denotes exports, and
m denotes imports.

The "income terms of trade" are also referred to as country's "capacity to import", for p determines Qm. Hence, it may be regarded as a superior concept to net barter terms of trade for the less developed countries' purposes.

Dorrance has improved upon the concept of the net barter terms of trade by formulating the concept of the income terms of trade. This index takes into account the volume of exports of a country and its export and import prices (the net barter terms of trade). It shows a country’s changing import capacity in relation to changes in its exports.

Thus, the income terms of trade is the net barter terms of trade of a country multiplied by its export volume index. It can be expressed as

Ty = Tc.Qx = Px.Qx/Pm = Index of Export Prices x Export Quantity/Index of Import Prices

Where Ту is the income terms of trade, Tc the commodity terms of trade and Qx the export volume index.

A.H. Imlah calculates this index by dividing the index of the value of exports by an index of the price of imports. He calls it the “Export Gain from Trade Index.”

Taking 1971 as the base year, if

Px = 140, Pm = 70 and Qx = 80 in 1981, then

Py = 140 x 80/70 = 160

It implies that there is improvement in the income terms of trade by 60 per cent in 1981 as compared with 1971.

If in 1981, Pi = 80, Pm =160 and Qx =120, then

Py = 80 x 120 / 120 = 60

It implies that the income terms of trade have deteriorated by 40 per cent in 1981 as compared with 1971.

A rise in the index of income terms of trade implies that a country can import more goods in exchange for its exports. A country’s income terms of trade may improve but its commodity terms of trade may deteriorate. Taking the import prices to be constant, if export prices fall, there will be an increase in the sales and value of exports. Thus while the income terms of trade might have improved, the commodity terms of trade might have deteriorated.

The income terms of trade is called the capacity to import. In the long-run, the total value of exports of a country must equal to its total value of imports, i.e., Px.Qx = Pm.Qm or Px.Qx/Pm = Qm. Thus Px.Qx/ Pm determines Qm which is the total volume that a country can import. The capacity to import of a country may increase if other things remain the same (i) the price of exports (Px) rises, or (if) the price of imports {Pm) falls, or (Hi) the volume of its exports (Qx) rises. Thus the concept of the income terms of trade is of much practical value for developing countries having low capacity to import.

It’s Criticisms:
The concept of income terms of trade has been criticised on the following counts:

1. Fails to Measure Gain or Loss from Trade:
The index of income terms of trade fails to measure precisely the gain or loss from international trade. When the capacity to import of a country increases, it simply means that it is also exporting more than before. In fact, exports include the real resources of a country which can be used domestically to improve the living standard of its people.

2. Not Related to Total Capacity to Import:
The income terms of trade index is related to the export based capacity to import and not to the total capacity to import of a country which also includes its foreign exchange receipts. For example, if the income terms of trade index of a country have deteriorated but its foreign exchange receipts have risen, its capacity to import has actually increased, even though the index shows deterioration.

3. Inferior to Commodity Terms of Trade:
Since the index of income terms of trade is based on commodity terms of trade and leads to contradictory results, the concept of the commodity terms of trade is usually used in preference to the income terms of trade concept for measuring the gain from international trade.

Single Factoral Terms of Trade (SFTT):
The concept of commodity terms of trade does not take account of productivity changes in export industries. Prof. Viner had developed the concept of single factoral terms of trade which allows changes in the domestic export sector. It is calculated by multiplying the commodity terms of trade index by an index of productivity changes in domestic export industries. It can be expressed as:

Ts = Tc.Fx = Px.Fx/Pm

Where Ts is the single factoral terms of trade, Tc is the commodity terms of trade, and Fx is the productivity index of export industries.

It shows that a country’s factoral terms of trade improve as productivity improves in its export industries. If the productivity of a country’s exports industries increases, its factoral terms of trade may improve even
though its commodity terms of trade may deteriorate. For example, the prices of its exports may fall relatively to its import prices as a result of increase in the productivity of the export industries of a country. The commodity terms of trade will deteriorate but its factoral terms of trade will show an improvement.

Its Limitations:
This index is not free from certain limitations. It is difficult to obtain the necessary data to compute a productivity index. Further, the single factoral terms of trade do not take into account the potential domestic cost of production of imports industries in the other country. To overcome this weakness, Viner formulated the double factoral terms of trade.

Double Factoral Terms of Trade (DFTT):
The double factoral terms of trade take into account productivity changes both in the domestic export sector and the foreign export sector producing the country’s imports. The index measuring the double factoral terms of trade can be expressed as

Td = Tc. Fx/Fm = Px/Fm . Fx/Fm

Where Td is the double factoral terms of trade, Px/Pm is the commodity terms of trade, Fx is the export productivity index, and Fm is the import productivity index.

It helps in measuring the change in the rate of exchange of a country as a result of the change in the productive efficiency of domestic factors manufacturing exports and that of foreign factors manufacturing imports for that country. A rise in the index of double factoral terms of trade of a country means that the productive efficiency of the factors producing exports has increased relatively to the factors producing imports in the other country.

Its Criticisms:
1. Not Possible to Construct a Double Factoral Terms of Trade Index:
In practice, however, it is not possible to calculate an index of double factoral terms of trade of a country. Prof. Devons made some calculations of changes in the single factoral terms of trade of England between 1948-53. But it has not been possible to construct a double factoral terms of trade index of any country because it involves measuring and comparing productivity changes in the import industries of the other country with that of the domestic export industries.

2. Required Quantity of Productive Factors not Important:
Moreover, the important thing is the quantity of commodities that can be imported with a given quantity of exports rather than the quantity of productive factors required in a foreign country to produce its imports.

3. No Difference between the Double Factoral Terms of Trade and the Commodity Terms of Trade:
Again, if there are constant returns to scale in manufacturing and no transport costs are involved, there is no difference between the double factoral terms of trade and the commodity terms of trade of a country.

4. Single Factoral Terms of Trade is more Relevant Concept:
According to Kindleberger, “The single factoral terms of trade is a much more relevant concept than the double factoral. We are interested in what our factor can earn in goods, not what factor services can command in the services of foreign factors. Related to productivity abroad moreover, is a question of the quality of the goods imported.” ##### Ahmed Xahir

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