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Critical Mass and Network Size with Application to the US Fax Market

  • Nicholas Economides
  • Charles Himmelberg

We analyze the equilibrium size of networks under alternative market structures. Networks are characterized by positive size externalities (commonly called "network externalities"). That is, the benefits of the addition of an extra node (or an extra customer) exceed the private benefits accruing to the particular node (or customer). A direct consequence of this demand structure is that perfect competition does not implement the optimal outcome. Because of the externality, there exists a range of prices within which three different network sizes can be supported as equilibria: a zero size network, an intermediate size that is unstable, and a large stable and Pareto optimal one. We expect that the market will select the largest of the three equilibrium networks. As a result, small networks will not observed. We call critical mass the size of the smallest network that can be supported in equilibrium. Alternative allocation systems internalize the network externality to different degrees, and therefore result in a variety of sizes of critical masses and price-network size paths. A welfare-maximizing planner supports a larger network than results in perfect competition. Surprisingly, a monopolist, even if allowed to influence consumers' expectations, always chooses a network of smaller size than in perfect competition. Oligopolists of compatible network goods support networks of smaller size than perfect competition and larger than monopoly. We extend our results to durable goods in a dynamic setting. In the presence of a downward time trend for industry marginal cost, the presence of network externalities increases the speed at which market demand grows. We use this prediction to calibrate the model and obtain estimates of the parameter measuring a consumer's valuation of the installed base (i.e., the network effect) using aggregate time series data on prices and quantities in the US fax market.

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File URL: http://raven.stern.nyu.edu/networks/95-11.pdf
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Paper provided by New York University, Leonard N. Stern School of Business, Department of Economics in its series Working Papers with number 95-11.

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Date of creation: Aug 1995
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Handle: RePEc:ste:nystbu:95-11
Contact details of provider: Postal: New York University, Leonard N. Stern School of Business, Department of Economics, 44 West 4th Street, New York, NY 10012-1126
Phone: (212) 998-0860
Fax: (212) 995-4218
Web page: http://w4.stern.nyu.edu/economics/

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  1. Cabral, Luis M. B., 1990. "On the adoption of innovations with 'network' externalities," Mathematical Social Sciences, Elsevier, vol. 19(3), pages 299-308, June.
  2. Joseph Farrell & Garth Saloner, 1984. "Standardization, Compatibility and Innovation," Working papers 345, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-40, June.
  4. Nicholas Economides, 1995. "The Economics of Networks," Working Papers 94-24, New York University, Leonard N. Stern School of Business, Department of Economics, revised Sep 1995.
  5. Howitt, Peter & McAfee, R Preston, 1988. "Stability of Equilibria with Externalities," The Quarterly Journal of Economics, MIT Press, vol. 103(2), pages 261-77, May.
  6. Nicholas Economides, 1997. "Network Externalities, Complementarities, and Invitations to Enter," Industrial Organization 9701004, EconWPA.
  7. Jeffrey Rohlfs, 1974. "A Theory of Interdependent Demand for a Communications Service," Bell Journal of Economics, The RAND Corporation, vol. 5(1), pages 16-37, Spring.
  8. Nicholas Economides & Fredrick Flyer, 1995. "Technical Standards Coalitions for Network Goods," Working Papers 95-12, New York University, Leonard N. Stern School of Business, Department of Economics.
  9. Economides, Nicholas & White, Lawrence J., 1994. "Networks and compatibility: Implications for antitrust," European Economic Review, Elsevier, vol. 38(3-4), pages 651-662, April.
  10. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
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