# Consider the table below. It shows the number of kilos of coffee or tea that Laura and Suzie can produce in 10 hours of work.                              ...

Consider the table below. It shows the number of kilos of coffee or tea that Laura and Suzie can produce in 10 hours of work.

Coffee               Tea

Suzie            10kg               20kg

Laura            15kg               30kg

If there are potential gains from trade, which one of the following statements is true?

i) Suzie should specialise in producing coffee and Laura should specialise in tea production; the price for a kg of coffee should be between 2 and 3 kgs of tea.

ii) Suzie should specialise in producing tea and Laura should specialise in coffee production; the price for a kg of coffee should be between 3 and 6 kgs of tea.

iii) Suzie should specialise in producing coffee and Laura should specialise in tea production; the price for a kg of coffee should be between 15 and 30 kgs of tea.

iv) Suzie should specialise in producing coffee and Laura should specialise in tea production; the price for a kg of coffee should be between 10 and 20 kgs of tea.

Or, alternatively

v) There are no potential gains from trade.

mathsworkmusic | Certified Educator

The model assumed is the Ricardian model of trade.

For Suzie and Laura, there are only gains to be made from trade if both can specialise in one or other of the two products, tea or coffee, where the production of one person complements the other. That is, one or other of them produces tea whilst the other person produces coffee. The person who produces tea necessarily does so because they are the one who has a comparative advantage in producing tea, and a complementary situation exists in the production of coffee, so that there is balance in the trade system. If one person has comparative advantage in producing both tea and coffee, there can be no gains in trade as the other person has nothing worthwhile (assuming tea and coffee are the only commodities in the world of Suzie and Laura) to give in payment for the tea and coffee.

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. Here, we substitute 'country' for 'person', where there are only two: Suzie (S) and Laura (L).

To work out which of the two ladies has the comparative advantage, if either, we can look at the opportunity costs each of them incurrs in terms of the goods x (coffee) or y (tea) when producing the other of the two goods. This is essentially the amount of goods y that the person could have produced had they not produced 1 unit of the goods x.

The opportunity cost to S (using Suzie as an example) if she produces 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 (in unit time) 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 S if she produces 1 unit of x, in terms of the goods y, is

O(S,x) = MPL(S,y)/MPL(S,x)    (1)

We are given in the question that the amount of coffee Suzie can produce in unit time (here 10hrs) is MPL(S,x) = 10kg, whereas the amount of tea she can produce in unit time is MPL(S,y) = 20kg. NB there is only one 'labourer' in this scenario, so the MPL is in fact just the product of labour (PL).

Substituting into equation 1 then, the opportunity cost to S if she produces 1 unit of coffee, in terms of units of tea, is given by

O(S,x) = 20/10 = 2

Since this is >1, Suzie is more effective at producing y (tea) than x (coffee), but this doesn't necessarily mean that she has a comparative advantage over Laura in the making of tea over coffee.

Let's look at the same measure for Laura:

O(L,x) = 30/15 = 2

The result is the same, meaning that both ladies incur exactly the same opportunity cost (2 parts tea to 1 part coffee) when making coffee instead of tea. For either lady to have a comparative advantage in making tea, we require that the opportunity costs are not equal, that is

O(S,x) != O(L,x)

Since the opportunity costs are equal however, there are no gains to be made from trade for either lady, so there is no trade. The two ladies would just make tea and coffee independently of one another in whatever quantities they needed/wanted for their own personal consumption.