04 Jun Question Problem Set 1 Econ 433 Instructions: You may work with other people in the class. However, the
Question
Problem Set 1
Econ 433
Instructions: You may work with other people in the class. However, the
people you work with must be identiÖed. 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 Öx 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) = b
1=2
c
1=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 ìautarkyîfor 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?
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