Survey of E-Commerce Research

Inframarginal Versus Marginal Analysis of Networking Decisions and e-Commerce

Yew-Kwang Ng

Department of Economics, Monash University,
Victoria, Australia 3800.

Email: Kwang.ng@buseco.monash.edu.au

For The International Symposium of e-Commerce and Networking Decisions,
Monash University, 6-7 July 2001.

I. What is the Connection Between E-commerce and Inframarginal Analysis of Networking Decisions?

Many participants of this International Symposium of the Economics of e-Commerce and Networking Decisions may wonder what is the economics of e-commerce and networking decisions. Having had a look of the preliminary program of the symposium, you may wonder what is inframarginal analysis and what is the relationship between inframarginal analysis and e-commerce? Some of the participants may think that this is a strange combination of two separate fields: very business-oriented discussion on real e-commerce and very academic economic analysis of networking decisions. Some may even think that this is a tricky way to sell boring economics by bundling it with the e-commerce stuff, which is interesting to many business economists. This speech is devoted to address this concern and to provide motivation for this symposium.

I know that many faculty members in business schools and in departments of marketing, accounting, management, and other business-oriented fields do not like, if not actually hate economics. Not only it is claimed by many non-economics faculty members that economics is quite irrelevant to real businesses and many businessmen can do very well without it, but also departments of economics are losing students and high profile faculty members to business schools. As myself an economist, it is an overstatement to say that I am sympathetic to this view. However, as social scientists, perhaps we should ask, do they have some good reasons to feel this way? Is our economics missing something important in the business world? My outline of inframarginal analysis may throw some lights in answering this question. More ambitiously, the incorporation of the inframarginal analysis of networking decisions may make economics more relevant to the real world. (Even before this extension, economic analysis has much relevancy and is very important for practitioners in the business areas; see

Real business decisions can be categorized in two classes: marginal decisions of resource allocation and inframarginal networking decisions. 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 (usually zero), the optimal decision is a corner solution. Formally, it relates to nonlinear programming, mixed integer programming, dynamic programming, the control theory, and other non-classical mathematical programming. In many cases, the inframarginal networking decision is much more important than the marginal decision. But since the marginal revolution, economists have focused their attention on the marginal analysis of resource allocation. The following example illustrates why the inframarginal decision might be more important than the marginal decision.

The first decision that a student has to make when she gets in the university is to choose a major. If she chooses economics as her major, then she does not go to classes of chemistry and physics, but she takes 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 the student shifts between majors. After she has chosen a major, she allocates her 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 labour in society.

The core of classical mainstream economics represented by William Petty and Adam Smith was about the development implications of division of labour. Although classical economists did not use the term of network effects, Smith did appreciate the nature of network effects of benefits of division of labour and specialization. He argued that the division of labour is limited by the extent of the market. In terms of modern economics, this Smith theorem implies that individuals' decisions to choose their levels of specialization are determined by the benefits of division of labour, which are dependent on the number of participants in the network of division of labour (the extent of the market). Allyn Young (1928) spelt this out in the Young theorem that not only is the division of labour dependent upon the extent of the market, but the extent of the market is also dependent on the level of division of labour. This circular causation is a common feature of network effects, just like the circular causation that the use value of a telephone set is dependent on the number of telephone sets in use, and also the number of telephone sets in use is dependent on the use value of each telephone set.

But when Alfred Marshall formalized neoclassical economics within a mathematical framework at the end of the 19th century, he assumed the dichotomy between pure consumers' decisions and firms' decisions to avoid the inframarginal analysis of corner solutions. Within the neoclassical framework, each pure consumer buys all goods from the market and does not choose her level of self-sufficiency or its reciprocal: the level of specialization, which determines the size of her trade network. Hence, the focus of economics shifted from the inframarginal analysis of specialization and trade networking decisions to the marginal analysis of resource allocation for a given network size. By following this neoclassical framework, neoclassical development economics departs from the then mainstream classical economics. Hence, the inframarginal analysis of networking decisions lost the central position that it occupied in the classical mainstream economics.

