Standard Explicit Solution to Optimal Growth Models

This paper shows that the standard optimal growth model can be solved explicitly by using a utility function describing preferences for consumption and savings. Such a maximising criterion including the flow of savings can actually be strongly motivated by two arguments. First, the basic assumption of a representative agent who wishes to consume and save a part of his income each time, can be interpreted as an implicit assumption of some degree of preference for thriftiness. Second, this function formalizes also the concept of Max Weber’s spirit of capitalism (with a direct preference for wealth), which makes the model similar to the one of Heng-Fu Zou (1994) except that his specification includes the capital stock. The resulting model offers an interesting application of the Pontryagin’s Maximum Principle, as well as elegant closed form solutions.