04 Jun Question Instructions: You may work with other people in the cl
Question
Instructions: You may work with other people in the class. However, the
people you work with must be identied. The handouts on ANGEL on Exchange
Economies and Ricardian Models will help guide you threough these problems.
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=2 c1=2 :
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
o¤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?
1
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?
g. Draw the world PPF assuming that labor is internationally mobile. Are
their further gains from labor mobility? Explain why/why not.
h. If Japan had only 20 workers, what would your answer be to g.?
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
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