1. This question looks at the theory of comparative advantage. Imagine a world in which there are just two countries, F and G, and just two goods, X and Y.

Consider the following six situations. Each one shows alternative amounts of goods X and Y that the two countries can produce for a given amount of resources. Assume constant costs. In each case give the (pre-trade) opportunity cost of X in terms of Y.

(a) Country F: 10 units of X or 20 units of Y. 1X = 2Y

Country G: 10 units of X or 10 units of Y. 1X = 1Y

(b) Country F: 12 units of X or 12 units of Y. 1X = 1Y

Country G: 6 units of X or 8 units of Y. 1X = 1.33Y

(c) Country F: 8 units of X or 8 units of Y. 1X = 1Y

Country G: 10 units of X or 10 units of Y. 1X = 1Y

(d) Country F: 20 units of X or 5 units of Y. 1X = 0.25Y

Country G: 18 units of X or 2 units of Y. 1X = 0.11Y

(e) Country F: 10 units of X or 8 units of Y. 1X = 0.8Y

Country G: 6 units of X or 6 units of Y. 1X = 1Y

(f) Country F: 2 units of X or 4 units of Y. 1X = 2Y

Country G: 3 units of X or 6 units of Y. 1X = 2Y

2. Referring to the six different situations given in Q1, and assuming no transport costs:

(a) In which situations will country F export good X and import good Y? (b), (e)

(b) In which situations will country F export good Y and import good X? (a), (d)

(c) In which situations will country F export both goods? none

d) In which situations will country F import both goods none

(e) In which situations will no trade take place?  (c), (f)

3. In situation (a) in Q1, assume that before trade the price ratios of the two goods were equal to their opportunity cost ratios. 

(a) What would the pre-trade price ratio (P_X/P_Y) be in country F? 2

(b) What would the pre-trade price ratio (P_X/P_Y) be in country G? 1

(c) Now assume that trade is opened up and that 1 unit of X exchanges for 1.5 of Y. Demonstrate how both countries have gained. 

Country F has gained because, before trade, to obtain 1 unit of X it had to sacrifice 2 units of Y (the opportunity cost of X was 2Y); whereas with trade, it can import 1 unit of X by exporting only 1.5 units of Y (the opportunity cost of X is now only 1.5Y).

Country G has gained because, before trade, to obtain 1 unit of Y, it had to sacrifice 1 unit of X (the opportunity cost of Y was 1X); whereas with trade, it can import 1 unit of Y by exporting only ²/₃ of a unit of X (the opportunity cost of Y is now only 0.67Y).