Summary: We examine equilibria in competitive insurance markets when individuals take unobservable labor supply decisions. Precautionary labor motives introduce countervailing incentives in the insurance market, and equilibria with positive profits can occur even in the standard case in which individuals exogenously differ in risk only. We then extend the model to allow for both privately known risks and labor productivities. This endogenously introduces two-dimensional heterogeneity in the insurance market since precautionary labor effects lead to differences in income and hence risk aversion. Under these circumstances, separating and pooling equilibria exist, which generally differ from those with exogenous two-dimensional heterogeneity considered by the existing literature. Notably, in contrast to standard screening models, profits may be increasing with insurance coverage, and the correlation between risk and coverage can be zero or negative in equilibrium, a phenomenon frequently observed in empirical studies.

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