On the Demand for Budget Constrained Insurance

Much of the traditional economic theory of insurance is based on the assumption that the risk against which insurance is to be purchased is entirely exogenous. This is usually modelled by simply allowing the individual to include insurance as a mechanism of covering risk, without any real analysis of how this insurance is paid for. However, in almost all real-life consumer insurance, the size of the risk is itself a choice variable (the type of car to purchase, the type of employment to take, the amount to invest in an insurable asset, etc.), and decisions are made taking budget constraints explicitly into account. While an enormous number of interesting theorems can be derived in the standard model, these results are typically not robust to the extention of making risk an endogenous choice variable and the explicit inclusion of a budget constraint. Here, we use a simple two state model of the demand for insurance in which we explicitly introduce a budget constraint and in which the insurable risk itself is a choice variable. In the model, we find that the standard result of full coverage being demanded if and only if the premium is such that the insurer earns an expected profit of 0 no longer holds as such, and it turns out that in a simple two state setting some of the ambiguity of the standard model’s comparative statics is avoided.