Inframarginal economics is to apply inframarginal analysis to studies of network effects of division of labor and various economic problems associated with different features of the network pattern of division of labor. To understand what is inframarginal analysis and the framework that distinguishes inframarginal economics from marginal economics and neoclassical economics that sometime also applies inframarginal analysis, we have to look at the difference between the core of classical mainstream economics and neoclassical economics.
The core of classical mainstream economics represented by William Petty and Adam Smith differed from neoclassical economics in two aspects. It focused on network effects of division of labor and it emphasized the role of the market (the invisible hand) in exploiting the network effects to reduce scarcity. As shown in Yang and Ng (Specialization and Organization, 1993) and Yang (Economics: New Classical Versus Neoclassical Frameworks, 2001), inframarginal analysis of individuals' networking decisions is essential for formalizing the classical development economics. Here inframarginal analysis is the total cost-benefit analysis across corner solutions in addition to the marginal analysis of each corner solution. If the optimum value of a decision variable takes on its upper or lower bound, the optimal decision is a corner solution. Formally, it relates to nonlinear programming, mixed integer programming, dynamic programming, the control theory, and other nonclassical mathematical programming.
The first decision that you have to make when you get in the university is to choose a major. If you choose economics as your major, then you do not go to classes of chemistry and physics, but you take classes of microeconomics, macroeconomics, and econometrics. We call such a decision an inframarginal decision, since values of decision variables discontinuously jump between zero and interior values as you shift between majors. After you have chosen a major, you allocate your limited time between the fields in this major. This decision of resource allocation for a given major (or occupation) is called marginal decision since standard marginal analysis is applicable to this type of decision. The aggregate outcome of all students' choices of their majors in a university generates division of students among majors and fields, which is analogous to a structure of division of labor in society.
But when Alfred Marshall formalized classical economics within a mathematical framework in the end of the 19th century, he did not know inframarginal analysis. He made an assumption of dichotomy between pure consumers' decisions and firms' decisions to avoid inframarginal analysis of corner solutions. Within the neoclassical framework, each pure consumer must buy all goods from the market and cannot choose her level of self-sufficiency or its reciprocal: level of specialization. Hence, the focus of economics shifted from inframarginal analysis of problems of economic development concerning how the degree of scarcity can be reduced by division of labor in society to marginal analysis of problems of resource allocation for given degree of scarcity. Neoclassical economics departures, by following the neoclassical framework, from classical development economics. Hence, inframarginal analysis of network effects of division of labor loses the central position that classical economic thinking on the division of labor occupied in the mainstream economics. Stigler (1976, pp. 1209-1210) accurately captured frustration among economists about the shift of the core of mainstream economics as follows. "The last of Smith's regrettable failures is one for which he is overwhelmingly famous - the division of labor. How can it be that the famous opening chapters of his book, and the pin factory he gave immortality, can be considered a failure? Are they not cited as often as any passages in all economics? Indeed, over the generations they are. The failure is different: almost no one used or now uses the theory of division of labor, for the excellent reason that there is scarcely such a theory. … there is no standard, operable theory to describe what Smith argued to be the mainspring of economic progress. Smith gave the division of labor an immensely convincing presentation - it seems to me as persuasive a case for the power of specialization today as it appeared to Smith. Yet there is no evidence, so far as I know, of any serious advance in the theory of the subject since his time, and specialization is not an integral part of the modern theory of production."
Since the 1950s, economists have applied inframarginal analysis to various decision problems. However, many economists still follow Marshall's assumption of dichotomy between pure consumers and firms, under which the corner solution is exceptional and the interior solution is the rule. Hence, implications of formal inframarginal analysis for investigating effects of network size of division of labor on economic development could not be fully explored until the late 1970s. This text shall show that if a Smithian framework is adopted, the interior solution is never optimal and corner solution is a rule rather than an exception. Hence, marginal analysis is not enough and inframarginal analysis is essential for exploring implications of the division of labor for economic development.
Since the end of the 1970s, a literature of endogenous specialization and network of division of labor emerged. It rapidly grows since the 1990s. It not only resurrects the spirit of the core of classical mainstream economics in a modern body of inframarginal analysis, but also provides new frameworks for inframarginal analysis of network of division of labor. Hence it creates an opportunity for bring the core of classical mainstream back to the core of modern mainstream economics, as Houthakker expected (1956, p. 182: "there is hardly any part of economics that would not be advanced by a further analysis of specialization").
The two pioneers of the literature, Sherwin Rosen (1978) and Gary Becker (1981) applied linear programming and nonlinear programming to formalize classical thinking on network effects of division of labor and specialization (William Petty, 1671, 1683, Adam Smith, 1776, Anonymous, 1701, Babbage, 1832, Allyn Young, 1928, H. Fawcett, 1863, George Stigler, 1951, 1976, H. Houthakker, 1956). In their models, individuals usually choose corner solutions when they choose their occupations. Individuals conduct total cost-benefit analysis to compare multiple local optimum corner solutions and to choose one from many occupations (corner solutions) after they conduct marginal analysis of each corner and interior solutions. This combination of total cost-benefit and marginal analyses is referred to by Coase (1946) and Buchanan and Stubblebine (1962) as inframarginal analysis. Many Ph.D. students from Department of Economics of University of Chicago followed this literature and rallied a wave of this literature in the 1980s and early 1990s (see, for example, Locay, 1990, Baumgardner, 1988a, b, Kim, 1989, and Tamura, 1991, 1992). In the 1990s, a framework of consumer-producer with the trade-off between economies of specialization and transaction costs was combined with the inframarginal analysis to endogenize individuals' levels of specialization and network size of division of labor (Yang and Ng, 1993). The combination of the inframarginal analysis (linear and nonlinear programming, mixed integer programming, dynamic programming, control theory, and other nonclassical programming) and the framework of consumer-producers is later called inframarginal economics. In the middle of the 1990s, referees acknowledged this "emerging and rapidly growing literature" which tries to develop an overarching and coherent mainstream core based on the interplay between the Smith-Young theorem and the notion of general equilibrium. The Smith-Young theorem that division of labor is dependent on the extent of the market, which is determined by the level of division of labor is interpreted as a circular causation between the benefit of specialization and the number of participants in the network of division of labor. This circular causation is a typical characteristic of network effect, analogous to the circular causation between use value of a telephone set and the number of telephone sets in use, on the one hand. It is an essential feature of general equilibrium, analogous to the circular causation between quantities demanded and supplied and prices in the fixed point theorem. The contributors to this literature suggest that as soon as the spirit of the core of the classical mainstream economics has been resurrected in the modern body of inframarginal economics, a new core of modern mainstream economics can more convincingly explain many economic phenomena, such as trade, e-business, globalization, business cycles, urbanization, cyclical unemployment, emergence of money and institution of the firm from evolution in division of labor.
