Econ 51: Final Exam
March 18, 2009
Instructions:
°
This is a closed book, closednotes exam. You are allowed to use a handheld calculator
(i.e. no laptop).
°
You have 180 minutes.
°
Please answer all 4 questions.
Please use a separate blue book for each question.
Please write on each blue book the number of the question, your name, and your
section number (or section time and TA).
°
Always remember:
think before you do the math
.
°
All questions start easy and get more di°cult, so make sure you organize your time
intelligently.
°
As always, throughout log means the natural logarithm.
°
Good luck!
1. Uncertainty and General Equilibrium (30 points)
Consider three securities.
One unit of security
c
pays a dollar in June if the Celtics win
the NBA Championship, and zero otherwise. One unit of security
l
pays a dollar in June if
the Lakers win the NBA Championship, and zero otherwise. One unit of security
f
pays a
dollar in June if neither the Celtics nor the Lakers win the NBA Championship, and zero
otherwise. Consider a market with two agents, Ray and Kobe, each endowed with 10 units
of security
c
, 10 units of security
l
, and one unit of security
f
. Security
f
is not tradable, so
agents have to hold their endowment of it. Ray believes that the Celtics will win it all with
probability 0.3 and that the Lakers will win it all with probability 0.3 (thus, he believes that
a third team will win it with probability 0.4). Kobe is more optimistic about the Lakers’
chances, and thinks that the Celtics have only a 0.2 probability to win, and that the Lakers
have a 0.4 probability to win.
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 Winter '07
 Tendall,M
 Equilibrium, Game Theory, Lakers

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