08 Jun uestion Econ 604, Fall 2015 Prof. Comolli Homework Problem Set #1, Sept.3 Due: beginning of next class, Sept.8
uestion
Econ 604, Fall 2015
Prof. Comolli
Homework Problem Set #1, Sept.3
Due: beginning of next class, Sept.8
We found in class that when individual agents in the economy have identical preferences but different
endowments, international trade creates gainers and losers; viz, agents whose endowments are valued less
under trade versus autarky are worse off and agents whose endowments are valued more under trade
versus autarky are better off. However, those who gain can compensate those who lose, at least in
principle, so that trade makes the overall economy better off (i.e., there are gains from trade).
Interestingly, the same is true when agents have identical endowments but different preferences. Agents
with a stronger preference for a good that has a higher relative price under trade versus autarky are worse
off with trade, but agents with a stronger preference for a good that has a lower relative price under trade
versus autarky are better off with trade. But it is still true that there are gains from trade, i.e. those who
gain from trade can in principle compensate those who lose such that the overall economy is better off.
The following homework problem asks you to investigate this case.
Assume that there are two agents C (Crusoe) and F (Friday) and two goods X (coconuts) and Y (fish).
Each agent has an endowment of X = 2, Y = 2 prior to exchange (i.e., self-sufficiency). Assume that C’s
utility function is given as
2/3
C
1/3
C
U C =X Y
and F’s utility function is given as
rates of substitution for C and F are obtained, respectively, as
1/3
F
2/3
F
U F =X Y
MRSC =2YC /X C
and
. The marginal
MRSF =YF /2X F
.
a) Compute the utility and MRS of C and F prior to exchange. Based on these MRS values, can C
and F gain from exchange? If so, briefly explain how they would exchange.
b) Derive C’s demand curve for X and F’s supply curve for X. Let p =
stand for the relative
PX /PY
price of good X. Hint: To obtain these curves, use the utility maximizing conditions
and
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