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. We distinguish mild and severe recessions. With mild recessions bankruptcy can be avoided for sure when the brand image is large enough. In case the recession is of intermediate strength, 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.