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Two hospitals compete for the exclusive services of health professionals, who are privately informed about their ability and motivation. Hospitals differ in their ownership structure and in the mission they pursue. The non-profit hospital sacrifices some profits to follow its mission but becomes attractive for motivated workers. In equilibrium, when both hospitals are active, the sorting of workers to hospitals is efficient and ability-neutral. Allocative distortions are decreasing in the degree of competition and disappear when hospitals are similar. The non-profit hospital tends to provide a higher amount of care and offer lower salaries than the for-profit one.

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When workers' intrinsic motivation matters, a wage increase has mixed consequences on applicants' productivity and motivation, as shown in public service, healthcare, education and politics.In a simple theoretical framework where ability and motivation are workers'private information, we rationalize these di¤erentiated responses and identify intuitive conditions for higher wages inducing self-selection of more (or less) productive and motivated workers. The selection patterns depend both on the statistical association between workers'characteristics and on the di¤erence between the incentivised returns to ability across sectors. We emphasize a crowding-out e¤ect of wage on workers' productivity that has not been analyzed in the theoretical literature before.

We study optimal non-linear contracts offered by a non-profit and a for-profit firm competing to attract workers, who are privately informed about their ability and motivation. Motivated workers are keen to be hired by the non-profit firm because they adhere to its mission. Workers with different ability self-select into firms depending on which organization holds a competitive advantage. This determines the sign and the composition of the wage differential between firms, which encompasses labor donations induced by motivation and the selection effect of ability. Our model thus rationalizes the mixed empirical evidence concerning for-profit vs non-profit wage differentials.