Will consumers purchase private insurance policies to supplement a deductible that might be part of a national health insurance plan? "If such supplementation does occur," say the authors, "demand for ambulatory health services may stress existing supply, leading to extensive nonprice rationing of services." Based on an economic model of the decision to purchase supplementary insurance, study results show that if the current tax subsidy of health insurance is ended, administrative costs and hence policy premiums covering all medical expenses that supplement a moderate (up to $200 per person) deductible will be so high that almost no one will buy them. Even if the subsidy is continued, there probably will not be much demand. Supplementary insurance covering only hospital expenditures is more attractive because administrative costs are much lower. Only about one in ten persons eligible for Medicare has chosen to supplement the $60 deductible for physician services, whereas more than half have purchased hospital supplementary policies.