| Abstract: | Abstract Proofs are given that only singularly can real 1750 – 2007 competitive price ratios be ‘natural', in the sense of being invariant under changes in demand tastes. Proofs are given that both 1750 – 1870 discrete technologies or 1890 – 2007 continuum technologies, with convexity properties sufficient for arbitrage-proof supply-demand equilibria, will be ‘intertemporally Pareto optimal', immune to leaving any deadweight (inefficient) losses on the table. Sraffa (1960), ignoring the vast post-1945 linear and non-linear programming mathematical literature of Danzig, Kuhn-Tucker-Bellman, von Neumann, Ramsey literature does not quite arrive at attainable distribution solutions. Where it tolerates increasing or decreasing returns to scale, there can be no competitive equilibria. When its matrix equations do obey first-degree-homogeneous functions, the book's stress on Basics or non-Basics is an irrelevancy leading to bizarre novel interpretations of Ricardo. Old age overtakes us all. Alas, Sraffs's proposed critique of twentieth century political economy we will never be able to know. |