The key technical difficulty caused by myriad of corner solutions and combinations of corner solutions as candidates for a general equilibrium in managing inframarginal economics was overcome in the middle 1980s. The technical substance was later extended by Wen and Yao to a generalized Wen theorem in the 1990s.
This new analytical framework was then applied to trade theory (Yang, 1994, 1996, Cheng, Sachs, Yang, 2000a, b, Yang, 1994, 1996, G. Li, 2001, D. Yang, 2001, Cheng, Liu, and Yang, 2000, Ng. S, 1995, Yang, and Zhang, 2000, forthcoming), development economics (Yang, 1991, Sachs and Yang, 2001, Sachs, Yang, and Zhang, forthcoming, Yang and Shi, 1992, Shi and Yang, 1995), growth theory (Borland and Yang, 1995, Yang and Borland, 1991, Wen, 1997, Zhang, 1997), the theory of endogenous externality, public goods, and endogenous transaction costs (Chu, 1997, Chu and Wang, 1998, Lio, 1997, 1998, Y-K. Ng and S. Ng 2001a, b, Yang, 2000a, Yang and Yeh, forthcoming, Fang and Zhu, 1999, Ng and Yang, 2000, Yang and Zhao, 2000, Liu and Yang, 2001), the theory of the firm and contract (Yang and Ng, 1995, Liu and Yang, 2000, Yang and Yeh, forthcoming, Yang 2000b, Sun, 2000), the economics of transaction costs (Yang, 1991, 1996, Lio, 1996, 1998), the economics of property rights (Yang and Wills, 1990, Lio, 1998), the economics of e-business and internet (K. Li, 2001), the economics of state (K. Li, 2001 and Liu and Yang, 2001), monetary theory (Cheng, 1998, 1999, Yang and Ng, 1993), theory of capital and investment (Yang, 1999, Yang and Borland, 1991, Wen, 1997), theory of urbanization (Yang and Rice, 1994, Sun and Yang, 2000), theory of industrialization (Shi and Yang, 1995, and Sun and Lio, 1996), theory of business cycles (Yang and Ng, 1993 ch. 18, Du, forthcoming), theory of insurance (Lio, 1998), theory of bounded rationality (Ng and Yang, 1997, Zhao, 1999, Yang and Yao, 2001), and theory of hierarchy (Shi and Yang, 1998, Yang, 2001, ch.20).
Yang and K. Ng (1993), Yang and S. Ng (1998), Yang (2001), and Sachs and Yang (2001) provide reviews of this literature. In the late 1990s, several pure theory papers (Sun, Yang, and Zhou, 1998, Sun, Yang, and Yao, 1999, and Sun, 1999) have established the existence theorems, the first welfare theorem, and core and equilibrium equivalent theorem for a general class of general equilibrium models with impersonal networking decisions and endogenous structure of division of labor. The papers use weighted digraphs to describe a network of division of labor and resource allocation. They show that the general increasing returns are network effects of division of labor, which may exist in the absence of economies of scale of a firm. The network effects are caused by impersonal networking decisions which are compatible with the competitive market. The most important function of the market is to coordinate individuals' impersonal networking decisions and to utilize network effects of division of labor.
With this sound theoretical foundation, Liu and Yang (2000), Murakami, Liu, Otsuka (1996), and Zhang (2000, 2001), Dasgupta (1995), North (1985) and Yang, Wang, and Wills (1992) have provided empirical evidence to support the theories developed in the literature of inframarginal economics.
A related literature of endogenous transaction cost has been developed since the 1980s. The review of this literature can be found from Hart (1995), Hart and Moore (1990), Hart and Holmstrom (1987), Milgrom and Roberts (1992), and Holmstrom and Milgrom (1995). The intersection between this literature of endogenous transaction costs and the literature of endogenous specialization is one of the most active areas in modern economics.
Two international symposia on inframarginal economics were held in 1995 and 2001, respectively. A website www.inframarginal.com was established in 1997. A platform has been established to make this website very active in facilitating research, teaching, thesis supervision, book writing, and timely exchange of research findings, teaching experience, and information on conferences, seminars, publications, journals, and workshops. A publication plan of a series of textbooks on inframarginal economics, a series of research books, and reading guide is implemented. A series of workshops will be developed at the USA, Australia, China, and Taiwan. The workshop program in the USA was initiated and is managed by Nobel Laureate James Buchanan. The best Ph.D. students from the leading universities in the USA are admitted. Their transportation and accommodation will be paid by the organizer. Society of Inframarginal Economics will be established before the end of 2001.