A Logarithmic–Quadratic Net Benefit Model of Commuting, Willingness-to-Pay, and Toll Equilibrium

Abstract

Paul T E Cusack

This paper develops a unified analytical framework linking commuting time, income, willingness-to-pay, and congestion pricing through a logarithmic–quadratic net benefit function. Using a derived relationship between economic output M, effort E, and time t, we show that equilibrium commuting behavior follows a logarithmic law:

M = Eln t

Empirical calibration using Greater Toronto Area (GTA) after-tax income (2013) yields a net benefit optimum corresponding to a 27% welfare gain. The model predicts equilibrium toll pricing consistent with observed commuter willingness-to-pay and transit elasticity. Results suggest a natural toll level near $5.60 per trip and validate a dual structure of time valuation and congestion costs.

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