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, the implications of formal inframarginal analysis of networking decisions could not be fully explored until the late 1970s. A literature of inframarginal analysis of impersonal networking decisions emerged at the end of the 1970s and the 1980s. It has been rapidly growing since the 1990s. This literature shows that if a Smithian framework without the dichotomy between pure consumers and firms is adopted, the interior solution is never optimal and a corner solution is the rule rather than an exception. Hence, marginal analysis is not enough and inframarginal analysis is essential for investigating networking decisions.

This literature not only resurrects the spirit of the classical mainstream economics in a modern body of inframarginal analysis, but also provides a new framework for the study of networking decisions. Hence it creates an opportunity to bring the study of networking decisions back to the core of modern mainstream economics. As is well known, e-commerce and the internet are characterized by networking decisions and network effects. The new literature of inframarginal analysis of networking decisions provides a powerful analytical instrument for the study of economics of e-commerce and the internet.

II. Inframarginal Analysis Versus Marginal Analysis and Strategic Versus Impersonal Networking Decisions

There are at least two types of reactions from economists to many new e-commerce phenomena. One of them is represented by Shapiro & Varian (1999). They have noted that, confronted by the New Economy, many instinctively react by searching for a corresponding New Economics to guide their business decisions. Executives charged with rolling out cutting-edge software products or on-line versions of their magazines are tempted to abandon the classic lessons of economics, and rely instead on an ever-changing roster of trends, buzzwords, and analogies that promise to guide strategy in the information age. Not so fast, say Carl Shapiro and Hal Varian. In their book, they warn managers, "Ignore basic economic principles at your own risk. Technology changes. Economic laws do not." According to this line of thinking, reinterpretation and application of marginal analysis in information economics to e-commerce phenomena is all we need. On the other hand, economists who contribute to the literature of inframarginal analysis of networking decisions disagree. According to them marginal analysis works only for problems of resource allocation for a given pattern of network and it is not enough for the analysis of networking decisions. Inframarginal analysis (total cost-benefit analysis across network patterns in addition to marginal analysis of resource allocation for a given pattern of network) is essential for networking decisions. I am an eclectic. I believe that traditional economics is still relevant for the new economy, but the power of economic analysis can be tremendously increased by complementing traditional economics with the inframarginal analysis of the network of division of labour.

A most important difference between the traditional marginal analysis of resource allocation and the inframarginal analysis of division of labour and networking decisions is that the former takes the network of economic organizations or the degree of division of labour of the economy as given. For example, the discussion of the benefits of e-commerce (e.g., Bakos 2001, Borenstein & Saloner 2001) focuses on the benefits to consumers and producers due to the lower search costs and the likely higher degree of competition. I am not aware of any discussion of the lower transaction costs leading to a higher degree of division of labour and the resulting economies of specialization. It may be thought that we are already in a fully specialized economy with virtually everyone having only one job or selling only one product. However, even in our era of high specialization, there is still much scope for increasing the degree of the division of labour. For one thing, things done at home are still being increasingly replaced by those done through the market, e.g. take-away food and dining out, specialized carpet cleaning and gardening. Secondly, further specialization can take place at the level of input usage by producers with the use of more specialized inputs and more roundabout methods of production. Thirdly, with lower market transaction costs, specialization between firms may replace specialization within a firm. This is especially characteristic of the small and medium-sized firms in Taiwan which may specialize in producing a certain input or a particular process, including the final assembly of a product. Thus, the development of e-commerce made possible by the internet could lead to a much higher degree of division of labour and provide benefits through the economies of specialization. This benefit is better analyzed by inframarginal analysis.
Let me use two examples to illustrate the usefulness of inframarginal analysis of the network of division of labour. The first is a common phenomenon in e-commerce: implicit bundling sale. An extensive literature of marginal analysis of bundling and tying sale (Bursten 1960, Stigler 1963, Adams & Yellen 1976, Schmalensee 1984, McAfee, McMillan & Whinston 1989, Whinston 1990, Hanson & Martin 1990, Varian, 1995, 1997, and Bakos & Brynjolfsson, 1999a, 1999b) has been developed. This literature focuses on bundling and tying that is associated with monopoly power. The following assumptions are made in this literature. Each consumer consumes at most one unit of a good and has a constant valuation of this one unit of good. Resale of a good is not allowed. In addition, different prices cannot be directly charged for individuals with different valuations because of un-observability of such valuations. These assumptions imply that utility is not specified as a function of amounts of all consumption goods and that no marginal substitution between goods is allowed (so-called independent valuations). Hence, interesting interactions and feedback loops between consumption quantities, prices, income, production decisions, and substitution between goods, which are the focus of a standard general equilibrium analysis, are not investigated in this literature. With the quite special assumptions, it is easy to see that bundling can impose indirect price discrimination under a uniform price of a bundle of goods even if no monopoly power exists. Bakos and Brynjolfsson (1999a, b) have nicely presented the intuition about this function of bundling.

