Income and poverty in a developing economy


We present a stochastic agent-based model for the distribution of personal incomes in a developing economy. We start with the assumption that incomes are determined both by individual labour and by stochastic effects of trading and investment. The income from personal effort alone is distributed about a mean, while the income from trade, which may be positive or negative, is proportional to the trader's income. These assumptions lead to a Langevin model with multiplicative noise, from which we derive a Fokker-Planck (FP) equation for the income probability density function (IPDF) and its variation in time. We find that high earners have a power law income distribution while the low-income groups have a Levy IPDF. Comparing our analysis with the Indian survey data (obtained from the world bank website: taken over many years we obtain a near-perfect data collapse onto our model's equilibrium IPDF. Using survey data to relate the IPDF to actual food consumption we define a poverty index (Sen A. K., Econometrica., 44 (1976) 219; Kakwani N. C., Econometrica, 48 (1980) 437), which is consistent with traditional indices, but independent of an arbitrarily chosen "poverty line" and therefore less susceptible to manipulation. Copyright © EPLA, 2010.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Uncontrolled Keywords: economics,poverty,probability theory,stochastic processes,statistics,Physics and Astronomy(all)
Publication ISSN: 1286-4854
Last Modified: 11 Apr 2024 07:08
Date Deposited: 19 Dec 2012 16:21
Full Text Link: http://iopscien ... 075/91/5/58003/
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2010-09-22
Authors: Chattopadhyay, Amit K. (ORCID Profile 0000-0001-5499-6008)
Ackland, Graeme J.
Mallick, Sushanta K.


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