Hiring and ring optimally in a large corporation

We give a simple stochastic model for the optimal size of staa of a large (especially, but not only, research) corporation as a function of its wealth and provide a quantitative theory with explicit prescriptions for increasing, decreasing or leaving constant the number of personnel in order to maximize total proot, discounted with xed interest rate. Features of the optimal policy seem in at least qualitative agreement with observed practice in that, for example, there are occasional large scale down-sizings similar to large layoos or incentive retirement plans observed in real corporations. In the optimal plan, this type of ring occurs only on an upswing, i.e. when the company's fortune ascends to a threshold relative to staa size. Small scale or \attrition" ring also occurs under the optimal policy, but this type of ring occurs only on a downswing, when the company's fortune descends to a threshold relative to staa size. The model is extremely simple and depends on only 5 estimable parameters; thus it should be useful for guiding, or at the least stimulating, thought about corporate sizing policy. 1. Deening the model Suppose the fortune, or available capital, of a research corporation at time t is X t , t 0, where x 0 = x and for 0 < t < dX t = ?dZ t + U t (dt + dW t) ? k ? d ? U t ? k + d + U t (1.1) describes the incremental evolution of the fortune, where W is a standard Wiener or Brownian motion process, U t is the level of research or the \size" of the (research) staa at time t, which is under our control and may uctuate up or down with U 0 = u, and U t 0 for all t. Z t , the total proot or dividend extracted up to time t (Z 0 = 0) is assumed, of course, nondecreasing,