What determines price is not "demand" but "cost"
Relative prices are determined by cost, not demand, is the most important proposition of the Theory of Value, which has been handed down from the classical school to Sraffa. The neoclassical champion, K. J. Arrow, has elaborated on this argument in a negative context, which I will quote from three places.
Evaluation of K. J. Arrow's "Non-Substitution Theorem"
Chapter 1 Historical Introduction, p.14
Samuelson [1951] and Georgescu-Roegen [1951] showed that with one primary factor it is still true that relative prices of produced goods are determined by the tehnology, independent of demand conditions. This is, in a certain sense, a suprising resuscitation of the classical theory in which prices are determined by supply conditions alone. Since competitive production always minimizes costs, it follows that the technique actually chosen for the production for any commodity is also independnt of demand conditions, though it will depend, in general, on technological conditions in other industries. For more extended discussion, see Section 2.11.
Chapter 2 Market Equilibrium: A First Approach, p.46
Since p* is determined without referece to demand conditions, it follows also that we now do not need any elaborate assumptions to ensure that all demand functions are continuous over SN. Indeed, the theory of household behavior can be left in a most rudimentary state. All we need is H and W, the most innocuous of the assumptions. For all these reasons, the L-economy has proved attractive to many economists. But the number of assumptions we have made suggests that this simplicity is achieved at certain costs.
Chapter2 Market Equilibrium: A First Apploach, p.47
After all this, we may judge that the L-economy is an interesting construction, if for no other reason than that it helps us to understand ealier theories, such as the labor theory of value, but it seems somewhat unlikely that a pure "cost of production theory" of prices is capable of reflecting adequately the complexities of the real world. There are several directions, however, in which the analysis can be extended. We note only one of these here.
In the above, Arrow, while giving a negative evaluation of the total, somehow devotes many efforts and pages to the "non-substitution theorem". This is probably because Arrow himself extended the theorem to n-goods, but even so, one would think that if it were so unhelpful, it could just be tucked away in a footnote in the form of an episode.
This is rather because Arrow himself saw the potential (theoretical threat) in the "cost of production theory," and a cynic like myself was tempted to wonder if this was not the case.
This theorem has been revived by Yoshinori Shiozawa as the "minimal price theorem," one of the core propositions of SMT theory* (Yoshinori Shiozawa, Masashi Morioka, and Kazuhisa Taniguchi).
*Microfoundations of Evolutionary Economics (Evolutionary Economics and Social Complexity Science, 15), 2019/7/10: 本に溺れたい
※For the "minimal price theorem" or "non-substitution theorem," see below.
1)塩沢由典『近代経済学の反省』1983年日本経済新聞社、pp.158-62
2)塩沢由典, 有賀裕二編著『経済学を再建する : 進化経済学と古典派価値論』2014年中央大学出版部、pp.93-8
3)SMT, Microfoudations of Evolutionary Economics, 2019, 2.4 Minimal Price Theorem, pp.69-86
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