Publication: The value of a "free" customer
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2009-03
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Abstract
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
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Customer lifetime value, CRM, Dynamic programming, GMM Estimation