Optimal insurance coverage has been analyzed by numerous researchers. Arrow [1963], Mossin [1968] and Smith [1968] describe insurance buying behavior of utility maximizing individuals. Their results, however, as well as those of later authors (e.g., Schlesinger [1981] and Turnbull [1983]) are qualitative in their nature. One of the important findings, for example, is that coverage decreases when the risk premium increases. To what degree coverage decreases is, however, not specified. Raviv [1979] concludes that Pareto optimal insurance policies involve a deductible and coinsurance above the deductible, but specific expressions as to the magnitudes are not treated. This paper extends these analyses by presenting explicit, albeit approximate, expressions for the amount of insurance coverage. Section 2 derives an expression for the expected utility maximizing individual who is free to choose any degree of coverage. Section 3 examines two other types of insurance contracts, and Section 4 summarizes the findings. Throughout, the results will be illustrated numerically for the "average" American household.