As reviewers of some papers in the literature point out, many internet and e-commerce phenomena are inconsistent with the particular assumptions made in this literature. For instance, there are more than a thousand of email or search engine providers and each of them bundles their services. Some of the services are charged positive prices and others are provided free of charge. Also, resale of such services is possible, quantities of such services can be any integer numbers (for instance each person may get several email accounts from each of several providers), and substitution between services are not trivial (that is, a consumer's valuation of a service is not a constant, or a consumer's utility is a function of quantities of such services and other goods).

Bakos and Brynjolfsson, (1999b, p. 3) defend their position by arguing that bundling sale with zero prices of some services is a phenomenon of disequilibrium. I disagree. A good of zero price implicitly bundled with goods of positive prices can be a general equilibrium phenomenon. A conventional market for petrol and air pump services may illustrate the point. There are many petrol stations which sell petrol at a competitive price and provide air pump services free of charge. This market structure has been in place for a long time. The bundling of petrol and air pump services must be a general equilibrium phenomenon. In this market, all consumers' preferences for petrol and air pump service might be very similar, so that the rationale for the type of bundling in the existing literature is irrelevant. The intuition for this phenomenon is quite straightforward. Pricing of air pump services and collection of related payment involves transaction cost to consumers as well as to petrol stations (waiting time, inconvenience, and tangible resource cost for pricing and payment collection). If the production cost of such services can be added to the price of petrol which is complementary to air pump services, then such transaction cost can be avoided. Bundling sale may incur endogenous transaction costs which are the distortions caused by individuals who use air pump services but do not buy petrol from the same petrol station. But as long as reduction of exogenous transaction costs of pricing process of air pump services outweighs the increase in endogenous transaction cost, a competitive market will generate pressure to compel all petrol stations to implement such a bundling price structure. We call this phenomenon implicit bundling. Implicit bundling is closer to mixed bundling than pure bundling investigated in the existing literature. Other implicit bundling cases include TV programs (TV shows are free of charge and associated advertisements are paid at positive prices by companies selling goods to viewers of TV programs) and an automobile company's marketing operation with positive prices of cars and free internet purchase services. (Suspect significant difference, the TV case is more the case of a marketing good.) Here, the key point is that competition pressure and prohibitively high pricing cost of some goods are essential for zero prices of goods bundled with goods of positive prices. Therefore, we need a model without monopoly power and with transaction costs and competitive (implicit) bundling. Using the Yang-Ng's (1993) framework of inframarginal analysis, Li (2001) has formalized this story.

He tells the story by formulating the trade-off between positive network effects of division of labour on aggregate productivity and transaction costs. As suggested by Allyn Young (1928), network effect is a notion of general equilibrium. Not only the network size of division of labour depends on the extent of the market (the number of participants in the network of division of labour), but also the number of participants is determined by all individuals' participation decisions in the network of division of labour, which relate to their decisions of their levels of specialization. This circular causation, noted by Young, is of course an essential feature of general equilibrium, analogous to the circular causation between quantities and prices in the general equilibrium (each individual's quantities demanded and supplied depend on prices, while the equilibrium prices are determined by all individuals' decisions of quantities). Hence, marginal analysis of a partial equilibrium model, such as those in the existing literature of bundling, does not work for our task.

