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6 - Microeconomic foundation of the kinetic exchange models

Published online by Cambridge University Press:  05 May 2013

Bikas K. Chakrabarti
Affiliation:
Saha Institute of Nuclear Physics, Kolkata
Anirban Chakraborti
Affiliation:
Ecole Centrale Paris
Satya R. Chakravarty
Affiliation:
Indian Statistical Institute, Kolkata
Arnab Chatterjee
Affiliation:
Aalto University, Finland
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Summary

In the earlier chapters, we introduced kinetic exchange models and discussed the mathematics behind them. However, one major point that is missing in the earlier discussions is the choice behaviour of the agents. The outcomes of the stochastic process do not reflect any optimization mechanism on the part of the agents. In this chapter, we will provide a simple economic model which intends to capture the basic features of the kinetic exchange models. We start with some usual assumptions regarding the preference pattern of the agents and the market mechanism. Eventually, it will be shown that the outcomes are exactly the same as those obtained in the kinetic exchange models, thus providing an elementary (but non-unique) way of interpreting the stochastic money evolution equations in economic terms. After that, we will discuss the dynamic features of the asset distribution in the economy if it has time-varying macroeconomic variables. To be precise, we will discuss a possibility of inequality reversal (as has been postulated and discussed in Kuznets (1955, 1965) and Angle (2010)) in the same framework.

Derivation of the basic kinetic exchange model

Following Chakrabarti and Chakrabarti (2009), we consider an N-agent exchange economy in discrete time. At every point of time, exactly two agents are randomly chosen from the pool of N agents, i.e. each agent has equal probability of being chosen for trade. The exact trading mechanism is described below. After they trade, the agents part and leave the market. In the next period again two agents are chosen for trade and the same process is repeated until the distribution of their assets reaches a steady state.

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Publisher: Cambridge University Press
Print publication year: 2013

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