Capital stock management during a recession that freezes credit markets

This paper considers the problem of how to price a conspicuous product while maintaining liquidity during a recession, which both reduces demand and freezes credit markets. Reducing price would help maintain cash flow, but low prices can erode brand image and, hence, long-term sales. The paper extends earlier work of the same authors by explicitly deriving a firm’s optimal cash management behavior, taking into account that a too low cash level results in bankruptcy. There are different sets of initial conditions for which qualitatively different solution trajectories are optimal. Along a single trajectory, it can be optimal to throttle forward then back how aggressively one spends down cash reserves, with the associated state constraint alternately being non-binding, binding, non-binding, then binding in such a way that the firm ceases operation.