Insurance contracts are frequently modelled as principal-agent relationships. The purpose of this paper is to examine the interaction between differential bargaining power and the efficiency of insurance contracts. The analysis is undertaken in a framework of state-contingent production, which allows us to consider, as separate choices, the level of effort committed by the client and the riskiness of the equilibrium state-contingent production vector. Our central result is that, in the presence of hold-up problems, the exercise of monopoly power by insurers leads clients to undertake socially costly self-protection, leading to suboptimal levels of insurance. Clients can exploit information asymmetries to offset the bargaining power of the insurer, but this process is also socially costly. Hence, competitive markets for insurance will yield a Pareto-superior outcome to the constrained Pareto-optimum reached in markets where insurers have monopoly power. More generally, in a bargaining situation, an increase in the bargaining power of clients will increase social welfare.