Ramsey’s Conjecture for the Model with Non-liquid Capital

Ramsey’s conjecture on social stratification states that economic agents divide into two classes: the class of thrifty agents, who jointly accumulate and share all the economy wealth, and the class of impatient ones forced to live on the wage level only. The present paper outlines the validity of Ramsey’s conjecture on social stratification for the household population in case when capital is non-liquid. The households’ behavior is described by the Ramsey type model of the rational representative consumer. We derive the solution in the synthesis form for the corresponding optimal control problem and use it in the social dynamics model for the household population, where the discount rates, according to Duesenberry’s relative income hypothesis, are set as functions dependent on ratio between capital holdings of specific agent and total capital available of economy. The agents behave in myopic manner, suggesting that the interest rate and the wage rate do not change over time. The connection between the Gini index and the Lyapunov function is also established. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.