Maximizing the model for Discounted Stream of Utility from Consumption when the rate of Production is Linear

Abstract

Osagiede et al. (2009) considered an analytic model for maximizing discounted stream of utility from consumption when the rate of production is linear. A solution was provided to a level where methods of solving order differential equations will be applied, but they left off there, as a result of the mathematical complexity involved in the solution procedure. In this paper, we propose a simplified mathematical procedure to the mathematical complexity encountered by Osagiede et al. (2009). The model generates solutions to problems of such linear systems when numerical values are supplied for all the parameters in the model, without rigorous mathematical computations. The model is easy to implement. The paper ended with an illustrative example. Based on the result in the equation, we can evaluate the discounted stream of utility for any value of between. Other issues such as that of existence and uniqueness of the solution of the utility model for system under consideration must also be examined. Such work is in progress and we hope that relevant results will be available soon. 300255275)(16020tteetK''t 50tandt.

Keywords: Discounted stream of utility, consumption, rate of production, linear

International Journal of Natural and Applied Sciences, 5(3): 251-254, 2009