02 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 identi…ed. 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 “autarky”for 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?
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.
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