Wealth-In-Utility and Time-Consistent Growth: Real Excursions with an “Overlapping” Welfare Function

Abstract

Abstract. This research explores the dynamic potential of point-wise utility functions optimization of representative agent economies. Such functions were generically considered to depend upon current consumption and wealth to be made available for next period usage or income generation, implying an endogenous (pseudo-)rate of time preference. At first inspection, the framework reproduced closely the dynamics and steady-state properties of the traditional Solow-Swan and Ramsey models – with population growth, exogenous technical progress, land, or increasing returns to scale - as well as, when human capital/knowledge was introduced, the Lucas-Uzawa endogenous growth set-up. General uncertainty – simulated at different decision stages - resulted in intuitively appealing solutions. Overlapping optimization of the capital stock generated forward-looking recursive dynamics. Homothetic preferences (CES or generalized Cobb-Douglas) - implying a constant consumption-(lead)wealth ratio along an optimal path and resulting in steady-state saving rates independent of CRS technologies features in simple structures -, were assumed for illustration, and also generic separable forms in the arguments. The latter were useful under uncertainty, allowing the inspection of the role of risk-aversion and diminishing marginal returns to capital in equilibrium and steady-state determination.

Keywords. Wealth-in-Utility (WIU); Capital-in-Utility (KIU). Overlapping Utility Functions. Consumption; Saving. Growth. Time (In)Consistency. Discounting; Rate of Time Preference. Growth under Uncertainty.

JEL. D91; D11. E19. O40.