On Hartwick's Rule for Regular Maximin Paths of Capital Accumulation and Resource Depletion

Abstract

In a series of recent papers, Hartwick (1977a, b, c, 1978b, c) has shown in a number of special models that keeping investment equal to the rents (really profits from the flow of depletion) from exhaustible resources under competitive pricing yields a path of constant consumption. We shall call this the Hartwick Rule . Our purpose is to examine this striking rule in a general context. We shall allow many types of consumption goods and endogenous labour supplies. We shall also allow heterogeneous capital goods, and treat exhaustible or renewable resources as special capital goods: exhaustible resources can be depleted but not produced, renewable ones can also be produced. One restriction we impose is that there is no population growth or technical progress. Hartwick (1977b) does allow these, but as they require a fortuitous coincidence of different exogenous rates if the rule is to remain valid, we do not think it worthwhile to attempt that generalization. In our general framework the Hartwick rule becomes keep the total value of net investment under competitive pricing equal to zero . This is then shown to be sufficient to give a constant utility path. The desirability of such a simple unified treatment should be evident. It even proves possible to generalize the rule to keep the present discounted value of total net investment under competitive pricing constant over time ; indeed, the generalized Hartwick rule is necessary and sufficient for constant utility. More importantly, while these rules give intergenerational equality, it remains to be seen whether they yield the best paths of this kind, i.e. Rawlsian paths. We therefore show that the generalized Hartwick rule is sufficient to give a constant utility maximin path, or a little more precisely, a regular maximin path as defined in Burmeister and Hammond (1977), provided that there is free disposal and an absence of stock reversal , as explained in Section 4.