According to the Washington Council on International Trade, comparative advantage is "the ability to produce a good at a lower cost, relative to other goods, compared to another country". The Ricardian model assumes that there is perfect competitionbetween the two countries in the model. Ricardo's idea, put forward in his 1926 bookPrinciples of Economics, was that countries export goods in which they have acomparative advantage as this leads to more efficient production.
To work out which of the two countries has the comparative advantage, we can look at the opportunity costs each country has in terms of the goods x or y when producing the other of the two goods. This is essentially the amount of goods y that the country could have produced had they not produced 1 unit of the goods x.
The opportunity cost to country A if they produce 1 unit of the goods x instead of producing goods y is equal to the marginal product of labour from producing y divided by the marginal product of labour from producing x. The marginal product of labour MPL is the extra quantity of goods produced when one extra labourer is employed to work on producing those goods. If the MPL from producing y is less than that from producing x, then the opportunity cost of producing x in terms of y is less because the gains from producing y instead of x is less.
The opportunity cost to country A if they produce 1 unit of x in terms of the goods y is
O(A,x) = MPL(A,y)/MPL(A,x) = 3/4 (labour directed to producing y is less effective than that directed to producing x)
That is, country A would have produced only 3/4 of a unit of goods y instead of producing 1 unit of goods x.
Similarly, the opportunity cost to country B to produce 1 unit of x in terms of the goods y is
O(B,x) = MPL(B,y)/MPL(B,x) = mu/2
a) In the Ricardian two-country model, if country A is exporting the goods x to country B, then it must be that country A has a comparative advantage in its ability to produce goods x. When A produces a unit of x, the amount of y that it could have produced instead is smaller than the amount of y that could be produced by country B instead of producing a unit of goods x. For the situation to be in balance such that country A is exporting x to country B then, the opportunity cost to A of producing goods x in terms of goods y must be less than that to B of producing goods x in terms of y, that is
O(A,x) < O(B,x) , giving
3/4 < mu/2, which implies that
mu > 6/4
b) Now, country B is exporting goods x to country A (equivalent to A importing x from B), so first of all we must have that
O(B,x) < O(A,x) , giving
mu/2 < 3/4 which implies that
mu < 6/4
We are now given that the international relative price of goods x to goods y is tau. According to the Ricardian trade model, if country B specialises in goods x and country A specialises in goods y (which is how things must be for the system to be in equilibrium - each country exporting one of the goods x or y, and importing the other), the relative price tau is bounded by the two opportunity costs O(B,x) and O(A,x) such that
O(B,x) < tau < O(A,x)
because the worth of the goods x and y now comes into play. If country B is giving up producing mu/2 of y when producing x, if the worth of (mu/2).y is more than the worth of x, country B would then be missing an opportunity in terms of absolute worth rather than quantities. For B to still be opting to produce x and A to produce y, their opportunity cost of x in terms of the worth of y must be less than the worth of producing a unit of x. Whereas for country A, the opportunity cost of x in terms of the worth of y must be more than the worth of producing a unit of x, since A in fact specialises in producing y.
We know from earlier that O(B,x) = mu/2 and O(A,x) = 3/4 so we have then that
mu/2 < tau < 3/4
as well as that mu < 6/4
The ranges for mu and tau that allow country A to import x from country B (B to export x to A) are
mu < 6/4
mu/2 < tau < 3/4