The Role of the Hamiltonian in Dynamic Price Index Theory

This paper is an attempt to investigate the cost-of-living index problem in a general equilibrium multi-sector growth model. Instead of using the utility function as a compensation criterion as Konüs’ (1924) did in his original contribution, we take advantage of the current-value Hamiltonian in constructing our dynamic price index. Since the Hamiltonian is a constancy-equivalent of future utilities (Weitzman, 1976), the dynamic price index is defined in terms of the minimum expenditure that, under alternative prices, would support the constancy-equivalent-utility level in the future. We show that, when properly deflated by the dynamic price index, the real comprehensive net national product becomes an ideal measure for dynamic welfare comparisons. For some special cases, we show that the dynamic price index reduces to the simple static index.