Empirical specification of healthcare resource distribution based on the law of competitor distribution

Abstract

Sustainable development relies on the efficient resource distribution among economic agents, requiring an integrated approach. A key principle of this concept is reducing inequality through more equitable resource distribution. This study examines the distribution of healthcare resources across countries amid rising intercountry disparities. The proposed hypothesis suggests that healthcare resource allocation follows a non-random pattern shaped by competitive dynamics. Using the law of competitor distribution, this paper models intercountry resource distribution through the “generalized theory of competition” to analyze rank-size dependencies. The World Bank and Organization for Economic Co-operation and Development data on health statistics were used as the initial dataset for constructing the rank-size dependencies of the of resource distribution. The findings indicate that the empirical distribution of healthcare resources deviates from the Pareto distribution law, reflecting the stochastic multiplicative nature of competition. When the empirical distribution was compared with the Pareto distribution, an uneven distribution of resources in the competition process was revealed. Further, the power law poorly approximated the size of the empirical distributions at both low and high ranks. To reduce inequality in the distribution of healthcare resources, the study advocates for an integrated development approach leveraging digital technologies.

Keywords

Sustainable development / Health and economic development / Health resource policies / Global health and inequality

Funding

None.

Conflict of interest

Mihajlo Jakovljevic is the Founding-Chief-Editor of this journal, but was not in any way involved in the editorial and peer-review process conducted for this paper, directly or indirectly. Separately, other authors declared that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

References

[1] Akarli, A. (2024). The Age of Dirigisme (1950-1980): Recovery, Catch Up, and Stagnation. In A Modern Economic History of Emerging Markets (1950-2020) Dirigisme, Globalization and Disruption. Cham: Springer Nature Switzerland. p. 51-100. https://doi.org/10.1007/978-3-031-55210-6_2

[2] Alanazi1, A.S., Alenazi, H., Alenezi, N., Aldidab H.F., & Alruwaili, H.K. (2021). Clinical healthcare technologies: An analysis of healthcare technologies used in medical clinics. International Journal of Bio-Medical Informatics and e-Health, 9(5):1-9. https://doi.org/10.30534/ijbmieh/2021/01952021

[3] Anderson, C. (2008). The Long Tail: Why the Future of Business is Selling Less of More. Hyperion - Acquired Assets; Revised edition. Publisher: Hachette Books. p. 267.

[4] Arnold, B.C. (2008). Pareto and Generalized Pareto Distributions. In: Chotikapanich, D. (eds) Modeling Income Distributions and Lorenz Curves. Economic Studies in Equality, Social Exclusion and Well-Being, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-0-387-72796-7_7

[5] Arnold, B.C. (2015). Pareto Distribution. United States: CRC Press, Taylor and Francis Group. https://doi.org/10.1002/9781118445112.stat01100.pub2

[6] Bedir, S. (2016). Healthcare expenditure and economic growth in developing countries. Advances in Economics and Business, 4(2):76-86. https://doi.org/10.13189/aeb.2016.040202

[7] Bergs, R. (2021). Spatial dependence in the rank-size distribution of cities-weak but not negligible. PLoS One, 16(2):e0246796.. https://doi.org/10.1371/journal.pone.0246796

[8] Bigler, C., Pita, Y., & Sony, K.C. (2025). Are we leaving women with disabilities in the Global South behind? How the reinforcement of different forms of violence leads to unsustainable development. Women’s Studies International Forum, 109:103051. https://doi.org/10.1016/j.wsif.2024.103051

[9] Borin, M.C., Barbosa, M.M., Pereira, C.O., Martins, C.R., dos Reis, D.P., Ribeiro, G.J.C., et al. (2023). Assessing the impact of fast-track drug registration by Anvisa in Brazil: A descriptive study of new drug registrations from 2017 to 2022. Global Health Economics and Sustainability, 1(2):0995. https://doi.org/10.36922/ghes.0995

[10] Brulé G., & Suter, C. (2019). Why Wealth Matters More Than Income for Subjective Well-being? I In: Brulé G., & Suter, C. (eds) Wealth(s) and Subjective Well-Being. Social Indicators Research Series. Vol. 76. Cham: Springer. https://doi.org/10.1007/978-3-030-05535-6_1

[11] Caeiro, F., & Norouzirad, M. (2024). Comparing estimation methods for the power-pareto distribution. Econometrics, 12:20. https://doi.org/10.3390/econometrics12030020

[12] Charles, I.I., & Uford, I.C. (2023). Comparative analysis and evaluation of business and financial performance of Amazon. Com: A three-year period critical review of exceptional success. European Journal of Business, Economics and Accountancy, 11(2), 69-92.

