A General Equilibrium Model of e-Commerce with Impersonal Networking Decisions

Heling Shi
Department of Economics, Monash University
Xiaokai Yang
Department of Economics, Monash University
Dingsheng Zhang
Department of Economics, Monash University
Institute for Advanced Economic Studies, Wuhan University

Abstract
The paper develops a general equilibrium model of impersonal networking decisions and bundling sale. It departures from the other models of bundling and tying sale by allowing substitution between goods, flexible quantities of goods, resale of any goods, competitive market, and ex ante identical utility function for all individuals. Hence, interactions and feedback loops among quantities, prices, network effects of division of labor, transaction costs, self-interested decisions, income, and productivity can be investigated. Inframarginal analysis (total cost-benefit analysis across corner solutions in addition to marginal analysis of each corner solution) of the model shows that the function of bundling sales in a competitive market is to get intangible information goods involved in the division of labor and commercialised production, meanwhile avoiding direct pricing of such goods, thereby promoting division of labor and aggregate productivity. One policy implication from this model is that antitrust prosecution should pay more attention to the intention of blocking free entry rather than bundling itself.
JEL code: L10, D50

Introduction
As was reported recently, Amazon.com, the world¡¦s biggest on-line book seller, has finally made a profit after burning nearly $US3 billion since it set up as an on-line book superstore in 1997. The shares soared 22 per cent in a day to $US12.61 on 23 January 2002. This gave Amazon.com the market capital value of $US2.15 billion, 233 times of this year¡¦s expected cash flows. Ironically, the current better-than-expected financial results are mainly coming from the effective integration of the ¡§New Economy¡¨ and ¡§Old Economy¡¨ by utilizing the free on-line catalogue and other promotional strategies (New Economy component) to sell books, toys, games, health and beauty products, kitchen gadgets and even a baby registry (Old Economy component).

The Amazon.com case revealed several special features normally associated with electronic commerce (e-commerce), namely, emergence or elimination of intermediation, tying sales which bundle several products in various combinations, increased share of income in the information and communication technology (ICT) industry, and higher risk and uncertainty in the ICT industry and other industries that relay on ICT. We believe the Amazon.com case represents a general trend rather than an exception. This paper tries to capture one of these special features, namely, bundling sale.

The purpose of the paper is to develop a general equilibrium model of e-commerce based on impersonal networking decisions and competitive market. We proceed this task in the following sequence. First we compare our task with the existing literature of bundling and tying sales. We then consider some common Internet phenomena which cannot be predicted and explained by the existing literature. Finally, we construct a model to investigate the effects of bundling sales on the network size of division of labor and their implications on productivity. Our main conclusions are that in a competitive market, (i) bundling is an institutional arrangement that is used to avoid direct pricing of goods with low trading efficiency, (ii) bundling is an effective way to exploit network effects of the division of labour, and (iii) bundling could achieve Pareto improvement, compared to non-bundling case. This study also casts doubt on the effectiveness of regulatory policy which targets bundling sales as a business conduct that might lessen competition in the market place.

An extensive literature has been developed to investigate the role of bundling and tying sales (Bursten, 1960, Stigler, 1963, Adams and Yellen, 1976, Schmalensee, 1984, McAfee, McMillan, and Whinston, 1989, Whinston, 1990, Hanson and Martin, 1990, Varian, 1995, 1997, and Bakos and Brynjolfsson, 1999a, b). This literature focuses on bundling and tying sale that is associated with monopoly power. The following assumptions are normally made in this literature. Each consumer consumes at most one unit of a good and has constant valuation of this one unit of good. Resale of a good is not allowed. In addition, differentiated prices cannot be directly charged for individuals with differentiated valuations of goods 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 substitution between goods is allowed (so-called independent valuations). Hence, 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 these specific assumptions, it is easy to see that bundling can impose indirect price discrimination even if competition among a few of producers is allowed. Bakos and Brynjolfsson (1999a, b) have nicely presented the intuition about this function of bundling.

In this literature, welfare effects of bundling are inconclusive. Adams and Yellen (1976) emphasize that adverse effects of bundling on welfare come from monopoly power rather than bundling itself. Bowman (1957). Blair and Kaserman (1978), Grimes (1994), Delong (1998), Chae (1992), Fishburn, Odlyzko and Siders (1997), Varian (1995), Chuang and Sirbu (1999), and Bakos and Brynjolfsson (1997, 1999) predict positive welfare effects of bundling. Matutes and Regibeau (1992), Tirole (1989), and Martin (1999) project adverse welfare effects of bundling sales. In addition, Whinston (1990) shows that welfare effects of tying in an oligopoly regime are ambiguous.

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 lots 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.

