THE private health insurance industry is large and important. As discussed by Karen Davis [2], it figures prominently in several plans for national health insurance. However, very little is known about the degree of competition in that industry or the effect that competition has on insurance and medical markets. This paper will examine theoretically and empirically the impact of varying degrees on competitiveness in this industry. In particular, the effects on the completeness of insurance (the proportion of expenses paid by the insurer) and thus medical demand will be studied.