[13] Chen, X., Liu, Z., Wei, L., Yan, J., Hao, T., & Ding, R. (2018). A comparative quantitative study of utilizing artificial intelligence on electronic health records in the USA and China during 2008-2017. BMC Medical Informatics and Decision Making, 18(Suppl 5):117. https://doi.org/10.1186/s12911-018-0692-9

[14] Chen, Y., Xiang, L., & Yang, H. (2024). Interregional value-added tax in the era of E-commerce: Tax policy design based on big data from online retailing. Journal of Social Computing, 5(1):46-57. https://doi.org/10.23919/jsc.2024.0006

[15] Clementi, F. (2024). Income distribution, inequality and poverty: Evidence, explanations and policies. Economies, 12:276. https://doi.org/10.3390/economies12100276

[16] Da Silva, A.A., Merolli, M., Fini, N.A., Granger, C.L., Gustafson, O.D., & Parry, S.M. (2025). Digital health interventions in adult intensive care and recovery after critical illness to promote survivorship care. The Journal of the Intensive Care Society, 26(1):96-104. https://doi.org/10.1177/17511437241311105

[17] DataBank. Health Nutrition and Population Statistics. Available from:. https://databank.worldbank.org/source/health-nutrition-and-population-statistics [Last accessed on 2024 Nov 01].

[18] Devine, M.T., & Siddiqui, S. (2023). Strategic investment decisions in an oligopoly with a competitive fringe: An equilibrium problem with equilibrium constraints approach. European Journal of Operational Research, 306(3):1473-1494. https://doi.org/10.1016/j.ejor.2022.07.034

[19] Erdas, M.L., Caglar, A.E., Uche, E., & Ahmed, Z. (2025). A new frontier in understanding the dynamics of environmental sustainability in the context of finance and low carbon energy investment: Evidence from artificial intelligence and Fourier approach. Energy, 315:134419. https://doi.org/10.1016/j.energy.2025.134419

[20] Farys, R., & Wolbring, T. (2021). Matthew effects in science and the serial diffusion of ideas: Testing old ideas with new methods. Quantitative Science Studies, 2(3):505-526. https://doi.org/10.1162/qss_a_00129

[21] Fraccascia, L. (2020). Quantifying the direct network effect foronline platforms supporting industrial symbiosis: An agent-based simulation study. Ecological economics, 170:106587. https://doi.org/10.1016/j.ecolecon.2019.106587

[22] Frank, R.H., & Cook, P.J. (2013). Winner-take-all markets. Studies in Microeconomics, 1(2):131-154. https://doi.org/10.1177/2321022213501254

[23] Gabaix, X. (2016) Power laws in economics: An introduction. Journal of Economic Perspectives, 30(1):185-206. https://doi.org/10.1257/jep.30.1.185

[24] Gailey, N. (2023). Human Capital and Demographic Futures in Eastern Europe and the Caucasus: Challenges of Population Aging, Depopulation, and Brain Drain. Angestrebter akademischer Grad/in Partial Fulfilment of the Requirements for the Degree of Doktor der Philosophie (Dr. phil.) Wien, 2023/Vienna, 2023 Studienkennzahl lt. Studienblatt/Degree Programme Code as it Appears on the Student Record Sheet: UA 796 310 120.

