  Write \(dU/dC = U_C\) and \(d^2 U/dC^2 = U_{CC}.\) Let \(\{C(t)\}\) be a feasible consumption stream. We first deduce a formal expression for the marginal rate of ethically indifferent substitution between consumption at any two brief periods of time. Suppose the intention is to reduce consumption at some future date \(t\) by a small quantity \(\Delta C(t)\) and raise consumption at a nearby date \(t+\Delta t\) while keeping consumption at all other dates the same as in \(\{C(t)\}\). The loss in well-being that would follow from the move is \(e^{-\delta t}U_{C(t)}\Delta C(t)\).  We now seek to determine the percentage increase in consumption that would be required at \(t+\Delta t\) if \(V(0)\) is to remain unchanged; because that’s the marginal rate of ethically indifferent substitution between consumption at \(t\) and consumption at \(t+\Delta t\). Denote that rate by \(\varrho(t)\). Then \(\varrho(t)\) must be the percentage rate at which discounted marginal well-being declines at \(t\). It also follows that \(\varrho(t)\) is the rate the DM at \(t = 0\) would use to discount a unit of consumption at \(t\) so as to bring it to the present (because that’s what is meant by the percentage rate at which discounted marginal well-being declines at \(t\) – for a formal demonstration, see Dasgupta, 2008). Some economists call \(\varrho(t)\) the consumption rate of interest (Little and Mirrlees, 1974), others call it the social rate of discount (Arrow and Kurz, 1970). \(\varrho(t)\) is a fundamental object in social cost-benefit analysis.