(Translated by https://www.hiragana.jp/)
Pricing and waiting time decisions in a health care market with private and public provision
IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/100996.html
   My bibliography  Save this paper

Pricing and waiting time decisions in a health care market with private and public provision

Author

Listed:
  • Alves, Vasco

Abstract

This paper describes a duopoly market for healthcare where one of the two providers is publicly owned and charges a price of zero, while the other sets a price so as to maximize its profit. Both providers are subject to congestion in the form of an M/M/1 queue, and they serve patient-consumers who have randomly distributed unit costs of time. Consumer demand (as market share) for both providers is obtained and described. The private provider’s pricing decision is explored, equilibrium existence is proven, and conditions for uniqueness presented. Comparative statics for demand are presented. Social welfare functions are described and the welfare maximizing condition obtained. More detailed results are then obtained for cases when costs follow uniform and Kumaraswamy distributions. Numerical simulations are then performed for these distributions, employing several parameter values, demonstrating the private provider’s pricing decision and its relationship with social welfare.

Suggested Citation

  • Alves, Vasco, 2019. "Pricing and waiting time decisions in a health care market with private and public provision," MPRA Paper 100996, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:100996
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/100996/8/MPRA_paper_100996.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Barzel, Yoram, 1974. "A Theory of Rationing by Waiting," Journal of Law and Economics, University of Chicago Press, vol. 17(1), pages 73-95, April.
    2. Hong Chen & Murray Frank, 1995. "Monopoly Pricing When Customers Queue," Industrial Organization 9504001, University Library of Munich, Germany.
    3. Cullis, John G & Jones, Philip R, 1986. "Rationing by Waiting Lists: An Implication," American Economic Review, American Economic Association, vol. 76(1), pages 250-256, March.
    4. Cary Deck & Erik O Kimbrough & Steeve Mongrain, 2014. "Paying for Express Checkout: Competition and Price Discrimination in Multi-Server Queuing Systems," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-13, March.
    5. Sofia Dimakou & Ourania Dimakou & Henrique Basso, 2015. "Waiting time distribution in public health care: empirics and theory," Health Economics Review, Springer, vol. 5(1), pages 1-27, December.
    6. Iversen, Tor, 1997. "The effect of a private sector on the waiting time in a national health service," Journal of Health Economics, Elsevier, vol. 16(4), pages 381-396, August.
    7. Israel Luski, 1976. "On Partial Equilibrium in a Queuing System with Two Servers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 519-525.
    8. Propper, Carol, 2000. "The demand for private health care in the UK," Journal of Health Economics, Elsevier, vol. 19(6), pages 855-876, November.
    9. Farnworth, Michael G., 2003. "A game theoretic model of the relationship between prices and waiting times," Journal of Health Economics, Elsevier, vol. 22(1), pages 47-60, January.
    10. Levhari, David & Luski, Israel, 1978. "Duopoly pricing and waiting lines," European Economic Review, Elsevier, vol. 11(1), pages 17-35, February.
    11. Phillip J. Lederer & Lode Li, 1997. "Pricing, Production, Scheduling, and Delivery-Time Competition," Operations Research, INFORMS, vol. 45(3), pages 407-420, June.
    12. Gravelle, Hugh & Schroyen, Fred, 2016. "Optimal hospital payment rules under rationing by random waiting," Discussion Paper Series in Economics 8/2016, Norwegian School of Economics, Department of Economics.
    13. V. V. Mazalov & A. V. Melnik, 2016. "Equilibrium Prices and Flows in the Passenger Traffic Problem," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-19, March.
    14. Lindsay, Cotton M & Feigenbaum, Bernard, 1984. "Rationing by Waiting Lists," American Economic Review, American Economic Association, vol. 74(3), pages 404-417, June.
    15. Hoel, Michael & Saether, Erik Magnus, 2003. "Public health care with waiting time: the role of supplementary private health care," Journal of Health Economics, Elsevier, vol. 22(4), pages 599-616, July.
    16. Lode Li & Yew Sing Lee, 1994. "Pricing and Delivery-Time Performance in a Competitive Environment," Management Science, INFORMS, vol. 40(5), pages 633-646, May.
    17. Dimitrios A. Andritsos & Sam Aflaki, 2015. "Competition and The Operational Performance of Hospitals: The Role of Hospital Objectives," Production and Operations Management, Production and Operations Management Society, vol. 24(11), pages 1812-1832, November.
    18. Melo, Emerson, 2014. "Price competition, free entry, and welfare in congested markets," Games and Economic Behavior, Elsevier, vol. 83(C), pages 53-72.
    19. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    20. Iversen, Tor, 1993. "A theory of hospital waiting lists," Journal of Health Economics, Elsevier, vol. 12(1), pages 55-71, April.
