Abstract
In this chapter, the systems with which we have thus far been concerned will provide an analytical framework for a critical review of several economic doctrines of historical significance. The ground we have covered in Chapter 2 is by no means unexplored territory in economic theory. Most of these ideas have appeared at various points in the economic literature. But they have not yet been fully integrated into the body of modern economic thought.
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Reference
For this interpretation, see Pasinetti (1977).
See Dorfman/Samuelson/Solow (1958), Morishima (1964).
Dorfman et al., ibid., point to this problem verbally at p. 258.
Matrix tB is not to be confused with matrix B of von Neumann’s model of joint production.
There have been several attempts to incorporate gestation periods for cap¬ital goods into the analysis, see Johansen (1978) or Duchin/Szyld (1985). In these works, multi—period processes of production are assumed for the capital—goods sectors, as we have done in Chapter 2. But still the production of intermediate goods is described by static i.e. timeless equations. Hence the inconsistency of the original model with respect to the time structure of production is only partly removed.
This interpretation of Leontief’s dynamic system has been subject to system—theoretic critique by Livesey (1971, 1974 ). Since matrix 113 will or¬dinarily not be invertible, the system cannot be transformed to the forward—recursive state—space form; that is, it is inconsistent or misspecified from a system—theoretic view. Apparently, this is due to the ambiguous way in which time is introduced in this model. See my (1988) for details.
Walras himself proposed such an elimination procedure. For a modern ex¬position see Dorfman/Samuelson/Solow (1958).
See Hicks (1941,1968).
See, for example, Arrow/Hurwicz (1958).
This way of looking at the process of production is suggested by Walras himself who introduces the device of tickets (“bons”) which are traded in the market to determine the allocation before the act of production itself commences. See Walras (1926, par. 207.). For a modern discussion of this interpretation, see Hicks (1941). is a preference preordering defined on the entire commodity space. Equa¬tion (3.1.61.) then degenerates to an eigenvalue problem. This means that although Nature supplies all the necessary goods, she does so in the wrong proportions, and production itself is the act of exchanging goods with Na¬ture such as to ensure the creation of the desired proportions. This process occurs at no cost (since no time is required, cf. Roemer (1981)), and thus the prices of goods produced emerge directly from the prices of the input resources surrendered in exchange. Substitute (3.1.60.) for W to find1
Given that the spaces spanned by pit and per) coincide as described and that some goods are basic commodities, (3.1.62.) alone suffices to determine the relative prices of a subsystem of commodities, without regard of the set of preferences. This is the kernel of Sraffa’s (1960) critique of utilitarian price theory.
A somewhat related discussion is Morishima (1977).
This appears to resemble the Marxian Transformation Problem, and, in¬deed, some similarities do exist. See Section 3.3. below.
See Eatwell (1976) for a related critique of this system.
Walras also takes insurance premiums into account. In order to illustrate these correctly, a market for stock insurance would have to be constructed, a problem which becomes rather difficult if loss rates depend on age or on the intensity of use.
See J.B. Clark (1888, 1899).
This function has already been used by Wicksell (1913).
For a review and critical treatment see Samuelson (1983).
No such complication would arise if production was atemporal. Then the production functions (3.1.101.) and (3.1.102.)
von Neumann’s system can be generalized in either of two directions, first by admitting consumption Cxt = CBzt, and second by attributing prices to external inputs. On the former, see Kemeny/Morgenstern/Thompson (1956), Morgenstern/Thompson(1967, 1976), on the latter, Morishima (1964, 1973, 1978 ).
This is why no assumptions regarding returns to scale are necessary.
Stationary prices must be mutually consistent or they will not continue to be stationary. But the question remains as to what a “long period” of price formation is when constant techniques are not assumed. Long periods in which techniques do change are not conductive to the gravitation of prices toward equilibrium. It seems reasonable to look at Sraffa’s system as a way to determine the set of prices which is consistent with a given production technique.
Note that we have employed an identical assumption in Section 2.1.2. above.
It may be noted that we must, of course, _assume that the proportions in which the age cohort z leaves process z, SC, are compatible with the proportions in which this cohort is employed in the process z + 1 which follows, Sz+l:z+1.
This is in contrast to more traditional interpretations, see, for example, Sweezy (1952).
See, for example, von Hayek (1931). A review of such pre-Keynesian de¬bates which remains vaulable today is Löwe (1926).
See Roemer (1981) for a review.
Marx defines this term precisely only in a footnote in (1894, Chapter 13).
Again, see Schefold (1979).
See Section 2.2. above.
Additionally, we have to assume that a new equilibrium with a common rate of profit in all sectors is reached instantaneously. Otherwise,ß would change into a vector which is itself independent of the price system. See Section 3.3. below.
On Sraffa and Marx, see Steedman (1977); on Sraffa and von Neumann, see Schefold (1980).
Of course, this reasoning cannot be applied to the Marxist version of so¬cialist theory, though it should be kept in mind that both Walras and Pareto were sympathetic with socialist ideas as well.
See, for example, Luenberger ( 1979, Sec. 8.4.).
An early formal elaboration is von Bortkiewicz (1906, 1907), a review of the discussion is included also in Engels’ preface to the third (1894) volume of “Capital”.
There clearly must be inputs of raw materials as well, but sine they bear no embodied labor values, these are not traded commodities.
See, for example, Samuelson (1957, 1971).
It is interesting to note that in his defense of the aggregate production function, Samuelson (1962) employs the assumption that the proportion of direct to indirect resource values is identical in all production lines, that is, that the organic composition of capital is equal in all industries. This implies that an aggregate production function and a unique wage-interest frontier exist if the transformation problem is neglected. The Cambridge Controversy has shown that the converse holds true as well. Given an economy with circulating capital, it is impossible to determine the rate of interest as a well-behaved function of the technique of production.
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Ritschl, A. (1989). Prices and Production in Economic Theory. In: Prices and Production. Contributions to Economics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-53716-5_4
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