Abstract
Based on the idea of basic separation of price and quantity adjustments, this chapter presents a new picture on how an economy as big as the world ordinarily works by the actions of agents whose capability is limited in rationality, sight, and actions. The first part (Sects. 2.2, 2.3, 2.4, 2.5, and 2.6) is devoted to showing why prices of industrial goods are stable. It gives a reason for price stability that is completely different from the standard menu-cost explanations. Section 2.7, which is an introduction to Chaps. 3, 4, 5, and 6, explains the mechanism by which the quantity adjustment proceeds in the economy as a whole. The result obtained in this chapter (and this book) is of paramount significance for the economics of the market economy, because this is the first result after Arrow and Debreu’s general competitive model that shows that “a social system moved by independent actions in pursuit of different values” can work without assuming an unrealistic capability for infinite rationality and complete information.
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Notes
- 1.
To prove these facts would be extremely difficult. We do not attempt to do so.
- 2.
Obviously we are opposed to Milton Friedman’s instrumentalist view of economic theory.
- 3.
Theories such as endogenous money theory, circulationist theory of money, and Modern Money Theory (as proper noun) may help readers to imagine a theory of money to be connected to the present theory.
- 4.
A copy of the publicity flyer when Mitsui Takatoshi started his business in Surugacho is transmitted to our day. As I could not have found any English paper that presents it, I reproduce here my translation of the text. The original of this flyer was lost through a series of fires. The present text is a copy that was copied by the eighth chief of the house of Mitsui in the fifth year of Kaei (1852) and is now conserved in Mitsui Bunko (Higuchi and Sato 2010). From this text of the flyer, we cannot know if Echigoya used price tags from the beginning. No words like shōfuda (price tags) are used in this flyer. There exist flyers of later years that refer to a price tag system, but the starting date of the price tag system is not well known.
-
Echigoya Hachirōemon in Surugachō humbly announces:
-
In this new occasion, as I have started a new endeavour and am selling any clothes at a specially cheap price, please come and buy at my store. We do no sales by visiting the home of any client. As we have fully accounted for services and costs of what we put on sale, we do not ask for a price even a penny higher than what we have fixed. Consequently, we do not abate any price even if any clients ask us to do so. Of course, we accept all prices in cash. We do not sell any good on account, even for a penny.
-
Cash payment, cheap price, no markups
Clothes shop
Echigoya Hachiōemon at 2-chōme Surugachō
Note: Echigoya Hachiōemon is the business name of Mitsui Takatoshi. “Markups”
here means the practice to announce a higher price than the shop expects so that it can have a discount margin in the price negotiation.
The original text in Japanese (written in a Chinese-Japanese mixed style):
駿河町越後屋八郎右衛門申上候今度私工夫を以呉服物何に不依格別下値に売出し申候間私店に御出御買可被下候何方様にも為持遣候義は不仕候尤手間割合勘定を以売出し候上は壱銭にても空値不申上候間御直き利被遊候而も負ハ無御座候勿論代物は即座に御払可被下候一銭にても延金には不仕候以上
呉服物現金 駿河町弐丁目
安売無掛値 越後屋八郎右衛門
-
- 5.
Lee distinguishes three pricing methods: administered prices, normal cost prices, and mark up prices. These are but the historical names used by those who studied pricing principles. Their pricing principle is the same. Variance of names is a proof that full-cost pricing was discovered many times on different occasions. We may have different definitions of the “direct unit cost,” and its behavior may differ according to assumptions we adopt. See also the comments on Postulate 9.
- 6.
Independent from the rationality argument, Sonnenschein-Mantel-Debreu theorem tells that demand function can approximately take any form as long as it satisfies the Walras law. Despite its formalistic appearance, neoclassical theory of demand requires empirical rules such as gross substitutability hypothesis in order that it becomes a workable theory. If we recognize this fact, it is much better to leave the theory vacant for the moment and simply assume Postulate 4.
- 7.
We do not think it is possible for a firm to determine the so-called profit-maximizing quantity. This kind of behavior is impossible, because the cost function does not behave as the standard theory assumes. In the typical situation, the marginal cost remains constant until the production reaches full capacity. Thus the average cost is decreasing if we take into account the fixed cost. We assume the production firm operates under the law of increasing returns.
- 8.
The concept of production period has a meaning here that is different from the same term in Austrian economics, in which the production period of a product means the total labor time (direct and indirect) for the production. We use it always as having the meaning of the span of time from input to output of a production process.
- 9.
This does not mean that we deny the near equality of demand and supply. We simply claim that the traditional formulation or interpretation of the law of demand and supply is completely misguiding.
- 10.
This is one of reasons why our theory can serve as the foundations of an evolutionary economics.
- 11.