[25] Ganguly, S., Sasi, A., Singh Sra, M., Tansir, G., Sharma, S., Sharma, S., et al. (2024). Assessment of patient satisfaction levels with teleconsultation services at a tertiary care cancer center in a developing country: A cross-sectional study. Supportive Care in Cancer, 32(12):838. https://doi.org/10.1007/s00520-024-09051-8

[26] Godfrey, C., Clement, E., Mein, R., Brockington, M., Smith, J., Talim, B., et al. (2007). Refining genotype phenotype correlations in muscular dystrophies with defective glycosylation of dystroglycan. Brain. 2007; 130(Pt 10):2725- 2735. https://doi.org/10.1093/brain/awm212

[27] Hamzah, I., Hamzah, H.Z., & Aurangzaib, F. (2024). Evaluating the relationship between private hospital expenditure and economic growth in Malaysia: An ARDL perspective. International Journal of Academic Research in Economics and Management Sciences, 13(4):473-491. https://doi.org/10.6007/IJAREMS/v13-i4/23631

[28] Hicks, J.R. (1939). The foundation of welfare economics. Economic Journal, 196:696-712.

[29] Hirakawa, H. (2024). China’s belt and road initiative and its prospect. In: The Dynamics of Asian Economic Development: Understanding Asia and its Ways Forward. Singapore: Springer Nature Singapore. p. 105-147. https://doi.org/10.1007/978-981-97-3106-0_4

[30] Hoyler, M., Finlayson, S.R., McClain, C.D., Meara, J.G., & Hagander, L. (2014). Shortage of doctors, shortage of data: A review of the global surgery, obstetrics, and anesthesia workforce literature. World Journal of Surgery, 38:269-280. https://doi.org/10.1007/s00268-013-2324-y

[31] Idris, F.M., Seraj, M. & Ozdeser, H. (2024). Impact of health expenditure on poverty in low- and middle-income countries: An autoregressive distributed lag bounds approach. Global Health Econ Sustain, 2(1): 2383. https://doi.org/10.36922/ghes.2383

[32] Jahanbakhsh Javid, N., & Amini, M. (2023). Evaluating the effect of supply chain management practice on implementation of halal agroindustry and competitive advantage for small and medium enterprises. International Journal of Computer Science and Information Technology, 15(6):8997-9008.

[33] Jakovljevic, M., Cerda, A.A., Liu, Y., García, L., Timofeyev, Y., Krstic, K., et al. (2021). Sustainability challenge of Eastern Europe-historical legacy, belt and road initiative, population aging and migration. Sustainability, 13(19):11038. https://doi.org/10.3390/su131911038

[34] Jakovljevic, M., Chang, H., Pan, J., Guo, C., Hui, J., Hu, H., et al. (2023). Successes and challenges of China’s health care reform: A four-decade perspective spanning 1985-2023. Cost Effectiveness and Resource Allocation, 21(1):59. https://doi.org/10.1186/s12962-023-00461-9

[35] Jakovljevic, M., Deceuninck, P., Pistollato, F., Daskalopoulos, E., Bernasconi, C., Carausu, F., et al. (2024). Return on investment in science: twenty years of European Commission funded research in Alzheimer’s dementia, breast cancer and prostate cancer. Cost Effectiveness and Resource Allocation, 22(1):51. https://doi.org/10.1186/s12962-024-00540-5

[36] Jefferson, M. (1989). Why geography? The law of the primate city. Geographical Review, 79(2):226-232.

[37] Kaldor, N. (1939). Welfare propositions of economics and interpersonal comparisons of utility. Economic Journal, 49(195):549-552. https://doi.org/10.1017/CBO9780511819025.016

[38] Karountzos, P., Giannakopoulos, N.T., Sakas, D.P., & Migkos, S.P. (2024). A tale of two economies: Diachronic comparative analysis of diverging paths of growth and inequality in the United States and the United Kingdom. Economies, 12(10):274. https://doi.org/10.3390/economies12100274

[39] Khemani, R.S. (2007). Competition Policy and Promotion of Investment, Economic Growth and Poverty Alleviation in Least Developed Countries (English). Foreign Investment Advisory Service (FIAS) Occasional Paper; no. FIAS 19 Washington, DC: World Bank. Available from:. https://documents.worldbank.org/curated/en/397801468174885108 [Last accessed on 2024 Sep 30].

