IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

Average shadow price and equilibrium price: A case study of tradable pollution permit markets

Listed author(s):
  • Liao, Chao-ning
  • Önal, Hayri
  • Chen, Ming-Hsiang
Registered author(s):

    Shadow prices indicate implicit values of limited resources at the margin and provide important information in decision making for resource management. In continuous economic models, shadow prices associated with demand-supply balance constraints represent consumers' willingness to pay and producers' marginal cost, hence they correspond to market equilibrium prices. As well known, however, marginal analysis fails in the case of discrete optimization, such as mixed integer programming. An alternative concept has been introduced in the literature to measure the value of an extra unit of a limited resource in such cases. This concept is based on average rather than marginal values, thus called the average shadow price, and interpreted in the same way as conventional shadow prices. Whether average shadow prices in a discrete economic model can serve as market equilibrium prices has not been addressed in the related literature. The present paper addresses this issue in an empirical setting. Using a tradable pollution permit market as an example, where firms' YES/NO type technology adoption decisions are represented by binary variables, we show that the average shadow price of tradable permits can be interpreted as the equilibrium price only when certain conditions related to the cost structure and emission levels hold. On the other hand, we show that an iterative procedure based on individual firms' cost minimizing behavior presents a better approach for finding a price that can eliminate or reduce the gap between demand and supply of permits in the market.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00391-3
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 196 (2009)
    Issue (Month): 3 (August)
    Pages: 1207-1213

    as
    in new window

    Handle: RePEc:eee:ejores:v:196:y:2009:i:3:p:1207-1213
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as
    in new window


    1. O'Neill, Richard P. & Sotkiewicz, Paul M. & Hobbs, Benjamin F. & Rothkopf, Michael H. & Stewart, William R., 2005. "Efficient market-clearing prices in markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 269-285, July.
    2. Montgomery, W. David, 1972. "Markets in licenses and efficient pollution control programs," Journal of Economic Theory, Elsevier, vol. 5(3), pages 395-418, December.
    3. John H. Duloy & Roger D. Norton, 1975. "Prices and Incomes in Linear Programming Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 57(4), pages 591-600.
    4. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.
    5. Bruce A. McCarl & Thomas H. Spreen, 1980. "Price Endogenous Mathematical Programming As a Tool for Sector Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 62(1), pages 87-102.
    6. Atkinson, Scott E. & Lewis, Donald H., 1974. "A cost-effectiveness analysis of alternative air quality control strategies," Journal of Environmental Economics and Management, Elsevier, vol. 1(3), pages 237-250, November.
    7. Crema, Alejandro, 1995. "Average shadow price in a mixed integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 625-635, September.
    8. Crema, Alejandro, 1999. "An algorithm to perform a complete right-hand-side parametrical analysis for a 0-1-integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 114(3), pages 569-579, May.
    9. Crema, Alejandro, 1997. "A contraction algorithm for the multiparametric integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 130-139, August.
    10. Scott Lee Johnson & David M. Pekelney, 1996. "Economic Assessment of the Regional Clean Air Incentives Market: A New Emissions Trading Program for Los Angeles," Land Economics, University of Wisconsin Press, vol. 72(3), pages 277-297.
    11. Mukherjee, Saral & Chatterjee, A.K., 2006. "The average shadow price for MILPs with integral resource availability and its relationship to the marginal unit shadow price," European Journal of Operational Research, Elsevier, vol. 169(1), pages 53-64, February.
    12. Kim, Sehun & Cho, Seong-cheol, 1988. "A shadow price in integer programming for management decision," European Journal of Operational Research, Elsevier, vol. 37(3), pages 328-335, December.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:196:y:2009:i:3:p:1207-1213. 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: (Dana Niculescu)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.