Measuring income and measuring sustainability

We examine what interpretation can be given to inclusive income, understood to be consumption plus the value of the net increase in all relevant capital stocks. We introduce the concept of instantaneously constant value income, defined as the maximum amount the economy can consume at a moment of time and keep the expected present value of utility of current and future generations constant. We argue that this income concept captures some of the concerns underlying sustainability. Our main result is that inclusive income equals instantaneously constant value income. We show that this result holds in a very general setting and, in particular, carries over to models incorporating technological progress when such progress can be captured by augmented stocks of knowledge. An important implication of our main result is that it provides a very simple method for deriving inclusive income, which does not involve any linearization of the Hamiltonian.