This paper presents three optimum dynamic models of the consumer, the solutions of which are given in a differential form. The first model is a generalization of the optimum model presented in [5] and it is important because it also analyzes the savings made from time to time. Both the optimum consumptions and the savings that can be achieved are solutions of a system of partial differential equations of first order. The results produce extremely interesting economic interpretations. The second model uses the Hamilton conditions in solving the problem of optimum. After a relatively difficult computation, we can determine the approximate shape of the maximum consumption as well as the utility corresponding to this consumption. The last dynamic model implies the existence of the money and capital market. It refers only to the case when there are two consecutive consumptions but the result can be generalized immediately. The resulted optimum solutions are given in a differential form and they imply relatively difficult calculations.