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The value of a "free" customer


  • Gupta, Sunil
  • Mela, Carl F.
  • Vidal-Sanz, Jose M.


We study the problem of a firm that faces asymmetric information about the productivity of its potential workers. In our framework, a worker’s productivity is either assigned by nature at birth, or determined by an unobservable initial action of the worker that has persistent effects over time. We provide a characterization of the optimal dynamic compensation scheme that attracts only high productivity workers: consumption –regardless of time period– is ranked according to likelihood ratios of output histories, and the inverse of the marginal utility of consumption satisfies the martingale property derived in Rogerson (1985). However, in the case of i.i.d. output and square root utility we show that, contrary to the features of the optimal contract for a repeated moral hazard problem, the level and the variance of consumption are negatively correlated, due to the influence of early luck into future compensation. Moreover, in this example long-term inequality is lower under persistent private information

Suggested Citation

  • Gupta, Sunil & Mela, Carl F. & Vidal-Sanz, Jose M., 2009. "The value of a "free" customer," DEE - Working Papers. Business Economics. WB wb092903, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
  • Handle: RePEc:cte:wbrepe:wb092903

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    References listed on IDEAS

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    Cited by:

    1. Peter Zubcsek & Miklos Sarvary, 2011. "Advertising to a social network," Quantitative Marketing and Economics (QME), Springer, vol. 9(1), pages 71-107, March.
    2. Avagyan, Vardan & Esteban-Bravo, Mercedes & Vidal-Sanz, Jose M., 2014. "Licensing radical product innovations to speed up the diffusion," European Journal of Operational Research, Elsevier, vol. 239(2), pages 542-555.
    3. Mercedes Esteban-Bravo & Jose M. Vidal-Sanz & Gökhan Yildirim, 2014. "Valuing Customer Portfolios with Endogenous Mass and Direct Marketing Interventions Using a Stochastic Dynamic Programming Decomposition," Marketing Science, INFORMS, vol. 33(5), pages 621-640, September.

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