In order to understand the Stoplet-Samuelson Theorem we need to understand the Hekscher-Ohlin model first, as the theorem is within the context of that model. In that model there are two countries with different factor endowments, one capital abundant and the other one labor abundant. There are two products, one capital intensive and the other one labor intensive. There are two factors, one is labor and the other one is capital.
In this context, the theorem shows that there is a positive relationship between the changes of the price of an output and the changes in the price of input factor used in a higher percentage (intensively) (for example: labor intensive or capital intensive) in producing the final product. And there is a negative relationship between changes in the price of an output and changes in the price of the factor not used intensively in producing that product.
To explain the theorem, we can have a look at the real world and think about what happens when the U.S. ( a capital abundant and labor scarce country) takes part of the international trade. Would the high-waged labor lose because of international trade? This is the first thing I would ask myself, and it seems to be logical that labor will lose competitiveness with other labor abundant countries, and therefore labor would lose because of international trade.
Samuelson and Stolper demonstrated that free trade lowers the real wage of the scarce factor and raises that of the abundant factor compared to autarky and that protection raises the real wage of the scarce factor of production and lowers the real wage of the abundant factor of production.
How did they demonstrate it?
A small country select a tariff as a trade barrier. As a result, this will increase the price of the import good in comparison with the exported good.
In case of homogenous products,
