Mathematical Perspectives on Consumer Spending during a Financial Crisis

Abstract

This paper explores the mathematical dynamics of consumer spending during a financial crisis using opponent process theory (OPT). Traditionally applied in psychology, OPT explains how initial emotional responses are followed by counteracting reactions to restore equilibrium. This study models the short-term boost in consumer spending and subsequent economic adjustments. Utilizing differential equations to represent these processes, this paper provides insights into the interplay between immediate policy effects and longer-term economic consequences. We focus on the United States (US) response to the 2008 Global Financial Crisis in this study. Results show evidence of diminishing response from prolonged stimuli due to demand saturation, resource allocation inefficiencies, and agent adaptation. Monetary stimuli may inflate debt/prices, outweighing benefits, and structural issues persist despite stimuli. Confidence and expectations impact response because perceived ineffectiveness weakens impact over time. Thus, while stimuli can initially boost activity, their sustained impact demands careful consideration of economic dynamics and agents’ responses.