Consider an economy that consists of two countries, A and B, that can produce two goods, indexed by 1 and 2. Labour is the only factor of production. The unit labour requirements in the production of goods 1 and 2 are given in the following table:
| | Good 1 | Good 2 |
|---|---|---|
| Country A | 1 | 2 |
| Country B | 8 | 40 |
Yic denotes the production of good i in country c and Rc the revenue of country c. Preferences are assumed to be identical across countries. The demand for each good is given by:
D1c = 2Rc * sqrt(p2c/p1c) and D2c = 2Rc * sqrt(p1c/p2c)
where pic is the price of good i in country c. Country A has 1000 units of labour available, and country B has 16000 units of labour. In both countries, production occurs under conditions of perfect competition and labour can move across sectors at no cost.
1. Express the price of both goods in country A as a function of wage and unit labour requirements.
2. What is the relative price of good 1 in terms of good 2 in country A under autarky?
3. What is the equilibrium output of each good in country A?
4. Which country has an absolute advantage in the production of good 1?
5. Which country has a comparative advantage in the production of good 1? Good 2?
6. If the relative price of good 1 in terms of good 2 is 0.4, what is the world supply of each good?
7. Construct the world relative supply curve.
8. Graph the relative demand curve along with the relative supply curve.
9. Find the equilibrium world relative price under free trade.
10. Show graphically that both countries A and B gain from trade.
11. How much of each good does either country produce under free trade? How much of each good will they import/export?
12. Under free trade, what is the wage ratio between country A and country B?