international economics

Last Name ______________________________________ First Name ________________________

Economics 238 New York University

Marc Lieberman Spring, 2012

Problem Set #2

The RicardianGeneral Equilibrium Model

Instructions: Print out this problem set and neatly PRINT your name at the top. Some of your answers will go on these pages. Staple all three pages of the problem set to your other answers before turning them in (on Monday, Feb 13at the beginning of lecture). Also put your name on each page of your answers.

The recitation sections on Thursday, Feb 9, will show you how to solve problems similar to these.

Make a photocopy of the problem set, because you will not be getting it back. Turn in your original, NOT the photocopy. You’ll use the photocopy to check against the answers to be posted after they are turned in..

One of the side benefits that would come from long-term peace in the Middle East is the opening up of trade between Israel and its Arab neighbors. For example, currently there is only limited trading between Israel—a high-productivity country (high output per hour), and Egypt—a low-productivity country. But a comprehensive peace would open up full and extensive trade between the two nations. This problem set uses this scenario to work through the Ricardian model for these two countries, with hypothetical numbers.

Suppose the potential for trade exists in only two goods: cotton and oranges. Assume the following information on technology in each country (labor hours required per unit of output) and resource endowments (total labor hours available per period):

	Egypt	Israel
1 ton cotton	100 hrs	20 hrs
1 ton oranges	500 hrs	20 hrs
Total Labor Hours Available	3,000 million	500 million

For all numerical solutions, show all your work neatly and circle your final answers.

1. Which country has an absolute advantage in producing cotton? …in producing oranges?

2. What is the opportunity cost of producing one more ton of cotton in Israel? In Egypt?

3. What is the opportunity cost of producing one more ton of oranges in Israel? In Egypt?

4. Which country has a comparative advantage in producing cotton? …in producing oranges? Briefly, how do you know?

_________________________________

So far, we’ve only considered production (supply) in each country. Now let’s consider consumption, which is based on demand.

Let Q^D_Egypt and Q^D_Israel represent the number of millions of tons of oranges Egyptians and Israelis, respectively, would want to buy at each relative price for oranges. Also, let P_O be the price per ton of oranges, and P_Cbe the price per ton of cotton. Finally, suppose that the demand curve for oranges in each country is as given in the table on the next page:

Demand Equations for Oranges:

In Egypt	in Israel
QDE = 5.5 - 0.5(PO/ PC) for all PO/ PC ≤ 5	QDI = 12 + 3(PO/ PC) for all PO/ PC ≥ 1

[Explanatory Note: From Israel’s demand equation, you can see that for all P_O/ P_C ≥ 1, Israel’s demand curve is positivelysloped. This is because, for all P_O/ P_C ≥1, Israelis would specialize in oranges, which would be the only source of income in Israel. So when the price of oranges rises, two things happen in Israel. On the one hand, a rise in the relative price of oranges would make them relatively more expensive, and thus decrease demand for them. (This is the substitution effect of the change in relative prices.) On the other hand, the rise in relative price would also increase total income in Israel, and thus increasedemand. (This is the income effectof the change in relative prices.) In this example, we assume that the income effect wins out: a rise in the relative price of oranges increases demand for oranges. This is why the slope is positive.

In Egypt, however, the demand curve for oranges must slope down. That’s because for all P_O/ P_C ≤ 5, Egypt importsoranges (and exports cotton). Therefore, as the relative price of oranges falls (which is does for Egypt when trade opens up), the substitution effect increases the quantity of oranges demanded. At the same time, a lower price for oranges means (or a higherrelative price for cotton) increases purchasing power in Egypt, increases the quantity of oranges demanded further.Thus, for oranges in Egypt, both the substitution effect and the income effect work in the same direction: a drop in relative price causes an increase in quantity demanded. Egypt’sdemand curve must slope downward for all prices at which it imports oranges.]

5. To illustrate the situation before trade, fill in the blanks in the following table

[Hint: Pre-trade, the relative price of oranges will reflect the opportunity cost of oranges in each country. So, use the demand equations in each country to find the quantity of oranges demandedin that country at the pre-trade relative prices. That’s also how many oranges each country will produceunder autarky. Then determine how much production of the other good—cotton—will take place in each country, based on how many labor hours are remaining to be used for cotton.]

		Egypt	Israel	World
Pre-Trade production of:	Cotton (tons)
Oranges (tons)
Pre-Trade consumption of:	Cotton (tons)
Oranges (tons)

6. Draw roughgraphs (rough means don’t worry about consistent scales, and no need for graph paper) illustrating supply and demand curves for oranges in each country, and indicate the autarky price ratios as well as the autarky production and consumption point for oranges in each country.

[Hint: don’t forget to put (P_O/ P_C) on the vertical axes and “millions of oranges” on the horizontal axes. Also remember: the supply curves will be horizontal up to the maximum possible production for each country.]

7. Draw roughgraphs of the PPFs for the two countries, with quantity of oranges on the horizontal axis. Indicate the pre-trade production and consumption point in each country as point “A”. (Don’

8. Now suppose that completely free trade opens up between the two countries. Explain briefly why the world price ratio P_O/ P_C (i.e., the price ratio of the goods when traded internationally) must end up between 1 and 5. [Be specific. Experiment with a value for (P_o / P_c) above and below the accepted range, and explain what would happen in each case. For example, choose (P_o/ P_c) = 2/3. What would Egypt want to export? What would Israel want to export? Would trade take place? Do a similar analysis for, say, (P_o/ P_c) = 6.]

9. Solve algebraically for the post-trade world relative price ratio P_O/ P_C (the price ratio aftertrade opens up).

[Hint: This will be the relative price P_O/ P_C at which exports of oranges from the country that has the comparative advantage in them (Israel) equal imports of oranges by the other country (Egypt). In Israel, total exports of oranges will be the maximum possible productionof oranges minus the oranges demanded in Israel, as given by its demand curve at each P_O/ P_C. In Egypt, total imports of oranges will be the number demanded in Egypt, as given by its demand curve at each P_O/ P_C. Set exports equal to imports, and solve for the P_O/ P_C that makes them equal.]

10. Fill in the blank below with the P_O / P_C you found above. Use this price ratio and the demand curves given in the problem to complete the following table:

P_O / P_C = _____________

		Egypt	Israel	World
Post-Trade production of:	Cotton (tons)
Oranges (tons)
Post-Trade consumption of:	Cotton (tons)
Oranges (tons)

11. Give the numerical value for the terms of trade for Israel, and also for Egypt.

12. On your PPF graphs, indicate Egypt’s and Israel’s Consumption Possibilities Frontier (CPF) after trade (use the price ratio P_O / P_C ), and each country’s post-trade production (point B in each graph) and post trade consumption(point C in each graph). Also indicate (e.g., by darkening) the trade triangle for each country.

13. Based on your numbers in the table, which good is Egypt exporting and in what quantity?

14. Based on your numbers in the table, which good is Israel exporting and in what quantity?

15. On your supply and demand graphs, illustrate post-trade productionand consumptionof oranges, as well as exportsand importsof oranges, in each of the two countries.

[Hint: What you find in this graph should be consistent with what you found for oranges in your PPF and CPF graphs]

16. Fill in the price ratio again, and fill in the following table of gains from trade in terms of consumption in each country (the increase in consumption of the good due to trade)

Gains from Trade with P_O / P_C = _________

		Egypt	Israel	World
Change in consumption of:	Cotton (tons)
Oranges (tons)