[In recent years spectral techniques have been used to assess the effects of applying various types of seasonal adjustment procedures to economic time series. Similar analyses using artificially generated time series have also been attempted. The effects, desirable or undesirable, of a particular method of seasonal adjustment can, however, only be assessed properly in the time domain and only in relation to the objectives of such adjustment. Despite the fact that such objectives have not been clearly formulated nor any definitive conception of the nature of seasonality developed, in this paper we do adopt a general approach consistent with what has been written on the subject since the time of Jevons. In terms of a simple three component model of an economic time series having properties similar to those found in many actual time series, we devise several "methods" of seasonal adjustments based on a minimum mean-square-error criterion of optimality. We show that such methods of seasonal adjustment produce seasonally adjusted series bearing the same relationship to the unadjusted series in spectral terms as that found by Nerlove and others in their studies of BLS and Census methods of adjustment. Our conclusion is not that spectral methods are useless, but rather that comparisons in the frequency domain must be interpreted with great care. Further research must emphasize objectives and models. Whether these are formulated in frequency terms or in the time domain is of secondary importance.]

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at.

A pairwise trading process is formulated subject to conditions of nonnegativity of traders' holdings and quid pro quo. It is shown that that: (i) There is a centralized procedure that achieves the equilibrium allocation for an arbitrary economy. (ii) It is not in general possible to find a decentralized procedure that achieves the equilibrium allocation for an arbitrary economy. (iii) In a monetary economy there is a decentralized procedure that achieves the equilibrium allocation. The usefulness of money is that it allows decentralization of the trading process.

However, his example is based on an extreme assumption that the capitalists' propensity to consume, c, is unity. If, like Marx, we instead assume that c 0. To show this we use the generalized von Neumann model [2, 3], of which Petri's example is no more than a special case with c = 1. Assume c 0. By the two Lemmas to the Generalized Fundamental Marxian theorem [1], we know that e > 0 implies IrW > 0 and gC implies e > 0. Hence e > 0 rr > 0 ro > 0 gO > 0. Conversely 7r°> 0 g° > Ogc > 0 e>0O. Thus e>0 0 O. Thus, provided the capitalists save at least a part of their incomes for accumulation, the Generalized Fundamental Marxian Theorem holds not only for the warranted rate of profit and the capacity rate of growth but also for the equilibrium rate of profit and rate of balanced growth.