Question 1. Consider two countries, Home and Foreign, each having 120 units of labor, the only input. In Home, 3 units of labor are required to produce one unit of clothing and 2 units of labor are required to produce one unit of food (In other words, one worker can produce 1/3 units of clothing or 1/2 units of food per unit of time). In Foreign, 1 unit of labor is required to produce one unit of clothing and 2 units of labor are required for one unit of food (In other words, one worker can produce 1 unit of clothing or 1/2 units of food per unit of time). Consumers in both countries have Leontief preferences, consuming clothing and food in the fixed proportion of one-to-one. (Therefore, we have
U(QC, QF) = min{QC, QF}.)
Note-1: The indifference curves associated with Leontief preferences are right angles, there are no substitution effects between the goods.
Note-2: Throughout this class, we always assume that trade is balanced, namely total exports = total imports given the world prices.
This is still true in this question.
(a) Draw the production possibilities frontiers for each country. (Put clothing on the vertical axis and food on the horizontal axis.) Draw indifference curves and indicate autarky equilibrium for each country (namely, autarky price, autarky consumption and autarky production).
(b) Which country has an absolute advantage in which good(s)? Which country has a comparative advantage in which good?
(c) Assume that trade is possible between countries. Draw the world relative supply curve for food and the world relative demand for food. (Put PF /PC on the vertical axis and QF / QC on the horizontal axis.) Find the free trade equilibrium relative price of food and
equilibrium relative quantity of food.
(d) In trade equilibrium, which country will produce which good(s) and how many units? What is the trade pattern (what good(s) home and foreign countries export and import? Do both countries benefit from trade?
Question-2. Consider first the Specific factors model with two countries (Home and Foreign) and two goods (cell phones and textile). At first, there are three factors of production in each country: Labor (denoted by L), capital specific to cell phone production (denoted by KC) and capital specific to textile production (denoted by KT).
Assume that:
• In each industry, increases in the amount of labor used are subject to diminishing returns, that is, the marginal product of labor declines as the amount of labor used in the industry increases.
• As you increase the amount of capital, marginal product of labor increases, whereas marginal product of capital decreases and vice versa.
• Home country has a comparative advantage in cell phone production and Foreign country has a comparative advantage in textile production. As a result,
(PC /PT)H < (PC /PT)F (Relative price of cell phones is lower in Home than in Foreign).
(a) Consider free trade between Home and Foreign. What is the trade pattern? Who will support and who will oppose to free trade in each country?
(b) Suppose that some of the workers from Home country migrate to Foreign country.
Which factors benefit and which factors lose in each country? What happens to the production of each good in each country? Use figures to support your answer.
Now, assume that we are in the long run. Home is capital abundant whereas Foreign is Labor abundant. Assume also that under autarky we still have (PC /PT)H < (PC /PT)F. (Of course, now the relevant framework is Heckscher-Ohlin model, and there is only one type of capital that can be used in the production of each good). Moreover, assume that there is some degree of substitutability between capital and labor. One example of this type of production function is Cobb-Douglas. This assumption means that any change in the wage/rental ratio implies a change in the labor/capital ratio.
(c) Given the information above, which good is capital intensive and which good is labor intensive?
(d) How would your answer to part (a) change?
(e) How would your answer to part (b) change?