Suppose the world has two countries, Home and Foreign. All variables in Foreign countries will be denoted with an asterisk (*). In each country, there are two sectors: Tradable (T) and Non-tradable (N). The “Tradable” sector produces goods that can be shipped, sold, and consumed in both countries (for example, electronics) while the “Nontradable” sector produces goods that can only be consumed in the local country (think haircut: Home haircut service can only be consumed by Home residents). In each country, residents can work for either sector T or N. Assume people can freely move between sectors within a country, but not across countries.
Argue that perfect mobility between sectors implies that the labor wage being offered in both sector must be the same.
Since residents in the home country can either work in sector T or N, the other country would be producing the other sector opposite to that of the home country. Thus if we assume that people can move freely between sectors,i.e perfect mobility between sectors take place then free trade can take place. There will not be full specialisation of any one good for the country and therefore this will result in one international price where demand equals supply. Additionally, since international price determine the factor price ratio in the domestic market(Stolper Samuelson Theory), the one international price will determine the factor price ratio which will be equal for both the countries.
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