Some people consider that target costing is in contradiction with full-cost pricing. They are wrong, for target costing is a series of activities before the launch of a new product, whereas the full-cost principle is applied to the production activities after the launch.
- 12.
Arrow-Debreu equilibrium ensures that prices have no reason to change for the markets (including futures markets) which are presently open. It tells nothing of what happens in the next market that will be open.
- 13.
The name “theory of value and distribution” is also often used to when referring to the “classical theory of value.” But we omit the term “distribution” because our theory is a theory of value and is related to “theory of distribution” only indirectly.
- 14.
Note that all four authors in Koopmans (Ed. 1951) referred to the Leontief model(s) in their titles.
- 15.
To be more precise, the theorem receded into the background and became seldom mentioned even in advanced microeconomics textbooks. Petri (2016, p. 18) reported that he could find no mention after 1995.
- 16.
For more detailed account of the treatment of the non-substitution theorem by neoclassical economists, see Petri (2016) although I think that “long-period framework” did not help him to clarify the question. All stories should be retold in a framework of process (or sequential period) analysis.
- 17.
We will use a different representation in Sect. 2.6 when we argue international trade.
- 18.
Matrix A has H rows and N columns.
- 19.
It might be preferable to denote the labor input coefficient as a 0 or l. However, to maintain continuity with the international trade economy, we use u instead of a 0 or l. The reason to avoid l is apparent. It is confusing with 1.
- 20.
This expression is conveniently used when we analyze international values.
- 21.
Note that the output coefficient is required to be 1 even in the markup form. Shiozawa (2017a) calls this imaginary economy composed of production techniques of markup form the equivalent economy.
- 22.
- 23.
In mathematical symbols, this condition is expressed by (2.6) for any production techniques h in T.
- 24.
The adjective “minimal” means here that the set has the minimal number of elements among the class of spanning sets.
- 25.
This theorem is often called Hawkins-Simon theorem. A square matrix A with positive diagonals and nonpositive off-diagonal entries is nonnegatively invertible when and only when there exists a positive vector u such that u > u A. I call this theorem the “nonnegative invertibility theorem.”
- 26.
We normally assume that an admissible value possesses a spanning set of competitive production techniques. The definition 5-2 in Shiozawa and Fujimoto (2018) is not exact, because it lacks condition (1) of Definition 4.7. The true meaning of this concept becomes clear when we examine international trade situation.
- 27.
In the definition of P, it is necessary to change labor input condition to ∑h s h·(1 + m(h)) u(h) ≦ L as we have done in Theorem 4.9.
- 28.
See Aoki (1977) for such processes.
- 29.
A nonsimultaneous case is studied in Shiozawa (1978).
- 30.
A problem remains when by-products are counted as costs or revenue in unit cost accounting. The essential question is the invertibility of matrix B−A when output coefficients matrix I is replaced by B. If the total value of by-products are sufficiently small in comparison to the value of the main product, we may assume that a nonnegative matrix (B−A)−1 exists because B−A can be seen as a small perturbation of I−A.
- 31.
Note that markup rate is defined for a given unit production period. It changes when the unit period changes as the interest rate changes according to the time span of the period. More precisely, they must satisfy the equation (1 + m w)52 = 1 + m a where m w is the markup rate for a week and m a for a year.
- 32.
Mathematically, joint production is defined as the property of a production technique h whose net product b(h) – a(h) has two or more than two positive entries, b(h) and a(h), being output and input vectors of the production h, respectively.
- 33.
Equations (2.27) are different from Sraffa’s formula in §75, p. 65, because d is counted as cost at the input point of time.
- 34.
There is no strictly determined capacity. It is possible to operate over the standard capacity of a production line, but such an operation risks increasing unexpected machine downs and line stops.
- 35.
The normal production volume for a product is defined by the management taking in consideration the design, the cost, and the expected market response of the product.
- 36.
Professor Takahiro Fujimoto (2012) is proposing a more refined system of cost accounting that he calls “total direct cost.” Unfortunately, the paper is not yet translated into English.
- 37.
The truncation time of a machine is the maximal number of periods that it can be used economically. This may be shorter than the physical endurance time. If the maintenance cost increases after a number of years, it may be better to buy a new machine than to continue to use the machine by repairing it.
- 38.
A. N. Whitehead closed his last lecture at Harvard (The Ingersoll Lecture, April 22, 1941) by saying “The exactness is a fake.” See Hocking (1961, p. 516).
- 39.
The index w is only nominal. We can choose any index.
- 40.
Financial economy comprises FIRE, i.e., finance, insurance, and real estate.
- 41.
The notion of “circular flow” (Kreislauf in German) among classical economists (see Kurz and Salvadori 1985, Chap. 13) may be an expression of their naïve ideas which tried to understand the economy as dissipative structure, although they could not clearly articulate them.
