On the Matthew effect in research careers: Abnormality on the boundary

The observation that a socioeconomic agent with a high reputation gets a disproportionately higher recognition for the same work than an agent with lower reputation is typical in career development and wealth. This phenomenon, which is known as Matthew effect in the literature, leads to an increasing inequality over time. The present paper employs an optimal control model to study the implications of the Matthew effect on the optimal efforts of a scientist into reputation. The solution of the model exhibits, for sufficiently low effort costs, a new type of unstable equilibrium at which effort is at its upper bound. This equilibrium, which we denote as Stalling Equilibrium, serves as a threshold level separating success and failure in academia. In addition we show that at the Stalling Equilibrium the solution can be abnormal. We provide a clear economic interpretation for this solution characteristic.