Abstract
This paper investigates investment and output dynamics in a simple continuous time setting, showing that financing constraints substantially alter the relationship between net worth and the decisions of an optimizing firm. In the absence of financing constraints, net worth is irrelevant (the 1958 Modigliani–Miller irrelevance proposition applies). When incorporating financing constraints, a decline in net worth leads to the firm reducing investment and also output (when this reduces risk exposure). This negative relationship between net worth and investment has already been examined in the literature. The contribution here is providing new intuitive insights: (i) showing how large and long lasting the resulting non-linearity of firm behaviour can be, even with linear production and preferences; and (ii) highlighting the economic mechanisms involved—the emergence of shadow prices creating both corporate prudential saving and induced risk aversion. The emergence of such pronounced non-linearity, even with linear production and preference functions, suggests that financing constraints can have a major impact on investment and output; and this should be allowed for in empirical modelling of economic and financial crises (for example, the great depression of the 1930s, the global financial crisis of 2007–2008 and the crash following the Covid-19 pandemic of 2020).
Highlights
This paper examines the impacts of financing constraints on firm operations and finances using the tools of continuous time dynamic stochastic optimisation
The consequence is corporate prudential saving, analogous to the household prudential saving extensively discussed in the literature on the consumption function
This paper investigated the impact of financing constraints on corporate output and investment in a simple continuous time setting with linear production and preferences
Summary
This paper examines the impacts of financing constraints on firm operations and finances using the tools of continuous time dynamic stochastic optimisation. As the threshold is approached, there emerges an increasing premium on the value of cash held inside the firm (relative to the outside cost of capital) and an increasing aversion to risk This modelling builds on the dynamic analyses of [1,2]. Since the firm cannot raise new equity capital, declines in net worth are financed by increases in firm borrowing When this state variable is comparatively high, near the upper boundary where dividends are paid, these shadow prices are close to those that would apply for a financially unconstrained firm that can raise new equity. Condition applies to the unconstrained model of Appendix A; and when this condition does not)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