[40] Kolesnichenko, O., Nakonechniy, I., & Kolesnichenko, Y. (2024). From digital to quantum epidemiology: The Quantum Data Lake concept for big data related to viral infectious diseases. Global Health Economics and Sustainability, 2(1):2148. https://doi.org/10.36922/ghes.2148

[41] Kryscynski, D., Coff, R., & Campbell, B. (2021). Charting a path between firm-specific incentives and human capital-basedcompetitive advantage. Strategic Management Journal, 42(2):386-412. https://doi.org/10.1002/smj.3226

[42] Kumar, A., & Schoenstein, M. (2013). Managing Hospital Volumes:Germany and Experiences from OECD Countries. OECD Health Working Papers, No. 64. Paris:OECD Publishing. https://doi.org/10.1787/5k3xwtg2szzr-en

[43] Laferrière, V., Staubli, D., & Thöni, C. (2023). Explaining excess entry in winner-take-all markets. Management Science, 69(2):1050-1069. https://doi.org/10.1287/mnsc.2022.4397

[44] Lamem, M.F.H., Sahid, M.I., & Anika, A. (2025). Artificial intelligence for access to primary healthcare in rural settings. Journal of Medicine, Surgery, and Public Health, 5:100173. https://doi.org/10.1016/j.glmedi.2024.100173

[45] Litvinenko, V.S., Petrov, E., Vasilevskaya, D., Yakovenko, A., Naumov, I., & Ratnikov, M. (2022). Assessment of the role of the state in the management of mineral resources. Journal of Mining Institute, 259:95-111. https://doi.org/10.31897/PMI.2022.100

[46] Manin, D.Y. (2009). Mandelbrot’s model for Zipf ’s law: Can Mandelbrot’s model explain Zipf ’s law for language? Journal of Quantitative Linguistics. 16(3):274-285. https://doi.org/10.1080/09296170902850358

[47] Nayak, B., Bhattacharyya, S.S., & Krishnamoorthy, B. (2021). Explicating the role of emerging technologies and firm capabilities towards attainment of competitive advantage in health insurance service firms. Technological Forecasting and Social Change, 170:120892. https://doi.org/10.1016/j.techfore.2021.120892

[48] Newman, M. (2017). Power-law Distribution. Available from:. https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.1740-9713.2017.01050.x

[49] Nguyen, T.C., Castro, V., & Wood, J. (2024). The impact of financial crises on social spending: Delving into the effects in developed and developing countries. International Journal of Finance and Economics, 29(4):4721-4741. https://doi.org/10.1002/ijfe.2901

[50] OECD Health Statistics. (2024). Available from: https://www.oecd.org/en/data/datasets/oecd-health-statistics.html [Last accessed on 2024 Oct 11].

[51] Patel, P. (2021). Modelling cooperation, competition, and equilibrium: The enduring relevance of game theory in shaping economic realities. Social Science Chronicle, 1:1-19. https://doi.org/10.56106/ssc.2021.003

[52] Plemmenos, N., Vlastos, D.D., & Theofilou, P. (2023). Association of burnout syndrome with mental resilience and quality of life among workers in the public and private sectors. Global Health Economics and Sustainability, 1(2):1751. https://doi.org/10.36922/ghes.1751

[53] Raghupathi, V., & Raghupathi, W. (2023). The association between healthcare resource allocation and health status: An empirical insight with visual analytics. Journal of Public Health (Berl), 31:1035-1057. https://doi.org/10.1007/s10389-021-01651-6

[54] Reedy, J.M., Pousty, D., Waliaula, B.W., & Maniga, J., Mamane, H., Mariita, R.M. (2024). Enhancing quality of life, public health, and economic development in the Global South through waterborne disease prevention with ultraviolet C light-emitting diode technology. Global Health Economics and Sustainability, 2(1):19874. https://doi.org/10.36922/ghes.1984

[55] Rigney, D. (2010). Front Matter. In: The Matthew Effect: How Advantage Begets Further Advantage. Columbia University Press. p. i-iv. Available from: https://www.jstor.org/stable/10.7312/rign14948.1 [Last accessed on 2025 Apr 11].

