MIDTERM EXAM
— PHYS 603 — Spring 2008
Tuesday, March 11, 2008, 9:30–10:45 am
Professor Victor Yakovenko
Office: 2115 Physics
You may use the textbook, your notes, homework, and any other materials.
Do not forget to write your name!
Each problem is worth 10 points.
1. UMD qualifier problem, January 2004: Probability distribution of money.
This problem explores an analogy between the BoltzmannGibbs probability distribu
tion of energy in statistical physics and the probability distribution of money in a closed
system of economic agents. Consider a system consisting of
N
1 economic agents.
At a given moment of time, each agent
i
has a nonnegative amount of money
m
i
≥
0
(debt is not permitted). As the agents engage in economic activity, money is constantly
transferred between the agents in the form of payments. However, the total amount of
money is conserved in binary transactions between agents:
m
i
+
m
j
=
m
0
i
+
m
0
j
. This
condition is analogous to conservation of energy in collisions between atoms in a gas.
We also assume that the system is closed, so the total amount of money in the system
M
is also conserved.
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 Fall '08
 V.Yakovenco
 Physics, Thermodynamics, Energy, Work, Statistical Mechanics, Probability distribution, Professor Victor Yakovenko

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