ABSTRACT
My analysis here solely addresses the J.B. Clark-Wicksteed-Ramsey-Solow differentiable marginal productivities that Sraffa (1960) rejected. Thus, it follows and supplements Erkko Etula’s article (Chapter 11, this volume) which tests for Capital Reversal’s intertemporal Pareto optimality or non-optimality under Leontief-Sraffa discrete-limited-substitutability technologies. It suffices for brevity to analyze here a corn-direct labor-scalar K scenario without joint production. Zealous readers can analyze vectoral heterogeneouscapital [L(t);K1(t),K2(t)] scenarios with or without joint products, and thereby duplicate my qualitative proofs. Let us look at the following simplest input/output model of the J.B. ClarkWicksteed-Ramsey-Solow type:
Q(t + 1) = gross harvest ≡ net consumption + capital replacement
≡ C(t + 1) + K(t + 1) (1.1)
This displays no “capital reversal” of the Joan Robinson-Ruth Cohen or Ian Steedman type. Thus it can form the comparison template for an alternative Clark-Solow case where there definitely will be “capital reversal.” In the absence of any Schumpeterian technological innovation, Equation (1) will confirm the Schumpeter-Senior-Böhm-Irving Fisher story of how the successful raising of K(t)/L(t) can steadily increase C(t + 1)/L(t + 1) in the steady state. Eventually in the limit K(t)/L(t) → golden-age (K/L)g where the (safe) interest rate has dropped to zero and the real corn wage will have become maximal:
W(t)/P(t)corn → maximal (W/P)g. (1.3)
Eventual euthanasia of the capitalist rentier, when it does take place, will be proved to be a lot more than what Robinson called flapdoodle capitalists’ filterdown swindlings. Instead it will be a non-controversial provable result about
competitive Robinson Crusoe models and competitive supply-and-demand models that have no sustainable monopoly or oligopoly features. Adam Smith famously claimed that competitive market equilibrium would be led – as if by an invisible hand – to maximize societies’ well-being. My math is more specific. The visible Darwinian hand of numerous selfish arbitragers who own their labor inputs or their scalar K producible inputs will-both under capital reversal and non-capital reversal – definitely achieve maximal corn production at every (exogenous or endogenous) level of K/L endowments. In 1912, Schumpeter sensed but never formulated a coherent proof of this true theorem (see Etula (2008) for a parallel proof to mine for the technologies that are of the LeontiefSraffa-von Neumann type) (N.B.: Neither Sraffa (1960) nor any Sraffian ever did cogently refute the seminal Ramsey (1928) model of Clarkian saving.) By use of elementary calculus, one deduces from Equation (1) the famous Ricardo-Hollander inverse trade-off locus of falling (safe) profit rate, i*, versus rising real competitive corn wage rate, w*, i.e.,
w* = ρ{r*}, ρ9 < 0 (2.1)
≡ (1/r*) singularly in (1.2)’s Cobb-Douglas case. (2.2)
Equation (1.2)’s case of equal Cobb-Douglas exponents = 1/2 is there only to speed readers’ understanding.
