Time and the Generations by Partha Dasgupta

Author:Partha Dasgupta
Language: eng
Format: epub
Tags: BUS099000, Business & Economics/Environmental Economics, POL044000, Political Science/Public Policy/Environmental Policy
Publisher: Columbia University Press
Published: 2019-06-24T16:00:00+00:00

The rate of return on investment is r − 1. The saving rate can now be defined as

from which it follows that

Notice that s (t) lies in the unit interval [0, 1]. Because consumption takes place at the beginning of each period, net saving is zero at t if s (t) = 1/r. Saving is positive if s > 1/r, and it is negative if s < 1/r.

Because Rawls rejected the Difference Principle for identifying the just saving rule, I studied equilibria that would emerge in a non-cooperative game among the generations with well-being functions (A3.1). I followed Rawls’ wording of the saving principle and studied Nash equilibria when each generation chooses its saving rate. Arrow (1973) agreed with the way I had formulated parental motivations (eq. (A3.1)) and the accumulation process (eqs. (A3.2)–(A3.4)), but applied an intergenerational max–min principle to infinite well-being streams. That is why we published our papers separately.

The character of Rawls’ saving policies under the two formulations were reviewed in Dasgupta (1974b). Each was found to have questionable features. Nash equilibrium saving rates were found to be intergenerationally inefficient (there are non-equilibrium saving rules under which all generations would enjoy higher levels of well-being). That would be found objectionable behind the veil of ignorance. I also found that, if refined versions of the concept of Nash equilibrium were deployed by the generations, there would be a plethora of equilibrium outcomes. Rawls would then require further normative directives for selecting one from among the multiplicity of refined Nash equilibria.

Arrow (1973) showed that if θr < 1, intergenerational max–min commends that there be no (net) saving (i.e., s (t) = 1/r), which means the stock of capital remains constant through time. Zero net saving per se is not to be rejected (Section 11 and Appendix 4 below show why); what is worrying for the theory, however, is that it commends zero net saving irrespective of the capital stock that society has inherited from the past. Arrow (1973) also showed that if θr > 1, the optimum saving behavior under intergenerational max–min is a sawtooth function of time (each period of positive saving is followed by a period of negative saving). Such a saving policy was shown by Dasgupta (1974b) to be intergenerationally inconsistent: the expectations of each generation are thwarted by the desired saving rate of the next generation.

Independently of us, Solow (1974b) put intergenerational max–min to work in a model in which a constant population produces output when working with produced capital and an exhaustible resource. But he was under no illusion that Rawls advocated max–min (p. 30):

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