Firm Behaviour Under the Threat of Liquidation: Implications for Output, Investment & Business Cycle Transmission

Cash balances of the firm follow a diffusion process, triggering liquidation when they cross a threshold value. Access to external funds is constrained. Shareholders are impatient. With these assumptions there is a precautionary motive for retaining earnings; the internal cost of funds and local risk-aversion are decreasing functions of net worth; and, in extensions of our basic model, output and investment are increasing functions of net worth. We numerically simulate aggregate behaviour of a population of such firms. Shocks to net worth lead to substantial and prolonged deviations from steady state, consistent with a financial mechanism of business cycle transmission.Financing constraints, output, investment

Construction of a linear ion trap and engineering controlled spin-motional interactions

This thesis outlines the design and construction of an experimental system for confining and manipulating 171Yb+ ions in a linear trap. The experimental system is used to demonstrate two complementary techniques relating to entangling gates in trapped ions. Firstly, phase-modulated pulse sequences are used to perform motion-mediated entangling gates in a manner that enables robustness to noise, parameter flexibility and the ability to generate entanglement in large ion registers. Secondly, phase- and amplitude-modulated pulse sequences with tuneable noise sensitivity are used to perform spectrally-resolved sensing of fluctuations in the motional frequency of trapped ions. Together, these techniques form a joint framework for the measurement and suppression of error in trapped ion entangling gates

The Net Worth Trap: Investment and Output Dynamics in the Presence of Financing Constraints

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)

The net worth trap: investment and output dynamics in the presence of financing constraints

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