Solow models on time scales

Abstract

We introduce a general Solow model on time scales and derive a nonlinear first-order dynamic equation that describes such a model. We first assume that there is neither technological development nor a change in the population. We present the Cobb– Douglas production function on time scales and use it to give the solution for the equation that describes the model. Next, we provide several applications of the generalized Solow model. Finally, we generalize our work by allowing technological development and population growth. The presented results not only unify the continuous and the discrete Solow models but also extend them to other cases “in between”, e.g., a quantum calculus version of the Solow model. Finally it is also noted that our results even generalize the classical continuous and discrete Solow models since we allow the savings rate, the depreciation factor of goods, the growth rate of the population, and the technological growth rates to be functions of time rather than taking constant values as in the classical Solow models.