This paper provides a theoretical analysis of the effects of national health insurance on consumption distribution, especially with regard to changes in premiums and coinsurance. In general, health insurance is expected to have an advantageous influence on consumption equity. However, under the simplifying assumptions imposed in the paper, we show that the redistribution consequences of these two measures are not always unambiguous. The conclusion we reach is that, in a perfectly competitive medical care market with constant marginal cost, an increase in premium rates will reduce the average societal consumption on the one hand and lessen consumption inequality on the other hand. However, lowering the rate of coinsurance may lead to higher inequality of consumption, while it still cuts down the consumption level in cases where the Arrow-Pratt measure of relative risk aversion is not greater than one.