Editing Stolper–Samuelson theorem (section)

==Derivation==
Considering a two-good economy that produces only wheat and cloth, with labor and land being the only factors of production, wheat a land-intensive industry and cloth a labor-intensive one, and assuming that the price of each product equals its marginal cost, the theorem can be derived.

The price of cloth should be:

: (1) <math>P(C)= ar + bw, \, </math>

with ''P''(''C'') standing for the price of cloth, ''r'' standing for rent paid to landowners, ''w'' for wage levels and ''a'' and ''b'' respectively standing for the amount of land and labor used, and do not change with the prices of goods.

Similarly, the price of wheat would be:

: (2) <math>P(W) = cr + dw \, </math>

with ''P''(''W'') standing for the price of wheat, ''r'' and ''w'' for rent and wages, and ''c'' and ''d'' for the respective amount of land and labor used, and also considered to be constant.

If, then, cloth experiences a rise in its price, at least one of its factors must also become more expensive, for equation&nbsp;1 to hold true, since the relative amounts of labor and land are not affected by changing prices. It can be assumed that it would be labor—the factor that is intensively used in the production of cloth—that would rise.

When wages rise, rent must fall, in order for equation&nbsp;2 to hold true. But a fall in rent also affects equation&nbsp;1. For it to still hold true, then, the rise in wages must be more than proportional to the rise in cloth prices.

A rise in the price of a product, then, will more than proportionally raise the return to the most intensively used factor, and decrease the return to the less intensively used factor.