A mathematical model of progressive literacy

We consider the two principal determinants of the dynamics of literacy in a developing country such as India: (a) a tendency of each family to improve or retain (but never retrogress) its literacy state with each successive generation, and (b) a differential in fertility, with number of off‐springs rising with decreasing literacy. The interplay of these contradictory trends is investigated in a mathematical model adapted and generalized from earlier work in the literature on modelling of social mobility and graded social systems. The model, besides being practically relevant, is exactly solvable and yields simple criteria and closed‐form solutions for different literacy distributions in terms of fertility and intergenerational transition proportions between male‐female “paired literacy states” of a society.

Keywords:

• (Progressive Literacy
• Differential Fertility
• Limiting Distributions)