Moreover, since we need an assumption of competitive market for investigating network effects of division of labour, we are not confined to the strategic networking decision associated with monopoly power. We need a general equilibrium model of impersonal networking decisions to investigate infinite feedback loops between network size of division of labour, each person's participation decision, prices, quantities, and different markets. Yang (2001) and Sun, Yang, and Yao (1999) have drawn the distinction between the strategic networking decision and the impersonal networking decision. For the latter, each decision maker is not concerned with whom she has a trade connection to. She is concerned with how many goods she will trade and how many she will self-provide. Her decision in choosing the number of types of traded partners determines her trade network size and pattern. Impersonal networking decisions take place in a market where no body can manipulate prices, so that implicit bundling with zero prices of some goods may emerge from competitive pressure and free entry. Such impersonal networking decisions generate network effects of division of labour that are not network externalities since we assume that each individual is capable of conducting inframarginal analysis (total cost-benefit analysis across corner solutions) in addition to marginal analysis of each corner solution. Inframarginal analysis means that each individual is capable of not only choosing locally optimal resource allocation for a given trade network pattern using standard marginal analysis, but also choosing a globally optimal trade network pattern by comparing several locally optimal values. Formally, inframarginal analysis is non-linear programming. Coase (1946, 1960), Buchanan and Stubblebine (1962), and Yang (2001) have shown that a lot of so-called network externalities can be internalized by individuals' inframarginal decisions. They are considered externalities by many economists since these economists effectively assume that individuals are incapable of doing inframarginal analysis and/or do not make the relevant inframarginal choices/changes. Many contributors to the literature of inframarginal analysis of network effects of division of labour and impersonal networking decisions (see surveys of this literature by Yang and S. Ng, 1998 and by Yang, 2001, and references therein) have shown that marginal cost pricing does not work when individuals conduct inframarginal analysis. Hence, non-marginal cost pricing is compatible with a competitive market with localized increasing returns and impersonal networking decisions.

Intuitively, Li's story can be told as follows. Suppose that an automobile manufacturer, such as General Motor, sells automobiles and internet services for purchasing cars online. Automobiles are tangible goods which are easy to price, but internet services are intangible, very difficult to price. General Motor can bundle two goods together by providing free internet services and by adding the operation cost of internet services to the price of automobiles. If such bundling can save consumers' transaction costs incurred in a purchase deal in excess of the added cost to the price of automobiles, General Motor will have a competitive edge compared to other automobile manufacturers who do not provide such bundled deal. Then a competitive pressure in the market will force all manufacturers to provide such bundled deal. Here, monopoly power, constant and independent valuations of one unit of good, non-resale, and other peculiar assumptions are not needed. In addition, even if all individuals have ex ante identical utility function which allows substitution between goods, productivity gains from bundling may be generated by network effects of division of labour. Without bundling, involvement of the good with prohibitively high transaction cost coefficient in a high level of division of labour and avoidance of direct pricing cost of such a good cannot coexist. Hence, positive network effects of division of labour on aggregate productivity cannot be fully exploited. With the bundling, both of the tasks can be achieved at the same time. Therefore, the network effects can be fully exploited and aggregate productivity can be promoted by the bundling. It is interesting to see that bundling in a competitive market has very important productivity implications even if all individuals have ex ante identical utility and production functions and substitution between different goods are non-trivial.

The inframarginal analysis of impersonal networking decision can also be extended to explain the unusually high P/E ratio of many e-commerce companies. If positive network effects of e-commerce can be created by founding of many e-commerce companies, but services provided by these companies are not easy to directly price, then the merger of e-commerce companies and other companies which sell tangible goods can indirectly price intangible e-commerce services via implicit bundling in e-commerce. The story about bundling between automobiles and internet purchase services is an example. Other examples include the merger of the AOL and Warner Brothers, which bundles intangible services of the AOL with tangible goods provided by Warner Brothers, and Amazon.com which bundles intangible e-commerce with tangible hard copies of books. Hence, some e-commerce companies can have unusually high P/E ratio since the market expects that such companies may be merged or bought by other companies selling tangible goods at quite high share prices if they really create significant network effects of division of labour. This phenomenon is difficult to explain using marginal analysis in the existing literature of bundling and tying sale.

