Consider two countries, the United States and India, producing two commodities, food and clothing. The United States needs one and a half hours of labor to produce a unit of food and one hour to produce a unit of clothing. India needs three hours of labor to produce a unit of food and one hour to produce a unit of clothing. The United States is endowed with 800 hours of labor while India is endowed with 1000 hours of labor.
1. Draw a table to show the unit labor requirements for each country for each commodity. Which country has an absolute advantage in the production of food? In the production of clothing? Why? Which country has a comparative advantage in the production of food? In the production of clothing? Why?
2. Draw the production possibility frontiers (PPF) for each country, placing clothing on the horizontal axis and food on the vertical axis. What is the marginal rate of transformation (MRT) in each country? Which country will export which good?
We now assume that the representative individuals in the two countries have preferences represented by the utility functions:and. The associated marginal rates of substitution (MRS) are as follows:
and
3. Determine the autarky production (= consumption) for the two countries. (Hint: It will help to use the equation for the production possibility frontier. Set the marginal rate of substitution (MRS) equal to the marginal rate of transformation (MRT) for each country.) Draw a diagram for each country showing the autarky equilibrium, drawing both the PPF and the indifference curves.
4. What is the autarky ratio of the price of clothing to the price of food for each country? If we assume pure competition, what will the wage rate in terms of food (w/pF) be in the United States? In terms of clothing (w/pC )? What will the wage rate in terms of food be in India? In terms of clothing?
5. Let the free trade equilibrium price ratio be 2/5 (price of clothing over the price of food). (Note that the free trade price ratio is between the two autarky price ratios.) (Since only relative prices matter, you may set the world price of food equal to one.) What are the amounts of food and clothing produced, consumed, exported and imported by each country? Show that trade is balanced for each country. Draw a diagram for each country showing the free trade equilibrium. How does this demonstrate gains from trade?
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