[56] Sadovnichiy, V.A., Akaev, A., & Davydova, O. (2024) Modeling and Forecasting the Evolutionary Economic Development of the BRICS and G7 Countries in the First Half of the Twenty- First Century. Available from: https://www.sociostudies.org/ journal/articles/3810305 [Last accessed on 2025 Apr 11].

[57] Said, S., Yongolo, N., Biswaro, S., Walker, R., & Kelly, C. (2024). Decolonization of health care in Tanzania. Global Health Economics and Sustainability, 2(2):2299. https://doi.org/10.36922/ghes.2299

[58] Sambodo, N.P., Bonfrer, I., Sparrow, R., Pradhan, M., & van Doorslaer, E. (2023). Effects of performance-based capitation payment on the use of public primary health care services in Indonesia. Social Science and Medicine, 327:115921. https://doi.org/10.1016/j.socscimed.2023.115921

[59] Santos, J. (2022). All roads lead to the global South: Brazilian- Russian relations within the BRICS framework. ISTORIYA, 13:13. https://doi.org/10.18254/S207987840023492-0

[60] Seekell, D.A., & Pace Michael, L. (2011). Does the Pareto distribution adequately describe the size-distribution of lakes? Limnology and Oceanography, 56(1):350-356. https://doi.org/10.4319/lo.2011.56.1.0350

[61] Sharma, M.G., & Popli, H. (2023). India on the path to universal health coverage-progress compared with other emerging economies of BRICS and ASEAN-5. Journal of Young Pharmacists, 15(2):326-333. https://doi.org/10.5530/jyp.2023.15.43

[62] Shuai, J., Zhao, Y., Shuai, C., Wang, J., Yi, T., & Cheng, J. (2023). Assessing the international co-opetition dynamics of rare earth resources between China, USA, Japan and the EU: An ecological niche approach. Resources Policy, 82:103446. https://doi.org/10.1016/j.resourpol.2023.103446

[63] Statistical Interpretation of Entropy and the Second Law of Thermodynamics. (2009). Available from:. https://openstax.org/books/college-physics-2e/pages/15-7-statistical-interpretation-f-entropy-and-the-second-law-of-thermodynamics-the-underlying-explanation [Last accessed on 2024 Oct 23].

[64] Tediosi, F., Finch, A., Procacci, C., Marten, R., & Missoni, E. (2016). BRICS countries and the global movement for universal health coverage. Health Policy Plan, 31(6):717-728. https://doi.org/10.1093/heapol/czv122

[65] The Mathew Effect. (2017) A Summary of “Outliers”. Available from: https://revisesociology.com/2017/08/18/the-mathew-effect-a-summary-of-outliers-chapter-one [Last accessed on 2024 Jul 05].

[66] Trubnikov, B.A., & Trubnikova, O.B. (2004). The five great probability distributions. Priroda. 11:11-18.

[67] Valls Martínez, M.C., Ramírez-Orellana, A., & Grasso, M.S. (2021). Health investment management and healthcare quality in the public system: A gender perspective. International Journal of Environmental Research and Public Health, 18(5):2304. https://doi.org/10.3390/ijerph18052304

[68] Wang, Y. (2024). Income-related inequality in health outcomes among older individuals in China: A measurement and decomposition analysis. Global Health Economics and Sustainability, 2(1):2243. https://doi.org/10.36922/ghes.2243

[69] What is the Statisitical Weight of a System? (2004). Available from: https://physics.stackexchange.com/questions/469948/what-is-the-statisitical-weight-of-a-system [Last accessed on 2024 Nov 12].

[70] Yuan, L., Xu, S., Xu, J., Cao, J., & Qian, Z. (2024). Variation in intensive care unit beds capacity in China from 2007 to 2021. Intensive Care Medicine, 50(3):472-474. https://doi.org/10.1007/s00134-024-07347-1

[71] Zhu, L., Gao, W., Zhang, S., Yu, F., Li, J., Feng, J., et al. (2024). Equality of healthcare resource allocation between impoverished counties and non-impoverished counties in Northwest China: A longitudinal study. BMC Health Services Research, 24:830. https://doi.org/10.1186/s12913-024-11312-5