Another e-commerce phenomenon that cannot be predicted by neoclassical marginal analysis is that the risk of coordination failure of network of division of labour and income share of transaction costs increase as the new technology of internet significantly improves the reliability of each transaction and reduces the cost of each transaction. This phenomenon is noted by Autor (2001) and Barber and Odean (2001). But they cannot find an appropriate analytical instrument to explain it. As Shapiro and Varian (1999) suggest, they rely on an ever-changing roster of trends, buzzwords, and analogies to verbally describe such a phenomenon. However, Shapiro and Varian's marginal analysis cannot help them either. As shown by Yang and Ng (1993) and Yang (2001), marginal analysis even does not work for explaining many impersonal networking decisions in conventional market and cannot formalize classical mainstream economics, which focused on network effects of division of labour. The marginal analysis is even less suitable for handling e-commerce phenomena. Hence, our conference focuses on theories and applications of inframarginal analysis of impersonal networking decisions. This distinguishes our symposium from the Symposium of E-Commerce at the USA (see Borensten and Saloner, 2001, Goolsbee, 2001, Autor, 2001, Barber and Odean, 2001, and Bakos, 2001). That symposium is characterized by verbal description and marginal analysis of partial equilibrium. Lio (1998) and Yang and Wills (1990) have developed several models of impersonal networking decisions. Inframarginal analysis in these models predicts the above e-commerce phenomenon. Their models specify the trade-offs among positive network effects of division of labour on aggregate productivity, coordination reliability of the network of division of labour, exogenous transaction costs in specifying property rights, and endogenous transaction costs caused by imprecise specification and enforcement of property rights. As a communication or transaction cost coefficient is reduced by new internet technology, the scope for trading off economies of division of labour against transaction costs is enlarged, so that the equilibrium network size of division of labour increases. However, this expansion of network of interdependent specialists will increase the length of a series connection of many professional occupations. If there is a transaction risk for each trade connection, the aggregate risk of coordination failure of the trade network will increase exponentially with the number of connections. Thus, the aggregate risk of coordination failure may increase as a result of a decrease in the risk of coordination failure of each trade connection. However, as long as positive network effects of division of labour outweigh negative network effects of increasing risk of coordination failure, the network size of division of labour and aggregate risk of coordination failure may increase side by side. Also, the income share of transaction costs may increase as a result of the expansion of network of division of labour, driven by improvements in communication efficiency. Many other e-commerce phenomena can be much better explained by inframarginal analysis than by marginal analysis.

More generally, all information about inframarginal decisions (or about whether any pair of players are connected) is associated with so-called "topological properties of an organism," which can be represented by a graph consisting of vertices (or nodes, points) and edges (or lines, curves). All information about marginal decisions of resource allocation relates to quantities of goods which is a non-topological property of an organism and can be represented by weights attached to edges of the graph. Hence, a weighted digraph can describe the topological as well as non-topological properties of an economic organism. Marginal analysis focuses on the non-topological properties of economic organisms, while inframarginal analysis focuses on the topological properties of economic organisms. The networking decision, which is essential for e-commerce, is an inframarginal decision.

Hence, it will be an exciting experience to learn inframarginal analysis from many sessions in this conference. Many papers presented in this conference will show you that the implications of the inframarginal revolution for the studies of e-commerce and beyond.

Borenstein & Saloner (2001, p.6) may be right that the "key impediments to capturing the cost savings of e-commerce and the Internet will probably not involve technical issues, but rather inertial forces". Similarly, it is inertia that allows academic journals to continue requiring the costly submissions of many single-sided, double-spaced hard copies of papers for publication rather than allowing electronic submissions (Ng 2001). So, wake up and do something!

