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 193
