Capital Accumulation and Horizontal Mergers in Differential Oligopoly Games

The existing (static) literature stresses the relevance of capital inputs in determining whether any given merger is (i) profitable and (ii) socially efficient, or not. We take a differential game approach to the same issue, proposing two different models based, respectively, on the capital accumulation dynamics introduced by Ramsey and Solow, respectively. We show that the change in the steady state size of productive plants induced by a merger may play a decisive role in determining whether such a merger is profitable, or socially efficient. However, unlike the static contributions in the same vein, we show that the parameter sets where, respectively, firms find it convenient to merge, and the merger is welfare-increasing, do not intersect at all, irrespectively of the capital accumulation dynamics being considered. This entails that a regulator concerned with the welfare performance of an industry should prevent firms from carrying out any horizontal merger.