The Ricardian model of trade
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.
Suzie 10kg 20kg
Laura 5kg 30kg
If there are potential gains from trade, which 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 6 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 20 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.
v) Suzie should specialise in producing tea and Laura should specialise in coffee production; the price for a kg of coffee should be between 1/2 and 1/3 kgs of tea.
vi) There are no potential gains from trade
I just posted to a very similar question, where the figures in the table were such that there were no gains from trade. Here, the figures differ in their ratios such that there is now an advantage for the two ladies, Suzie and Laura, in trading their produce with one another. See the first reference link below to see the post to the other question.
To recap, 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.
To work out which of the two ladies has the comparative advantage, if either, we can look at the opportunity costs each of them incurs 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. 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). The amounts for Suzie are the same as in the other question based on a very similar scenario (see first link below).
Substituting into equation 1, 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. The amounts for Laura are different to the amounts in the other very similar question (see link below). Now, from this table we have
O(L,x) = 30/5 = 6
Whereas in the other question, the results were the same, meaning that neither lady had the comparative advantage in producing tea over coffee, here
O(L,x) > O(S,x)
so that Laura has a comparative advantage over Suzie in producing tea rather than coffee. In this scenario, Laura would produce tea and sell it to Suzie in exchange for coffee (which Suzie would specialise in making)
So now, given there are potential gains from trade which of the statements i)-v) given in the question is true?
First, we know that Suzie should specialise in producing coffee (S produces goods x, and L produces goods y), so ii) and v) are eliminated.
We now need to work out bounds for the (international relative) price P of goods x (coffee) to goods y (tea). According to the Ricardian trade model, if S specialises in goods x and L specialises in goods y, the relative price is bounded by the two opportunity costs O(S,x) and O(L,x) such that
O(S,x) < P < O(L,x)
Since we know that O(S,x) = 2 and O(L,x) = 6 then we have that the price P of x (coffee) in terms of y (tea) satisfies
2 < P < 6
so that the price of coffee in terms of tea is bounded by 2kg and 6kg of tea.
Therefore statement i) is true