### Abstract

Original language | English |
---|---|

Article number | 58003 |

Number of pages | 6 |

Journal | Europhysics Letters |

Volume | 91 |

Issue number | 5 |

DOIs | |

Publication status | Published - 22 Sep 2010 |

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### Keywords

- economics
- poverty
- probability theory
- stochastic processes
- statistics

### Cite this

*Europhysics Letters*,

*91*(5), [58003]. https://doi.org/10.1209/0295-5075/91/58003

}

*Europhysics Letters*, vol. 91, no. 5, 58003. https://doi.org/10.1209/0295-5075/91/58003

**Income and poverty in a developing economy.** / Chattopadhyay, Amit K.; Ackland, Graeme J.; Mallick, Sushanta K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Income and poverty in a developing economy

AU - Chattopadhyay, Amit K.

AU - Ackland, Graeme J.

AU - Mallick, Sushanta K.

PY - 2010/9/22

Y1 - 2010/9/22

N2 - 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 © EPLA, 2010.

AB - 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 © EPLA, 2010.

KW - economics

KW - poverty

KW - probability theory

KW - stochastic processes

KW - statistics

UR - http://www.scopus.com/inward/record.url?scp=78751650022&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/91/58003

DO - 10.1209/0295-5075/91/58003

M3 - Article

VL - 91

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 5

M1 - 58003

ER -