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Raising Capital from Heterogeneous Investors

Author

Listed:
  • Marina Halac
  • Ilan Kremer
  • Eyal Winter

Abstract

A rm raises capital from multiple investors to fund a project. The project succeeds only if the capital raised exceeds a stochastic threshold, and the rm offers payments contingent on success. We study the rm's optimal unique-implementation scheme, namely the scheme that guarantees the rm the maximum payoff. This scheme pays investors differential net returns (per unit of capital) depending on the size of their investments. We show that if the distribution of the investment threshold is log-concave, larger investors receive higher net returns than smaller investors. Moreover, higher dispersion in investor size increases the rm's payoff. Our analysis highlights strategic risk as an important potential driver of inequality.

Suggested Citation

  • Marina Halac & Ilan Kremer & Eyal Winter, 2018. "Raising Capital from Heterogeneous Investors," Working Papers 245773051, Lancaster University Management School, Economics Department.
    • Handle: RePEc:lan:wpaper:245773051
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    2. Jay Pil Choi & Christodoulos Stefanadis, 2022. "Network Externalities, Dominant Value Margins, And Equilibrium Uniqueness," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1805-1827, November.
    3. Mamadou L Gueye & Nicolas Quérou & Raphaël Soubeyran, 2021. "Inequality Aversion and the Distribution of Rewards in Organizations," Working Papers hal-03134262, HAL.
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    5. Roweno J. R. K. Heijmans, 2023. "Unraveling Coordination Problems," Papers 2307.08557, arXiv.org, revised Aug 2023.
    6. David Easley & Yoav Kolumbus & Eva Tardos, 2025. "Markets with Heterogeneous Agents: Dynamics and Survival of Bayesian vs. No-Regret Learners," Papers 2502.08597, arXiv.org, revised Jun 2025.
    7. Lin William Cong & Yizhou Xiao, 2024. "Information Cascades and Threshold Implementation: Theory and an Application to Crowdfunding," Journal of Finance, American Finance Association, vol. 79(1), pages 579-629, February.
    8. Chan, Lester T., 2025. "Weight-ranked divide-and-conquer contracts," Theoretical Economics, Econometric Society, vol. 20(3), July.
    9. Raphael Soubeyran, 2021. "Pro-social Motivations, Externalities and Incentives," Working Papers hal-03212888, HAL.
    10. Tzur, Hana & Segev, Ella, 2025. "Entrepreneurs’ optimal decisions in equity crowdfunding campaigns," European Journal of Operational Research, Elsevier, vol. 327(2), pages 673-689.
    11. Moran Koren, 2023. "The Gatekeeper Effect: The Implications of Pre-Screening, Self-selection, and Bias for Hiring Processes," Papers 2312.17167, arXiv.org.
    12. Samuel Kapon & Lucia Del Carpio & Sylvain Chassang, 2024. "Using Divide-and-Conquer to Improve Tax Collection," Working Papers 335, Princeton University, Department of Economics, Center for Economic Policy Studies..
    13. Heijmans, Roweno J.R.K. & Suetens, Sigrid, 2025. "Comparing Subsidies to Solve Coordination Failure," Discussion Papers 2025/9, Norwegian School of Economics, Department of Business and Management Science.
    14. Itai Arieli & Moran Koren & Rann Smorodinsky, 2024. "Information aggregation in large collective purchases," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 295-345, August.
    15. Heijmans, Roweno J.R.K., 2023. "Unraveling Coordination Problems," Discussion Papers 2023/20, Norwegian School of Economics, Department of Business and Management Science.
    16. Krishna Dasaratha & Benjamin Golub & Anant Shah, 2023. "Equity Pay In Networked Teams," Papers 2308.14717, arXiv.org.
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    20. Machado, Caio, 2024. "Uneven recessions and optimal firm subsidies," Journal of Public Economics, Elsevier, vol. 239(C).

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    Keywords

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    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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