Essays in Honour of Karl-Göran Mäler
Edited by Bengt Kriström, Partha Dasgupta and Karl-Gustaf Löfgren
Chapter 1: An Example of Dynamic Control of Negative Stock Externalities
Kenneth J. Arrow 1 INTRODUCTION In this chapter, I want to carry through a rigorous analysis of the dynamic control of a simple case of negative externalities arising from stocks. As Starrett showed in his classic paper (1972), negative externalities imply nonconcavity of the benefit function. Non-concavity in turn implies that the firstorder conditions for an optimum are not sufficient. In a dynamic context, where the policy in each period leads to accumulation of stocks, the first-order conditions are those of the Pontryagin (Pontryagin et al. 1962) principle. Just as in a static optimization problem, there will in general be several solutions, all of which satisfy the Pontryagin conditions but only one of which will correspond to the global maximum. This fact has two important implications. One is that the optimal solution will involve specialization in some sense. Concretely, with negative externalities, it may be best to abandon one area to the negative externality, say pollution, rather than try to spread the externality over all areas in some balanced way, as we would expect from analysis of the concave case. The second is methodological; the existence of a supporting price system, which is what the Pontryagin principle supplies, is not at all sufficient for an optimum. It may support even the worst possible outcome. This probably has implications for the foundation of the principle of net national product (where ‘net’ includes allowance for the depletion of environmental stocks), which is based on the Pontryagin principle (see Dasgupta and Mäler...
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