Cash transfer program and education investment: A model for social evolution

Assume that the households of a country are socially classified according to the monthly total income, and that they can be part of a lower, a middle or an upper class. By using multi-agent systems, here we model and simulate the economic evolution of households which earn a wage, pay taxes and invest in education. The return of the education investment is monthly added to the salary of the family, and it is function of the corresponding grand total put in education along the time. When a family is unemployed, we consider that it receives cash due to a social program made by the government. The time evolution of the percentages of households belonging to each class is investigated by varying the government investment in such a program of cash transfer and the proportion of employed households in the population. We show that the government should invest in the unemployed lower class if it intends a growth of the middle class. We also propose and analyze a mean-field approximation written in terms of ordinary differential equations. In addition, we verify that our model fits real data from Brazil, in the period between 2003 (when the cash transfer program Bolsa Família was launched) and 2011.