In this thesis, we studied two of the most important exogenous economic growth models; Solow and Ramsey models and their effects in microeconomics by using dynamic programming techniques. Dynamic programming (DP) is a general approach to solve economic growth problems. The main differences between Solow and Ramsey models are discussed in details. Bellman value function for the growth models is applied to the two models and an analytic formula are derived. Concerning the models under study, we then discussed the steady states for the model and derived a closed formula for the capital. This formula was checked by computer using Python codes where a new concave assumed value function is given; , to be compared with a value function given by other . These two initial functions have the same properties of being monotone and concave up. The comparison shows the excellence and advantages of our assumption. We reached the true value function faster.