Ch. 3: The Specific Factors Model: Trade and Income Distribution

The Ricardian model shows that countries as a whole gain from trade, but because labour is its only factor it cannot say who wins and who loses inside a country. Opening a country to trade does generate winners and losers. The specific factors (SF) model (Feenstra and Taylor, Chapter 3) explains who gains and who loses. It keeps the idea from the Ricardian model that free trade raises the relative price of the export good and lowers the relative price of the import good, and it traces how these price changes affect the earnings of the different factors of production. The lecture again uses two countries, Greece and Denmark, and two goods, agriculture (A) and manufacturing (M).

Factors of production: specific and mobile

The model is called the specific factors model because each sector uses one factor that cannot be used in the other sector:

• Land (T) is specific to agriculture: it is used only in producing A.
• Capital (K) is specific to manufacturing: it is used only in producing M.
• Labour (L) is used in both sectors; it is the mobile factor and moves between sectors until wages are equal.

Employment in A is L A and employment in M is L M, and full employment requires L = L A + L M.

Note on the slides: one slide states the pairing the other way round (A produced with labour and capital, M with labour and land). The rest of the lecture (the effects of trade and of migration on landowners and capitalists) only makes sense with land specific to A and capital specific to M, which is also the textbook assumption, so that pairing is used here. What matters for the exam is the logic: the factor specific to the sector whose relative price rises gains, and the factor specific to the other sector loses.

An important difference from the Ricardian model: in the SF model a country produces both goods after free trade. It exports one of them (the exportable) and imports the other (the importable). There is no complete specialisation, because the specific factor in each sector keeps production there profitable.

Diminishing marginal product of labour

Because the specific factor is fixed in each sector, adding more workers raises output by smaller and smaller amounts: the marginal product of labour (MPL) declines as the labour input increases (diminishing returns). The lecture shows two diagrams:

The VMPL curve is the labour demand curve

A competitive firm hires workers as long as the value a worker adds exceeds the wage, and stops when VMPL equals the wage W. When the wage is W 0, optimal employment is L 0 (where the VMPL curve crosses W 0). When the wage rises to W 1, optimal employment falls to L 1 < L 0. The VMPL curve therefore shows the quantity of labour demanded at each wage: the VMPL curve is also the labour demand curve of the sector.

The distribution of income between wages and profits

At wage W 0 and employment L 0, the total value of output produced by L 0 workers equals the area under the VMPL curve from 0 to L 0. This area splits into two parts:

• Area A (rectangle W 0 × L 0): the total wage payment to the L 0 workers.
• Area B (the triangle under the VMPL curve and above the wage line): what is left over, the profits or earnings of the specific factor (rent to landowners in A, return to capitalists in M).

So in each sector the value of output = wage bill + income of the specific factor. The specific factor earns the surplus that arises because the earlier workers add more value than the wage they are paid.

Equilibrium allocation of labour between sectors

The key diagram puts both sectors in one box. The horizontal axis has length O A O M = L, the total labour force. Employment in A is measured from the left origin O A to the right, and employment in M from the right origin O M to the left. The labour demand curve of A (P A × MPL A) slopes down from the left; the labour demand curve of M (P M × MPL M) slopes down from the right (so it rises from left to right in the picture).

Because labour is mobile, wages must be equal in the two sectors. Equilibrium is at the intersection point (called ε0 on the slides): the wage is W 0, employment in A is O A E 0 = L A and employment in M is E 0 O M = L M. At any other allocation the wage would be higher in one sector and workers would move there.

Opening to trade: the effect of a rise in the relative price of the export good

Opening to international trade means that the relative price of the exportable good, the good in which the country has CA, rises. Assume the exportable is A. Without loss of generality the price of M is held constant, so P A rises to P' A > P A.

1. The labour demand curve of A shifts upwards in proportion to the price rise (from P A × MPL A to P' A × MPL A).
2. At the old wage, sector A wants more workers, so workers move from M to A. The new equilibrium is at point ε1 with employment O A E 1 in A (higher) and E 1 O M in M (lower).
3. The (nominal) wage rises from W 0 to W 1, but by less than the price of A in percentage terms, because the M labour demand curve does not shift and more labour in A lowers MPL A.

Effects on real incomes:

Hence international trade generates winners and losers: the specific factor in the export sector gains, the specific factor in the import-competing sector loses, and the mobile factor (labour) may gain or lose. This matches the story of the fishing village: boat owners gained and those tied to garment making lost.

Worked numerical example

Suppose L = 100 workers and the MPL in each sector falls linearly: MPL A = 20 minus 0.2 L A and MPL M = 20 minus 0.2 L M. Initially P A = P M = 1.

Autarky equilibrium. Equal wages require 20 minus 0.2 L A = 20 minus 0.2 (100 minus L A), so L A = L M = 50 and W = 20 minus 10 = 10. Land rent (area under VMPL A above the wage) = 0.5 × (20 minus 10) × 50 = 250. Capital income in M is likewise 250. The wage bill is 10 × 100 = 1,000.

Trade raises P A by 20% to 1.2 (P M stays 1). Now 1.2 (20 minus 0.2 L A) = 20 minus 0.2 (100 minus L A), which gives 24 minus 0.24 L A = 0.2 L A, so L A = 24/0.44 = 54.5 and L M = 45.5. The wage becomes W = 20 minus 0.2 × 45.5 = 10.91.

The numbers show the magnification pattern: the specific factor in the export sector gains more than the price rise (43% versus 20%), labour gains less than the price rise (9%), and the specific factor in the import sector loses. Total income at the new prices rises, which again reflects the gains from trade: the winners gain more than the losers lose (valued at world prices), so compensation is possible in principle.

Why this matters for trade policy

Because the losses from trade are concentrated on owners of specific factors in import-competing industries (and, in the short run, on workers who must move), these groups have a strong incentive to lobby for protection. The gains, spread over consumers and the export sector, are less visible. This explains the political demand for tariffs and quotas examined in the trade policy chapters, and it explains why governments sometimes use compensation schemes such as trade adjustment assistance. In the textbook the SF model is seen as a medium-run model: in the long run capital and land can also be moved or redeployed, and the Heckscher-Ohlin model replaces it.

Comparison with the Ricardian model