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 competition*between the two countries in the model. Ricardo's idea, put forward in his 1926 book*Principles of Economics,* was that countries export goods in which they have a*comparative 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**