Pareto Optimal Insurance Policies in the Presence of Administrative Costs

In his classical article in The American Economic Review, Arthur\nRaviv (1979) examines Pareto optimal insurance contracts when there\nare ex-post insurance costs c induced by the indemnity I for loss x.\nRaviv’s main result is that a necessary and sufficient condition for the\nPareto optimal deductible to be equal to zero is c0(I) = 0 for all I > 0(or I=0).\nWe claim that another type of cost function is called for in household\ninsurance, caused by frequent but relatively small claims. If a\nfixed cost is incurred each time a claim is made, we obtain a non-trivial\nPareto optimal deductible even if the cost function does not vary with\nthe indemnity. This implies that when the claims are relatively small,\nit is not optimal for the insured to get a compensation since the costs\noutweighs the benefits, and a deductible will naturally occur.\nWe also discuss policies with an upper limit, and show that the\ninsurer prefers such contracts, but the insured does not. In Raviv’s\npaper 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.\nWe show that the result is right, but the proof is wrong.