    21. Knudsen, Niels Chr, 1972. "Individual and Social Optimization in a Multiserver Queue with a General Cost-Benefit Structure," Econometrica, Econometric Society, vol. 40(3), pages 515-528, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kucukyazici, Beste & Zhang, Yue & Ardestani-Jaafari, Amir & Song, Lijie, 2020. "Incorporating patient preferences in the design and operation of cancer screening facility networks," European Journal of Operational Research, Elsevier, vol. 287(2), pages 616-632.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brekke, Kurt R. & Siciliani, Luigi & Straume, Odd Rune, 2008. "Competition and waiting times in hospital markets," Journal of Public Economics, Elsevier, vol. 92(7), pages 1607-1628, July.
    2. Gravelle, Hugh & Siciliani, Luigi, 2008. "Ramsey waits: Allocating public health service resources when there is rationing by waiting," Journal of Health Economics, Elsevier, vol. 27(5), pages 1143-1154, September.
    3. Siciliani, Luigi, 2006. "A dynamic model of supply of elective surgery in the presence of waiting times and waiting lists," Journal of Health Economics, Elsevier, vol. 25(5), pages 891-907, September.
    4. Siciliani, Luigi & Stanciole, Anderson & Jacobs, Rowena, 2009. "Do waiting times reduce hospital costs?," Journal of Health Economics, Elsevier, vol. 28(4), pages 771-780, July.
    5. Wenhui Zhou & Weixiang Huang & Vernon N. Hsu & Pengfei Guo, 2023. "On the Benefit of Privatization in a Mixed Duopoly Service System," Management Science, INFORMS, vol. 69(3), pages 1486-1499, March.
    6. Philipp Afèche & Haim Mendelson, 2004. "Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure," Management Science, INFORMS, vol. 50(7), pages 869-882, July.
    7. Dixon, Huw & Siciliani, Luigi, 2009. "Waiting-time targets in the healthcare sector: How long are we waiting?," Journal of Health Economics, Elsevier, vol. 28(6), pages 1081-1098, December.
    8. Sá, Luís & Siciliani, Luigi & Straume, Odd Rune, 2019. "Dynamic hospital competition under rationing by waiting times," Journal of Health Economics, Elsevier, vol. 66(C), pages 260-282.
    9. Qian, Qu & Zhuang, Weifen, 2017. "Tax/subsidy and capacity decisions in a two-tier health system with welfare redistributive objective," European Journal of Operational Research, Elsevier, vol. 260(1), pages 140-151.
    10. Gad Allon & Awi Federgruen, 2008. "Service Competition with General Queueing Facilities," Operations Research, INFORMS, vol. 56(4), pages 827-849, August.
    11. Bodas, Tejas & Manjunath, D., 2019. "Revenue maximization in service systems with heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 278(2), pages 686-698.
    12. Simona GRASSI, 2006. "On the characteristics of a mixed system of provision of a private good. An application to health care," Departmental Working Papers 2006-14, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    13. Akbar Marvasti, 2006. "A Contingent Valuation of Customer Delay in Medical Services," Eastern Economic Journal, Eastern Economic Association, vol. 32(1), pages 31-45, Winter.
    14. Cary Deck & Erik O Kimbrough & Steeve Mongrain, 2014. "Paying for Express Checkout: Competition and Price Discrimination in Multi-Server Queuing Systems," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-13, March.
    15. Johannesson, Magnus & Johansson, Per-Olov & Soderqvist, Tore, 1998. "Time spent on waiting lists for medical care: an insurance approach," Journal of Health Economics, Elsevier, vol. 17(5), pages 627-644, October.
    16. Kucukyazici, Beste & Zhang, Yue & Ardestani-Jaafari, Amir & Song, Lijie, 2020. "Incorporating patient preferences in the design and operation of cancer screening facility networks," European Journal of Operational Research, Elsevier, vol. 287(2), pages 616-632.
    17. Hugh Gravelle & Luigi Siciliani, 2008. "Is waiting‐time prioritisation welfare improving?," Health Economics, John Wiley & Sons, Ltd., vol. 17(2), pages 167-184, February.
    18. Somayeh Sadat & Hossein Abouee-Mehrizi & Michael Carter, 2015. "Can hospitals compete on quality?," Health Care Management Science, Springer, vol. 18(3), pages 376-388, September.
    19. Goddard, John & Tavakoli, Manouche, 2008. "Efficiency and welfare implications of managed public sector hospital waiting lists," European Journal of Operational Research, Elsevier, vol. 184(2), pages 778-792, January.
    20. Panos Pashardes & Nicoletta Pashourtidou, 2011. "Consumer welfare from publicly supplemented private goods: age and income effects on demand for health care," Empirical Economics, Springer, vol. 41(3), pages 865-885, December.

    More about this item

    Keywords

    Waiting times; queueing; private health care; competition;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • I11 - Health, Education, and Welfare - - Health - - - Analysis of Health Care Markets
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:pra:mprapa:100996. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.