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Unformatted text preview: MIDTERM EXAM PHYS 603 Spring 2008 Tuesday, March 11, 2008, 9:3010:45 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 Boltzmann-Gibbs 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 non-negative amount of money m i (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 i + m 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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