Factor-Price Equalization Theorem:

According to the factor-price equalisation theorem when the prices of goods are equalised between countries due to  international trade,  the prices of the factors  (i.e. capital and  labour) also get equalised between countries. This implies  that freer trade will equalise the wages of workers and the rentals earned on capital throughout the world in the ultimate analysis.

The theorem derives from the assumptions of the H-0 model, of which  the most  critical  is  the assumption that  the two countries share the same technology  and that markets are perfectly competitive.  In perfect competition, factors are paid on the basis of the value of their marginal productivity which in  turn depends  upon  the  prices of the goods. Thus, when prices differ between countries so will their marginal productivities and hence so will their wages and rents. However, once prices of goods are equalised, as they are in free trade demonstrated earlier,  the  value of marginal  products are also equalised between countries and hence  the countries must also share  the same wage rates and rental rates.

However,  it should be noted  that the factor-price equalisation is unlikely to apply perfectly in the real world. The H-0 model assumes that technology is the ske  between countries in order to focus on the effects of different factor endowments.  If production technologies differ across countries,  as we assumed in the Ricardian model,  then factor prices would not equalise once goods prices
equalise.