Firm Dynamics Depend on Cash and Capital

Models of the firm traditionally have one state variable for tractability. Our innovation is to solve a dynamic model of a firm with two states – cash and capital, which jointly determine a firm’s optimal default, investment, payout, and risk management decisions. Our two-dimensional model allows for diminishing returns to scale, non-linear issuance costs, and fixed debt. The model connects disperse strands of the empirical literature, and we find support in the data for novel non-linearities: (1) equity issuance scaled by capital is declining and convex in capital and (2) payout scaled by capital is concave in capital. JEL classification: E22, G12, G32, G33, G35