Maximin: a direct approach to sustainability

Abstract

We solve directly a general maximin (sustainment, intergenerational-equity) problem. Because the shadow values of a maximin problem do not correspond to the shadow values from a general discounted-utility solution, they correspond to the prices of only a very special competitive economy. Virtual discount factors for the economy arise. They do not correspond to hyperbolic discount factors. Hartwick's rule is derived and generalized naturally to take into account non-autonomous and non-deterministic features of the economy. Under uncertainty, Hartwick's rule is the analytic expression of a form of precautionary principle. Hotelling's rule is a necessary condition, but may be more complex than has been appreciated in simple models. Some interpretations of strong sustainment are special cases of weak sustainment but, paradoxically, may be more difficult to solve. Maximizing welfare or sustaining utility?In this paper, we discuss the conditions for sustaining, primarily 'weakly' sustaining, an abstract economy, on the assumption that it is sustainable. An erudite survey by Pezzey and Toman (2002-3) sums up what they call the neoclassical treatment of weak sustainability. That treatment utilizes a welfare integral, which Pezzey and Toman call general because the force of interest (or instantaneous rate of discount) need not be constant. Let U denote current utility or felicity, a function of a vector of consumption goods C; GPV(t) the general present value (welfare), as of time t; and θ (t) the factor that discounts from time t to time 0. Thensubject to various conditions including transition equations for capital stocks. The problem faced by a planner is a standard control problem, to maximize GPV(t).We thank Urs Brandt, Jon Conrad, Kim Long, the late Philippe Michel, Tapan Mitra, Robert Solow, Koichi Suga, Franz Wirl and three referees for helpful comments and FCAR and SSHRCC for financial support.

Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives

“…"Rawls sketches a theory of "just saving" to modify the difference principle. 4 Wealth creation is necessary for the effective defense of rights and liberties.…”

An environmental-economic measure of sustainable development

“…A maximin path maximizes the standard of living of the poorest generation, looking forward from the present (Cairns and Long 2006). What is sustained (supported from below) along a feasible path of the economy is the minimum level of consumption of any generation over the very long run.…”

“…If the economy pursues the maximin objective in a regular maximin problem, the standard of living remains constant over the indefinite future (Burmeister and Hammond, 1978;Cairns and Long, 2006). 2 This means that if a planner decides to apply 2 A comparison with "strong" sustainability is in order.…”

“…A maximin program could be followed for maximizing the sustained level of the environmental index (Cairns and Long, 2006 On the one hand, genuine savings extends the concept of savings in the national accounts to include changes in the quantities of capital goods, especially environmental goods, that do not have market prices. It is equal to the current change in social welfare, which is usually defined to be the integral of discounted social utility.…”

Characterizing the sustainability problem in an exhaustible resource model

“…Regularity entails that reduced consumption on a finite time interval can be transformed into a uniform addition to consumption for the rest of the path and implies that any maximin path is egalitarian and efficient. In the discrete-time setting, conditions for regularity were studied by Dasgupta and Mitra (1983) and Cass and Mitra (1991), while in the continuous-time literature on maximin paths, it has been common simply to assume regularity (see, e.g., Withagen and Asheim, 1998;Cairns and Long, 2006). In Theorem 4 we show that under an additional assumption (namely that the production function has the property that the resource is 'important') the egalitarian path 2 The Cass-Mitra characterization is in a discrete-time model, where (as noted by Dasgupta and Mitra, 1983) Hartwick's rule does not hold for efficient equitable paths (which are always maximin paths as well).…”