IDEAS home Printed from
   My bibliography  Save this paper

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.

Suggested Citation

  • Nicholas Economides & Charles Himmelberg, 1995. "Critical Mass and Network Size with Application to the US Fax Market," Working Papers 95-11, New York University, Leonard N. Stern School of Business, Department of Economics.
  • Handle: RePEc:ste:nystbu:95-11

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Nicholas Economides, 1997. "The Economics of Networks," Brazilian Electronic Journal of Economics, Department of Economics, Universidade Federal de Pernambuco, vol. 1(0), December.
    2. Cabral, Luis M. B., 1990. "On the adoption of innovations with 'network' externalities," Mathematical Social Sciences, Elsevier, vol. 19(3), pages 299-308, June.
    3. Economides, Nicholas, 1996. "Network externalities, complementarities, and invitations to enter," European Journal of Political Economy, Elsevier, vol. 12(2), pages 211-233, September.
    4. Economides, Nicholas & White, Lawrence J., 1994. "Networks and compatibility: Implications for antitrust," European Economic Review, Elsevier, vol. 38(3-4), pages 651-662, April.
    5. 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.
    6. Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-440, June.
    7. Peter Howitt & R. Preston McAfee, 1988. "Stability of Equilibria with Externalities," The Quarterly Journal of Economics, Oxford University Press, vol. 103(2), pages 261-277.
    8. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item


    networks; critical mass; fax; externalities;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • D4 - Microeconomics - - Market Structure, Pricing, and Design


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ste:nystbu:95-11. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Viveca Licata). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.