An Application of Gamma Distribution to the Income Distribution and the Estimation of Potential Food Demand Functions

Poverty and hunger are the central issues against the sustainable development. Today, more than 800 million people are suffering from insufficient nutrition according to FAO (FAO, 2010). However, on the other hand, it is often pointed out that the per capita food production already meets the demand for the per capita food requirement. The above contradictory observation suggests that many people cannot access the food market because of the low income. The availability of electricity and other energy is also the case. Since these issues are mainly caused by the inequity of income distribution, its quantitative analysis is indispensable to evaluate the societal policy towards the sustainable future. However, since the existing indicators such as Gini coefficients do not represent the income distribution explicitly, they fail to assess the effects of social policy for the improvement of purchasing power of poor people. Population of absolute poverty who gets less than 1.25 US dollar per day is also provided by World Bank. This indicator does not show the distribution pattern of middle to high income classes. The authors would thus point out the need for an alternative method. This paper describes an application of Gamma distribution to the income distribution patterns. The parameters are statistically estimated based on the income quintile data provided by World Bank. The results show how the income distribution has changed historically by country. Based on the future income distribution and the simulation results of the author’s crop market model, we evaluate the share of people who cannot afford the major crop. The authors also propose a procedure to estimate the potential food demand function considering the income distribution changes, suggesting that the future demand could be affected by not only the per-capita income growth but the income distribution changes.