Consider two countries Portugal (Home) and England (Foreign, denoted by *) and two goods: Cheese (C) and Wine (W). Consider the information given below:
Qc=Qc(Lc)=(1/aLc)Lc ; Qw= Qw(Lw)=(1/aLw)Lw
aLw=2 ; aLc=1 ; L=3000
a*Lw=3 ; a*Lc=6 ; L*=6000
ii. What is the relative price of C in terms of W in autarky in the two countries?
iii. In which good does each country have a comparative advantage and why?
Given, Qc = (1/aLc)Lc and Qw = (1/aLw)Lw
where, aL denotes unit labor requirements, L denotes total labor supply and Q is the demand.
For cheese: Qc = 3000/1 = 3000 and Qc* = 6000/6 = 1000
For Wine: Qw = 3000/2 = 1500 and Qw* = 6000/3 = 2000
Home (Portugal): Qc = 3000, Qw = 1500.
i.e., opportunity cost of 1 unit Cheese = 1500/3000 = 0.5 unit Wine
Foreign (England): Qc* = 1000 and Qw* = 2000
i.e., opportunity cost of 1 unit cheese = 2000/1000= 2 unit Wine.
So, in Portugal, we can generate 1 unit cheese for every 0.5 unit Wine, while in England, we can generate 1 unit Cheese for 2 units of Wine. or in other words, in Autarky, in Portugal cheese costs half as much as wine and in England, Cheese costs twice as much as wine.
Portugal has comparative advantage in making Cheese, while England has comparative advantage in making Wine. From the calculations, shown above, we can observe that Portugal can make 3000 units of cheese or 1500 units of wine, whereas England can make 1000 units of cheese or 2000 units of wine. So, from point of view of better utilization of resources, it would be ideal if England traded wine for cheese. That way both the countries can be benefited.
Hope this helps.