An analysis of insurance in the newsboy problem

In this paper we study the standard newsboy problem, but under two new assumptions when compared to the existing literature. First, we assume that the wholesaler sets the wholesale price optimally, and in doing so, takes into account the salvage value at which the newsboy can return unsold items to the wholesaler. Second, we assume that the salvage value is a choice variable of the newsboy, and in that way, it acts as an insurance device. The newsboy’s optimal salvage value then represents an optimal demand for insurance. We study in particular the optimal pricing problem of the supplier, and show that it can be expressed as a mark-up equation. We also show that insurance is provided at an actuarially unfair price. As regards the optimal demand for insurance by the newsboy, the problem is too complex for a closed form solution to be possible, so we resort to a simulation which returns the results that a strictly positive level of strictly partial insurance is demanded when the newsboy is strictly risk averse, and the optimal level of insurance coverage increases with risk aversion.