A Note on Optimal Development in a Multi-sector Nonconvex Economy

Abstract

The study by Mitra (1990) provides a convenient point of departure for reviewing and extending some of the analytical results proved by Gale (1967) in his masterly paper on optimal growth programmes in multi-sector economies. The main result of his paper was a proof of the existence of a Ramsey-Weizsacker optimal programme. But, as he noted, ‘to obtain this existence proof we have found it necessary to investigate first a number of subjects which have been central to much of the recent literature on dynamic production models including (1) optimal balanced growth programmes (‘golden rule’ paths) (2) asymptotic properties of ‘good’ programmes (‘turnpike’ theorems) and (3) dynamic prices associated with optimal programmes, … each of which is used in obtaining the final result’. Both in (1) and (3), Gale’s emphasis was on developing a ‘duality’ theory (involving an appropriate Kuhn-Tucker theorem) linking optimally with competitive prices relative to which suitable profit and utility maximisation take place along an optimal programme.

Research support from the National Science Foundation and the Warshow endowment at Cornell University is gratefully acknowledged. Thanks are due to Professor Tapan Mitra for comments on an earlier draft and suggestions on expository improvements.