This thesis analyzes the qualitative implications of the strategic interaction on the standard Ramsey model in terms of catching up. We have shown that the strategic interaction among agents in the economy leads the poor to be able to catch up with the rich, which is not the case for the standard Ramsey model where the initial wealth differences perpetuate. Secondly, within this framework, we incorporate the relative wealth effect and conclude that the catching up amoung agents depends on the share of two classes in the economy. If the share of two classes is same, there exist unique symetric steady state, whereas if the share of two classes are different the steady state is assymetric. Morever, the steady state level of aggregate capital stock is higher than the that of standard Ramsey model. Finally, we introduce the relative consumption effect and reach the conclusion that whatever the share of classes, the gap between the initial wealth level of two classes will disappear in the long run. In addition, the steady state level of aggregate wealth level is same with the that of standard Ramsey model.