- 42.
It is usually explained that cultivation starts from the most fertile land and shifts to less fertile land. Although theoretically this is the plausible order of cultivation, real history does not obey this rule.
- 43.
If the farm is cultivated by the owner of the land, the farmer obtains a virtual rent.
- 44.
General equilibrium theory is ambiguous about the logic of the rent. If the land is not exploited, the rule of free goods stipulates that it does not produce any rent. However, how is the total activity level determined? Neoclassical economists simply assume that there is some mechanism that makes all constraints satisfied if we admit the rule of free goods. If the economic system can be deemed as a linear programming, the rule of free goods is equivalent to the principle of complementary slackness. However, an economy is not a linear or any other type of mathematical programming system.
- 45.
This section is based on the new theory of international values. Readers are requested to refer Shiozawa (2017a) for general ideas. However, this section contains some new results which do not appear in Shiozawa (2017a). For a more detailed account of the new idea, please see Shiozawa and Fujimoto (2018).
- 46.
Trade economies of classes RI and RII can be reduced to R0 economy by a suitable transformation. Thus, the propositions proved for R0 economy hold for economies in the class RI or RII. Theorem 6.1 also holds for economies in RI or RII. Although R0 has an interesting mathematical structure (Shiozawa 2015), we do not enter in this topic here.
- 47.
Note we are using markup form coefficients.
- 48.
For the details, see Shiozawa and Fujimoto (2018).
- 49.
A facet of a polytope P of dimension N is a face of codimension 1, i.e., of dimension N−1, which is a set defined as an intersection of P and a hyperplane H when P is included in one of the half spaces divided by H.
- 50.
This result was already known in the 1950s. See McKenzie (1953).
- 51.
How to extend the results obtained on the no transportation cost assumption to the positive transaction cost case (including extra transaction costs to cross the country boundary) is explained and treated in Shiozawa (2017a, Section 9).
- 52.
- 53.
The new concept of regular value is different from the one given in Definition 3.7 in Shiozawa (2017a), but is in fact equivalent.
- 54.
Expectation may play some role in the decision. But it cannot be the major determinant. It is a kind of pulling oneself up one’s bootstraps.
- 55.
We are accustomed to think in the world where the mean and variance exist. However, if the sequence obeys Lévy stable distribution law, the variance does not exist even when the mean exists (when 1 < α < 2 for Lévy index α). In such a case, it is evident that we cannot obtain a reasonable estimate of the variance by an observation of finite length.
- 56.
For this, it is necessary to assume that customers wait until the next period, when the demand exceeds the prepared stock. This is equivalent to assuming a negative inventory stock.
- 57.
The inventory z(t) can be interpreted in two ways. Here we have defined as inventory which is carried over to time t. Another method is to define it as stock left at the period [t, t + 1).
- 58.
If firms possess material stock for input use, we can imagine a case the product is obtained only one period after the decision. Morioka uses this convention.
- 59.
In the above consideration, we have assumed that there is no beginning in our series. When we assume that the series start at a specific point of time −T, we must redefine the transformation f, because variables x(−T−M), x(−T−M + 1), …, x(−T−1) are not known at −T.
- 60.
Note that matrices K and A are no more commutative, i.e., K A ≠ A K in general.
- 61.
- 62.
Diagonalizability is not a severe condition. As it is dense in the matrices of the same dimension and the sufficient condition is given in a simple algebraic inequality, the same condition is also a sufficient condition for non-diagonalizable matrices.
- 63.
Eigenvalues of an input-output table’s coefficients may depend on the degree of aggregation. The coefficient for manufacturing of the 14-sector table is 0.44427204. According to my computation by Mathematica, the matrix for 19 sectors from mining to miscellaneous manufacturing extracted from input coefficients (37-sector table, 2011, Japan) has the biggest eigenvalue, 0.57006. The next biggest eigenvalues are 0.435129, 0.421933, 0.382724, and 0.288406. See also Morioka’s results in Chap. 4 (Subsect. 4.1.2).
- 64.
See also conditions (1), (2), and (3) in Sect. 2.4.5.
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Acknowledgment
Special thanks are given to Robin Jarvis who has polished my poor English and made this paper readable. Of course, he has no responsibility for the errors that I may have committed in this paper. I want to dedicate this chapter to the late Masahiko Aoki, my teacher and a colleague, who by his dual stability paper (Aoki 1977) inspired me to write Shiozawa (1983b) and now this chapter some 40 years later.
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Shiozawa, Y., Morioka, M., Taniguchi, K. (2019). A Large Economic System with Minimally Rational Agents. In: Microfoundations of Evolutionary Economics. Evolutionary Economics and Social Complexity Science, vol 15. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55267-3_2
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