Public health insurance and optimal income taxation

If individuals differ not only in their inherent capacity to earn income, but also in the probability that they will fall ill, can subsidized public health insurance be justified on the grounds that it serves as an efficient tool to redistribute welfare? This question is analyzed in a model where the social welfare function is a weighted average of individual expected utilities, and where taxation is by a linear income tax. The answer is ‘yes’, except in certain special cases.