Labor contracts in a model of imperfect competition

We propose a definition of involuntary unemployment which differs from that traditionally used in implicit labor contract theory. We say that a worker is involuntarily unemployed if the marginal wage implied by the optimal contract exceeds the marginal rate of substitution between leisure and consumption. We construct a model where risk-neutral firms have monopoly power and show that such monopoly power is necessary for involuntary unemployment to arise in the optimal contract. We numerically compute examples and show that such unemployment occurs for a wide range of parameter values.