Pareto Optimal Insurance Policies in the Presence of Administrative Costs

In his classical article in The American Economic Review, Arthur Raviv (1979) examines Pareto optimal insurance contracts when there are ex-post insurance costs c induced by the indemnity I for loss x. Raviv’s main result is that a necessary and sufficient condition for the Pareto optimal deductible to be equal to zero is c'(I) = 0 for all I >= 0. We claim that another type of cost function is called for in household insurance, caused by frequent but relatively small claims. If a fixed cost is incurred each time a claim is made, we obtain a non-trivial Pareto optimal deductible even if the cost function does not vary with the indemnity. This implies that when the claims are relatively small, it is not optimal for the insured to get a compensation since the costs outweighs the benefits, and a deductible will naturally occur. We also discuss policies with an upper limit, and show that the insurer prefers such contracts, but the insured does not. In Raviv’s paper it was also shown that policies with upper limits are dominated by policies with no upper limit, when there are ex-post costs to insurance. We show that the result is right, but the proof is wrong.