Deardorff's Glossary of International Economics

Trade and Transformation Curve Diagram

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Small country
Large country
Expansion - Neutral
Small country
Large country
Expansion - Export biased
Small country
Large country
Expansion - Import biased
Small country
Large country


X, Y Outputs of goods X and Y
TX , TY Maximum output of goods X and Y
TXTY Transformation curve
pj Price of good j, j=X,Y
p Relative price of good X
Pi Production point in equilibrium i
Ci Consumption point in equilibrium i
ui Utility (community welfare) in equilibrium i
0 Free trade (initial position)
a Autarky
1 New position with tariff or expansion


The trade and transformation curve diagram combines information about technology and endowments represented by a transformation curve with information about prices represented by price lines to determine levels of production, consumption, and therefore trade. By using community indifference curves the diagram also provides an easy representation of effects on a country's welfare.

The basic diagram shown above starts with the transformation curve, TXTY, the position and shape of which depend on the technologies for producing the two goods, X and Y. It is usually drawn concave to the origin, as shown, representing either diminishing returns due to specific factors in the two industries or differences in their relative factor intensities in the Heckscher-Ohlin Model. The curve is linear in the Ricardian Model, and kinked-linear with Leontief technologies. The position and shape also depend on factor endowments, the curve extending further in the direction of the good for which the country has relatively the most specific or intensive factors.

Prices are added to the diagram via a downward-sloping price line, along which the combined value of goods is constant. A competitive economy maximizes the value of output at the prices facing producers, so if these are domestic prices, production is determined by a tangency between the transformation curve and the price line, as at P0 above. The value of a country's output is also its income, so this price line is also the budget line of consumers in the aggregate. Representing their preferences by a family of community indifference curves, the consumption point is found as a tangency with this price line, as at C0 above. The level of aggregate welfare is the utility reached by this indifference curve, u0 above.

Finally, the quantities traded are found by comparing production and consumption. This can be done by adding the trade triangle to the diagram. Its horizontal side shows the trade of good X (in this case an export, since production is to the right of consumption), and its vertical side shows trade in good Y (import, here).

The diagram can be used for a wide variety of theoretical exercises, including the following.
Comparison of free trade and autarky
In autarky, the country must produce what it consumes. Therefore the best that it can do is to consume on the highest indifference curve that it can reach. This is also what a competitive economy will actually do, since the same price line that induces production at Pa induces consumption there as well. The figure shows immediately that the level of welfare is lower in autarky than with free trade, and also that a country will export the good whose relative price in autarky is lower than the price that will prevail with trade. Trade causes the output of the export good to rise and that of the import good to fall.
Effects of a tariff
A tariff causes the domestic price of the imported good to be higher than the world price, and thus the domestic relative price of the exported good, X in this case, to be lower. If the country is small, so that the world price remains unchanged with the tariff, then the tariff faces producers with a flatter price line, to which they respond by producing less of good X and more of good Y, at a tangency of the transformation curve with this flatter price line. The budget line of the country as a whole is still given by world prices, however, now passing through this new production point, P1. To have balanced trade, consumption must be on this line, at a point of tangency between an indifference curve and another domestic price line parallel to that facing producers. The effects of the tariff in the small country include a drop in welfare compared to free trade, and a reduction in the quantities traded. The large-country case differs, in that the world price of the exported good rises when less of it is supplied to the world market, and this steepens the price line, both world and domestic, as shown. The main difference from the small-country case is that the large country's welfare may rise, as shown.
Production possibilities can expand due either to an advance in technology or to an accumulation of factors. In either case, the transformation curve shifts outward, but it can do this in various ways depending on the cause of the expansion. The diagrams above show three cases, neutral and biased toward goods X and Y respectively. For a small country, trade expands in the first two of these cases, but it declines in the third. For a large country, these changes imply that the world price of X falls and rises respectively. When it falls, as it does most with export-biased expansion, this undermines the benefits of the expansion and may conceivably lower welfare altogether, although it does not in the case shown.


  1. The diagrams are drawn assuming homothetic preferences. That is why the consumption points move radially outward in the small-country cases of expansion. Without that, effects of trade could be somewhat different, depending on which good has the higher income elasticity.
  2. The diagrams all assume balanced trade. Without that, there must be a capital inflow or outflow, which will enable the country to consume either more or less than its income from producdtion. This can be handled by shifting price lines out and in respectively.
  3. The tariff analysis assumes that the tariff revenue is redistributed to consumers. That is why the price line they face is further out than the one faced by producers, since consumer income includes these transfers.