Ch. 4: International Factor Movements: Migration in the Specific Factors Model

Trade in goods is one way countries interact; the movement of factors of production (labour through migration, capital through foreign direct investment) is another. The course outline lists international factor movements (Feenstra and Taylor, Chapter 5) as the last topic of Part A. In the lecture on international trade, income distribution and migration, the specific factors model is used to analyse the effects of an inflow of migrants on the wages of domestic workers, on the incomes of landowners and capitalists, and on the total income of the host country. The main result is the immigration surplus: immigration lowers wages but raises the income of the owners of the specific factors by more, so the total income of the domestic citizens rises.

Assumptions: full employment in the domestic economy

• Wages in the domestic economy are flexible and adjust to changes in labour supply so that full employment prevails. (Immigration therefore does not create unemployment in the model; it lowers the wage.)
• Labour is the mobile factor, used in both sectors; land (in agriculture, A) and capital (in manufacturing, M) are the specific factors and their amounts do not change.
• Immigrants are identical to domestic residents in their labour market skills, so they are perfect substitutes and earn the same wage.
• The domestic economy remains small after the inflow: the relative price of goods P A/P M, determined on world markets, is not affected. The labour demand curves (P × MPL) therefore do not shift because of price changes.

The diagram in words

The analysis uses the box diagram of the specific factors model. Initially the labour supply is L, the length of the horizontal axis O A O M. The labour demand curve of A is drawn from the left origin O A and that of M from the right origin O M. Equilibrium is at point ε0 with employment O A E 0 = L A in agriculture and E 0 O M = L M in manufacturing, and wage W 0.

Then M migrants arrive. The labour supply becomes L + M, so the box becomes wider: the right origin moves from O M to O' M, with O A O' M = L + M. The M labour demand curve is drawn from the new origin and therefore shifts to the right by the number of migrants (the distance E 0 E 2 in the slides). The new equilibrium is at ε1 where the A curve crosses the shifted M curve.

Employment rises in both sectors: the migrants are absorbed partly in agriculture and partly in manufacturing, because the lower wage makes it profitable for both sectors to hire more workers. As a result, the income of domestic workers declines, while the income of both capitalists and landowners increases.

Gains and losses measured by areas

On the slide the horizontal strip between W 0 and W 1 is divided into areas labelled A, B, Γ (Gamma) on the agricultural side and H (Eta), K, Λ (Lambda) on the manufacturing side; below W 1, the areas Z, Δ (Delta), Π (Pi) and I lie under the demand curves over the section of the axis where the migrants are employed.

Another way to see the surplus. The E 0 E 2 immigrants raise the value of production in sector A by the area under the A demand curve over their employment there (Z + Δ + Γ) and in sector M by the corresponding area (Π + I + H). They are paid only the wage W 1 for each unit of labour, which equals Z + Δ + Π + I. So the immigrants add more to total production than they receive in wages, and the difference Γ + H stays with the domestic population. The reason is diminishing marginal product: the first migrants hired add more value than W 1, but all migrants are paid the wage of the last one.

Worked numerical example

Use the same economy as in the specific factors chapter: MPL A = 20 minus 0.2 L A, MPL M = 20 minus 0.2 L M, P A = P M = 1, and initially L = 100 domestic workers. The equilibrium is L A = L M = 50 with W 0 = 10; land rent = capital income = 0.5 × 10 × 50 = 250 each.

Now 20 migrants arrive, so L + M = 120. The M labour demand curve shifts right by 20. With equal wages, L A = L M = 60 and W 1 = 20 minus 0.2 × 60 = 8.

Check of the surplus as two triangles: in each sector employment rises by 10 and the wage falls by 2, so each triangle is 0.5 × 2 × 10 = 10, and Γ + H = 20. Check via output: output rises by 180, immigrants receive 160, and 180 minus 160 = 20 remains for domestic citizens. The losses of workers (200) are more than offset by the gains of landowners and capitalists (220).

Interpretation and wider implications

• Immigration is like trade: it raises total income of the host country but has strong distributional effects. Workers who compete with immigrants lose; owners of the factors that work with labour (land, capital) gain.
• The immigration surplus is small relative to the redistribution: in the example 20 against transfers of 200. This helps explain why immigration is politically controversial.
• The result depends on the assumptions: full employment and flexible wages (otherwise immigration could raise unemployment in the short run), identical skills (with different skills, immigrants may complement rather than compete with domestic workers), fixed specific factors (in the long run capital may flow in, raising the MPL again and dampening the wage fall), and a small economy (prices do not change).
• By the same logic, in the source country emigration raises the wage of the workers who stay and lowers the incomes of the owners of land and capital there.
• The same framework applies to other factor movements: an inflow of capital into manufacturing raises MPL in M, shifts the M labour demand curve up, raises wages and lowers the return of the other specific factor, while the foreign owners of the capital earn its return.

Mock exam application

A mock exam question asks which changes in the incomes of workers, capitalists and landowners in the receiving country B are possible after migration from A to B in the SF model. The model requires: (1) workers lose; (2) landowners and capitalists both gain; (3) the combined gains exceed the workers' loss (positive immigration surplus). Checking the options: