Is there an optimal market withdrawal decision? A simple mathematical model and analysis

This paper takes up the interesting phenomenon and behavior observed in practice of some firms which appears contrary to the normally expected market-share maximizing behavior. In practice, many firms have been found to not pursue market share relentlessly and aggressively, (which we refer to as the Active Phase) but prefer rather to level off their market share after a point of time (the Passive Phase) or exit the market. In this paper, we analyze such behavior through a simple mathematical model and examine whether there could be economic reasons for such behavior, and whether it would make for a good economic and financial decision. We find that in the Infinite Horizon case, it would not be optimal to withdraw from active marketing but to actively pursue market share indefinitely, whereas in the Finite Horizon case, we find that there could be a point of time where the Passive Phase could also be a viable option to pursue, and a profitable/beneficial economic decision.