An almost linear stochastic map related to the particle system models of social sciences

We propose a stochastic map model of economic dynamics. In the past decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of income and wealth. Another area of enquiry is the formation of opinion in a society. The model proposed attempts to produce positively skewed distributions and power law distributions as has been observed in the real data of income and wealth. Also, it shows a non-trivial phase transition in the opinion of a society (opinion formation). A number of physical models also generate similar results. In particular, kinetic exchange models have been successful especially in this regard. Therefore, we compare the results obtained from these two approaches and discuss a number of new features and drawbacks of this model.