Income and poverty in a developing economy

Authored by A. K. Chattopadhyay, G. J. Ackland, S. K. Mallick

Date Published: 2010-09

DOI: 10.1209/0295-5075/91/58003

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

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: http://go.worldbank.org/SWGZB45DN0) 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 (C) EPLA, 2010

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