The rate at which growth must occur in a Harrod–Domar model if it is to be sustainable. If national income is Y, saving is S, and investment is I, saving is assumed to be a constant proportion of income so that S = sY. Investment is assumed to be given by an accelerator model, where investment is given by
I = ν(dY/dt),
where t is time. For ex ante saving and investment to be equal requires that
sY = ν(dY/dt).
This implies that the growth rate of Y must beThis is the only rate at which equilibrium growth is possible, so long as the saving ratio s and the capital–output ratio v are taken as fixed.