References

Adams,W. J. and Yellen, J. L. (1976), "Commodity Bundling and the Burden of Monopoly", Quarterly Journal of Economics, 90 (3): 475-498.
Arrow, K., Y-K. Ng, and X. Yang eds. (1998): Increasing Returns and Economic Analysis, London, Macmillan.
Autor, D. (2001), "Wiring the Labour Market," Journal of Economic Perspectives, 15, 25-40.
Bakos, Y. (2001) "The Emerging Landscape for Retail E-commerce", Journal of Economic Perspectives, 15, 69-80.
Bakos, Y., Brynjolfsson, E. (1999a), " Bundling Information Goods: Pricing, Profits and Efficiency", Management Science, 45, 12.
Bakos, Y., Brynjolfsson, E. (1999b), "Bundling and Competition on the Internet", Working Paper, Stern School of Business, New York University.
Barber, B. and Odean, T. (2001), "The Internet and the Investor," Journal of Economic Perspectives, 15, 41-54.
Borenstain, S. and Saloner, G. (2001), "Economics and Electronic Commerce," Journal of Economic Perspectives, 15, 3-12.
Buchanan, J. and Stubblebine, W. (1962), "Externality," Economica, 29, 371-84.
Burstein, M. L. (1960), "The Economics, of Tie-In Sales." The Review of Economics and Statistics, 42, 68-73.
Coase, R. (1946), "The Marginal Cost Controversy," Economica, 13, 169-82.
Coase, R. (1960), "The Problem of Social Cost," Journal of Law and Economics, 3, 1-44.
Goolsbee, A. (2001), "The Implications of Electronic Commerce for Fiscal Policy (and Vice Versa)." Journal of Economic Perspectives, 15, 13-24.
Hanson, W., Martin, R. K. (1990), "Optimal Bundling Pricing", Management Science, 36(2): 155-74.
Li, K. (2001), "A General Equilibrium Analysis of the Division of Labour: Violation and Enforcement of Property Rights, Impersonal Networking Decisions and Bundling Sale." Ph.D. Dissertation, Department of Economics, Monash University.
Lio, M. (1998), "Uncertainty, Insurance, and Division of Labor," Review of Development Economics, 2, 76-86.
McAfee, R. P., McMillan, J., Whinston, M. D. (1989), "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values", Quarterly Journal of Economics, 104: 371-83.
Ng, Y-K. (2001), "Paper Submission in the Electronic Age", Newsletter of Royal Economic Society (UK), July.
Petty, William (1671), Political Arithmetics, in C. H. Hull ed. Economic Writings of Sir. William Petty, reissued, New York, Augustus M. Kelly, 1963.
Petty, William (1683), Another Essay on Political Arithmetics, in C. H. Hull ed. Economic Writings of Sir. William Petty, reissued, New York, Augustus M. Kelly, 1963.
Schmalensee, R. (1984), "Gaussian Demand and Commodity Bundling", Journal of Business, 57(1): s211-230, part 2.
Shapiro, C. and Varian, H.R. (1999), Information Rules A Strategic Guide to the Network Economy, Boston, Mass. : Harvard Business School Press.
Smith, Adam (1776): An Inquiry into the Nature and Causes of the Wealth of Nations. Reprint, edited by E. Cannan. Chicago: University of Chicago Press, 1976.
Stigler, G. (1963), "United States v. Leow's Inc.: a note on block booking", Supreme Court Review, 152-157.
Sun, G., Yang, X. and Yao, S. (1999): "Theoretical Foundation of Economic Development Based on Networking Decisions in the Competitive Market", Harvard Center for International Development Working Paper No. 17.
Varian, H. L. (1995), "Pricing Information Goods", in: Proceedings of Scholarship in the New Information Environment Symposium, Harvard Law School.
Varian, H. L. (1997), "Versioning Information Goods", http://www.sims.berkeley.edu/ ~hal/pages/ sciam.html, 25/3/99
Whinston, Michael (1990), "Tying, Foreclosure, and Exclusion." American Economic Review. 80 (4), 837-59.
Yang, X. (2001), Economics: New Classical versus Neoclassical Framework, Oxford: Blackwell.
Yang, X. and Ng, Y-K. (1993): Specialization and Economic Organization, a New Classical Microeconomic Framework, Amsterdam, North-Holland.
Yang, X. and Ng, S. (1998), "Specialization and Division of Labor: a Survey," in Arrow, Ng, and Yang.
Yang, X. and Wills, I. (1990): "A Model Formalizing the Theory of Property Rights". Journal of Comparative Economics, 14: 177-98.
Young, Allyn (1928): "Increasing Returns and Economic Progress", The Economic Journal, 152: 527 542.

Some Articles about Inframarginal Economics and E-Commerce:

1. Ke Li & Xiaokai Yang, A General Equilibrium Model with Impersonal Networking Decisions and Bundling Sales. (Application Theory, E-commerce)
2. Dingsheng Zhang, He-Ling Shi & Xiaokai Yang, "A General Equilibrium Model of e-Commerce with Impersonal Networking Decisions".
3. Chu, Chih-Ning & Chou, Jerome, "A Criterion from the General Equilibrium Model on Providing an Open or a Closed Source Software".
4. Heling Shi & Hayden Mathysen, "E-commerce, transaction cost, and the network of division of labour: a business perspective".

Inframarginal Economics Society www.inframarginal.com