The labour (cost) theory of value, cannot explain the exchange values in international trade due to the immobility of labour as factor of production between different countries which prohibits the application of this theory to trade taking place between countries.
Commodities would exchange in the ratio of the quantities of labour embodies in them if labour were perfectly mobile between countries.
Any divergence between their exchange ratio and their cost ratio would be eliminated by the market forces of demand and supply.
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If the product of an industry can be sold at more than the value of labour it contains, additional labour will be transferred to that industry from other occupations.
The supply of the commodity will expand until the price falls to become equal to the value of labour embodies in it.
Conversely, if the commodity sells for less than the value of its labour contents, labour will move away from that industry into other lines of production.
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Thus, the supply of the commodity will decrease and its price will rise until the price equals the labour cost of production of the commodity.
The labour cost principle implies that in different branches of production there is a tendency of wages towards equality within a country so that prices of goods will be equal to the returns to labour in all lines of production and regions within the country.
However, this equilibrating mechanism does not operate between two countries due to the assumption of immobility of labour between the countries.
Thus trade will emerge if the exchange ratio between the two commodities is different in two countries.