Assume the United States and Japan are the only two countries in the world. In the U.S., four man-hours of labor are required to produce each car and each unit of wheat, while in Japan two man-hours of labor produce one car and four man-hours of labor produce one unit of wheat.

1. This problem helps you work out why some agents in an economy may gain from trade while others may lose and helps x some basic concepts in general equilibrium. Consider an Endowment economy. That is, nothing is

produced, rather supply is whatever people are endowed with.

There are two agents, Robinson and Friday, who live on separate islands, and two goods, Coconuts and Bananas. Robinson owns 8 coconuts and 2 bananas while Friday owns 2 coconuts and 8 bananas. Both Robinson and Friday have identical homothetic preferences and have identical demand functions as a result.

Their common utility function is given by

U(b; c) = b1=2c1=2:

Recall that as a result of maximizing their utility subject to their budget constraints, they follow the rule that they spend half their income, whatever it turns out to be, on each good.

Draw an Edgeworth box and place the endowment point in it. As we proceed, keep adding the information you have gathered and depict it in the Edgeworth box. It will keep you grounded. You will have to do this anyway in part c:

a: Set the demand for bananas equal to the supply for Robinson and solve for the price of bananas. Do the same for coconuts. (This gives you the equilibrium prices under autarky as they cannot trade with each other, merely with themselves in their roles as buyer and seller) Can you solve for the equilibrium prices for both coconuts and bananas or only for the relative price? Why? If the price of bananas is 1; what is the price of coconuts in autarky for Robinson? What is his utility level in autarky?

b: Repeat part a: for Friday.

c: Depict equilibrium in autarkyfor Robinson and Friday in the Edgeworth box.

d: What happens if Robinson and Friday can trade? What are equilibrium relative prices (setting the price of bananas at 1) and utilities? Depict their consumption choices and trades in an Edgeworth box diagram. How much is traded by whom?

e: Are Robinson and Friday better or worse o¤due to trade with one another?

Why? Depict this in the Edgeworth box to illustrate your answer.

f: Now suppose that Robinson and Friday are discovered by the world which ers to trade at a slightly higher relative price for coconuts than you solved for in d: Are both Robinson and Friday better o¤? Who gains who loses? Why?

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Again, use a diagram to illustrate your answer. (Hint: if you are a net buyer of

a good (seller), an increase in its price hurts (helps) you.)

g: Can you think of a redistribution of endowments between Robinson and

Friday that they would both be willing to make before being discovered by the

rest of the world and which would make them both gain from the event that

they were discovered by the world? Explain why your proposal works. (Hint:

what is the e¤ect of a price change if you are neither a borrower or a lender?)

h: Trade makes some people better o¤ and others worse o¤ in practice.

However, by combining trade with redistribution, everyone could be made better

o¤ due to trade.” Comment on this statement in the light of your answer to the

earlier parts.

2. Assume the United States and Japan are the only two countries in the

world. In the U.S., four man-hours of labor are required to produce each car

and each unit of wheat, while in Japan two man-hours of labor produce one

car and four man-hours of labor produce one unit of wheat. Suppose also that

both the U.S. and Japan have 60 man-hours of labor available. Suppose that

everyone in the world always consumes exactly one car for each unit of wheat.

No other commodities exist or are needed. Consider the price of wheat relative

to that of a car, that is, assume that the price of a car is unity throughout.

a. (i) Explain how each owner of a unit of labor would decide what to

produce in the U.S., given that the price of a unit of wheat is pw.

(ii) Draw the PPF (production possibility frontier) for the U.S.. What

would the production decision be if we choose production to maximize the value

of output subject to the outputs being feasible, that is, lying on or below the

PPF?

(iii) Compare your answers to the two parts above. Do they di¤er? What

does this tell you?

b. Draw the PPF for Japan, and for the world under trade. Note that labor

is immobile across countries under trade.

c. What are the autarky relative prices in the U.S. and in Japan? Relate

these to the comparative advantages of the U.S. and Japan.

d. What would the U.S. and Japan produce and consume under autarky?

e. Under trade, what will each country produce, and what will it export and

import? What is the world relative price with trade? Who gains from trade?

f. A member of the Close America party argues that since the Japanese

are better at everything than we are we will be competed out of the market and

trade will hurt us. Hence we should close trade and just rely on ourselves. Do

you agree with him/her?

3. (a) Imagine a world in which productivity rises by 1 percent annually in all

countries. What will be the trend growth in the U.S. standard of living? Now,

however, suppose that while the United States continues to raise its productivity

by only 1 percent per year, the rest of the world manages to achieve 3-percent

productivity growth. What would you expect to be the trend growth in our

living standards? Are we losing competitiveness?

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In his article on the reading list (the links are there) What Do Undergrads

Need to Know About Trade? Krugman says If we can teach undergrads to

wince when they hear someone talk about “competitiveness,” we will have done

our nation a great service. What does he mean?

(b) Give an example of an old world plant product that did better in the

new world. Give the most surprising (to you) new world product commonly

used. See The Colombian Exchange:A History of Disease, Food, and Ideas by

Nunn and Qian on the reading list.

(c) How can commodity price convergence be used to get an idea of the

extent of globalization? What evidence would you o¤er to support the following

statement: (see When did globalization begin? Kevin ORourke and Je¤ery

Williamson.

Globalization did not begin 5,000 years ago, or even 500 years ago. It began

in the early nineteenth century. In that sense, it is a very modern phenomenon.

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