We believe that zero price of a good implicitly bundled with goods of positive prices can be a general equilibrium phenomenon. We use the following two stories to illustrate the intuition.

The first story is about the conventional petrol station market. There are many petrol stations which sell petrol at a competitive price and also provide air pump services free of charge. This market structure has been in place for long time. Therefore, the bundling of petrol and air pump services must be regarded as 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.i 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 other tangible resource cost for pricing and collecting payment). If the cost of providing 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 sales may generate endogenous transaction costs which are the distortions caused by individuals who might use air pump services but do not buy petrol from the same petrol station. But as long as the reduction of exogenous transaction costs of pricing air pump services outweighs the increase in endogenous transaction costs, a competitive market will generate pressure to compel all petrol stations to implement such a bundling price structure. We call this phenomenon implicit bundling which charges a positive price of a good and zero price of another good without an explicit bundle. Implicit bundling is closer to mixed bundling than pure bundling investigated in the existing literature.
This reasoning can be illustrated by another more e-commerce related story. Suppose that an automobile manufacturer, such as General Motor, sells automobiles and also provide on-line sale services. Automobiles are tangible goods which are easy to be priced, but on-line sale services are a sort of public good, very difficult to be priced. General Motor can bundle two goods together by providing free on-line services, meanwhile adding the cost of constructing and maintaining a website 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, the 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.

Please note that the emergence of bundling sale in our stories does not rely on ad hoc assumptions, such as, monopoly power, constant and independent valuations of one unit of good, non-resale, and others. In addition, even if all individuals have ex ante identical utility function which allows substitution between goods, productivity gains from bundling could 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. With bundling, both of these 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 therefore 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.

This paper will formalize these stories using a general equilibrium model with well specified ex ante identical utility and production functions for all individuals. We shall formulate the trade-off between positive network effects of division of labor 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 labor depends on the extent of the market (the number of participants in the network of division of labor), but also the number of participants is determined by all individuals¡¦ participation decisions in the network of division of labor, 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 fixed point theorem (each individual¡¦s quantities demanded and supplied depend on prices, while the equilibrium prices are determined by all individuals¡¦ decisions of quantities). Hence, a partial equilibrium model, such as those in the existing literature of bundling, does not work for our task.

Moreover, since we construct our model on the assumption of competitive market for investigating network effects of division of labor, we are not confined to the strategic networking decision which is 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 labor, 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 price of some goods may emerge from competitive pressure and free entry/exit.
It is worth noting that such impersonal networking decisions are not the commonly called network externalities in our framework, 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). Mathematically, inframarginal analysis means that each individual is capable of not only choosing locally optimum 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 optimum values of objective functions. 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 assume, implicitly, that individuals are incapable of doing inframarginal analysis. Many contributors to the literature of inframarginal analysis of network effects of division of labor and impersonal networking decision (see surveys of this literature by Yang and Ng, 1998 and by Yang, 2001, and references there) 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.

More specifically, we will specify a general equilibrium model with a continuum of ex ante identical consumer-producers who prefer diverse consumption and specialized production due to economies of specialization in the production of three goods. There is a trade-off between transaction costs and positive network effects of division of labor on aggregate productivity. Hence, if the transaction cost coefficient for a unit of goods traded is very large, the positive network effect is outweighed by transaction costs. Therefore, individuals choose autarky where market, institution of the firm, and bundling sale do not occur. As the transaction cost decreases, the general equilibrium discontinuously jumps to a higher level of division of labor. Markets emerge from the division of labor.

If the transaction cost for labour is smaller than that for goods, the institution of the firm and related labor markets emerge from the division of labor. Otherwise, the markets for goods will emerge to organize the division of labor in the absence of the institution of the firm and related labor markets. If the transaction cost coefficient for a particular good is extremely large and the equilibrium level of division of labor is sufficiently high, then this good will be implicitly bundled with other goods to avoid prohibitively high pricing cost; while getting this good involved in the large network size of division of labor and commercialised production.

Our model is similar to the model of Li and Yang (2001) with one notable revision. Li and Yang (2001) assumes that the bundling ratio between tangible goods that are priced and intangible services that are free of charge is chosen by the seller. This is inconsistent with common practice in e-commerce where it is the buyer rather than the seller who chooses bundling ratio subject to her resource endowment constraint. When a firm sells information goods via the Internet, the firm usually cannot choose bundling ratio of priced goods and free services. This feature makes the current model more relevant to e-commerce; while the Li-Yang model is more relevant to bundling sales like holiday packages.

This paper proceeds as follows. Section 2 is devoted to describe the model. Section 3 solves equilibrium and its comparative statics and reports main findings. The final section concludes the paper.

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