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).

中文翻译：

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净值陷阱：存在融资约束的投资和产出动态

本文研究了一个简单的连续时间设置中的投资和产出动态，表明融资约束极大地改变了净资产和优化公司的决策之间的关系。在没有融资限制的情况下，净资产是无关紧要的（适用1958年的Modigliani-Miller无关紧要的主张）。当考虑到融资约束时，净资产的下降会导致公司减少投资和产出（这会减少风险敞口）。净资产与投资之间的这种负相关关系已经在文献中进行了研究。此处的贡献提供了新的直观见解：（i）显示即使是线性生产和偏好，企业行为的非线性也可能持续多长时间。（ii）突出涉及的经济机制-影子价格的出现既产生了公司审慎的储蓄又引起了规避风险。即使在具有线性生产和偏好函数的情况下，这种明显的非线性现象的出现也表明融资约束可能对投资和产出产生重大影响；在经济和金融危机的经验模型中应该考虑到这一点（例如，1930年代的大萧条，2007-2008年的全球金融危机以及2020年Covid-19大流行之后的崩溃）。表明融资限制可能对投资和产出产生重大影响；在经济和金融危机的经验模型中应该考虑到这一点（例如，1930年代的大萧条，2007-2008年的全球金融危机以及2020年Covid-19大流行之后的崩溃）。表明融资限制可能对投资和产出产生重大影响；在经济和金融危机的经验模型中应该考虑到这一点（例如，1930年代的大萧条，2007-2008年的全球金融危机以及2020年Covid-19大流行之后的崩溃）。