Time-discounting in behavioural economics is modelled using mechanical system dynamics through the economic engineering framework. The economic engineering framework is being developed at the Delft Center for Systems and Control, and uses mechanical system dynamics to model economic processes and systems. Time-discounting is the calculation of the present value of the received utility from future consumption. Presently behavioural economists have
not been able to reach a consensus on how to model time-discounting behaviour. Two theories dominate economic literature: exponential discounting theory and hyperbolic discounting theory. These theories are treated separately by economists and have separate fields of application. Exponential discounting theory and hyperbolic discounting theory are shown to be related through the dynamics of the damped harmonic oscillator. Exponential and hyperbolic discounting theory are linked to the dynamics of the critically damped and overdamped mechanical system respectively. The dynamics of the underdamped mechanical system are linked to the time-discounting behaviour of a trader. Moreover, the parameters of the damped harmonic oscillator are interpreted economically, resulting in the following analogues: the natural frequency is analogous to the risk-free discount rate, the damping ratio is analogous to time-preference, and the real part of the eigenvalues are analogous to the exponential discount rate. Modelling time-discounting using mechanical system dynamics therefore results in a time-discounting model based on economic first principles.