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Abstract
We present a stochastic agentbased 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 FokkerPlanck (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 lowincome 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 nearperfect 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
Original language  English 

Article number  58003 
Pages (fromto)   
Number of pages  6 
Journal  Europhysics Letters 
Volume  91 
Issue number  5 
DOIs  
Publication status  Published  Sep 2010 
Keywords
 STATISTICALMECHANICS
 WEALTH
 DISTRIBUTIONS
 CORRUPTION
 SYSTEMS
 GROWTH
 MODELS
 NEEDS
 MONEY
 GAMES
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 2 Finished

Edinbugrh Soft Matter and Statistical Physics Programme Grant Renewal
Cates, M., Poon, W., Ackland, G., Clegg, P., Evans, M., MacPhee, C. & Marenduzzo, D.
1/10/07 → 31/03/12
Project: Research
