Jacob Schwartz (9 January 1930 - 2 March 2009)

Jacob T. Schwartz was a mathematician at the Courant Institute of Mathematical Sciences at New York University. He once gave a series of lectures on mathematical economics, published as Lectures on the Mathematical Method in Analytical Economics, Gordon and Breach (1961). This book, coming out a year after Sraffa's work, seems to very little known. Its findings parallel Sraffa's in many ways:

"Our interest...will...be...in the use of the input-output model as a framework for ...abstract economic analysis." (p. 8)

"If each time labor appears as an input in production we replace this input by the corresponding real wage bill, we come to a hypothetical situation in which the only inputs required for the production of commodities are other (non-labor) commodities. Thus we may, if it is convenient for one or another theoretical purpose, consider our model to refer to a self-enclosed world of material commodities, produced out of each other with no additional input." (p. 10)

"The proper conclusion at this point is that the rate of profit ρ is not successfully determined by the Walrasian theories from considerations of production coefficients, utility functions, and so forth. What our analysis shows, in fact, is that the determination of the rate of profit is not purely a question of economics at all, but is rather a social-political question involving, among other things, union-management relations, pressures, and counterpressures, etc. Thus an initial skepticism about classical equilibrium analysis is justified. What this analysis aims to give us is a set of prices. But all the price-ratios are already determined by a small part of the theory, to wit by the competitive equality of profit rates. All that remains to be determined on the score of prices, is the rate of profit - but, as we have just seen, the Walrasian determination of this rate is questionable... What are determined more successfully are the amounts of production - but this is more a humble matter of consumption habits at given prices than a highly recondite matter of consumption schedules at a variety of hypothetical prices." (pp. 196-197)

"As our analysis in Lecture 16 shows, as long as we assume a fixed scheme of production the Keynesian conclusion that wage cuts by lowering wage-generated commodity demand must lower demand for labor is inescapable. The neoclassical contention thus depends on the possibility of shifts in the production scheme; a conclusion which the neoclassicist would be the first to emphasize, since the whole apparatus of neoclassical theory, revolving about the notion of marginal product accruing to an increment of each input facor, does in fact center on an analysis of variations in production. This means that the equilibrium analysis of Lecture 16 has come to such distinctly Keynesian conclusions as it has only by assuming away the basis for the neoclassicist's argument. At the present point, therefore, we shall attempt to generalize the analysis of Lecture 16 to include the possibility of shifts in the production scheme, hoping to estimate the extent to which such shifts are likely to affect our earlier conclusions." (p. 239)

"We may at this point remark once more that our analysis of prices shows that even in the framework of the present general model [with a choice of technique] price ratios are determined up to a single parameter from the conditions of production. As we have emphasized in the final paragraph of Section 1, Lecture 3, this conclusion constitutes strong presumptive evidence against theories which attempt to tie prices to consumer demand. More generally, we see that by allowing variation in the scheme of production, we in fact introduce no changes in the fixed-matrix Leontief model other than to make the Leontief matrices dependent on the [rate of profits]." (p. 248)

I prefer Sraffa's book partly on the basis of style.