Public Affairs 856 - Problem Set 1:

Problem 1- Suppose that each worker in the home country can produce three can or two televisions. Assume chat Home has four workers.

a. Graph the production possibilities frontier for the home country.

b. What is the no-trade relative price of cars at Home?

Problem 2- Suppose that each worker in the foreign country can produce two can or three televisions. Assume that Foreign also has four workers.

a. Graph the production possibilities frontier for the foreign country.

b. What is the no-trade relative price of can in Foreign?

c. Using the information provided in problem 2 regarding Home, in which good does Foreign have a comparative advantage and why?

Problem 3- Suppose that in the absence of trade, Home consumes nine can and two televisions and Foreign consumes two can and nine televisions. Add the indifference curve for each country to the figures in problems 2 and 3. Label the production possibilities frontier (PPF), the indifference curve (U₁), and the no-trade equilibrium consumption and production for each country. Label Home and Foreign no-trade consumption points as A and A^*, respectively.

Problem 4- Now suppose the world relative price of cars is P_C / P_TV = 1.

a. What good will each country specialize in? Briefly explain why.

b. Graph the new world price line for each country in the figures in problem 3, and add a new indifference curve (U₂) for each country in the trade equilibrium.

c. Label the exports and imports for each country. How does the amount of Home exports compare with foreign imports?

d. Does each country gain from trade? Briefly explain why or why not.

Problem 5- a. Suppose that the number of workers doubles in Home. What happens to the Home PPF and what happens to the no-trade relative price of wheat?

b. Instead of doubling the number of workers in Home, suppose that there is technological progress in the wheat industry, so that Home can produce more wheat with the same amount of labor. What happens to the Home PPF, and what happens to the relative price of wheat? Describe what would happen if a similar change occurred in the cloth industry.

Problem 6 - Heckscher-Ohlin Model of Trade.

On the diagram below, the endowment of Home is marked (K/T)^H (by the way, this is sometimes called a "Johnson Diagram", after Harry Johnson; refer to Handout on Heckscher-Ohlin). The PPF for the same country is also shown below.

Where K is capital, T is land, r_T is the rental rate for land, and r_T is the rental rate for capital.

a. What are the factor ratios in use in the oil and food industry for the price ratio (P_O/P_F)³? What about (P_O/P_F)²?

b. What happens to the relative returns to factors as the price ratio changes from (P_O/P_F)² to (P_O/P_F)¹? Can you explain this result intuitively?

c. At (P_O/P_F)1 what are the factor ratios used in each industry? [Hint: Mark this ratio on the Johnson Diagram] Can you explain why the factors in Home can be fully employed at this relative price of commodities?

Assume Home and Foreign are endowed with factor ratios of (K/T)^H and (K/T)^*.

d. Which country has more resources per unit of land (T)?

e. Which country has the lower price of Oil in autarky? (Assume both goods are produced.)

f. Draw in some autarky price ratios in figure 3. Where must the world price ratio fall? What world price ratio supports specialization in both countries?

g. Is there a world price ratio where neither country specializes in production of one good? What happens to relative factor returns in both countries when trade occurs? Why?

Consider the pair of trading countries Home and Foreign (the endowment line is positioned differently now). Let (P_O/P_F)^W be the equilibrium world price of the commodities.

h. What are the factor ratios in food and clothing industries in Foreign? In Home? What are the relative returns to factors in Foreign and Home?

i. What country produces relatively more Oil, and why?

j. If consumption preferences are identical in both countries, which one will export Oil?

k. If (PO/PF)^* is the autarky commodity price ratio in Foreign, which group of factor owners in Foreign will oppose the introduction of trade?