True or false?
The correct answer is true. The free market output would be the socially optimal output in the sense that the marginal gain from either expansion or contraction of output would be less than the marginal cost. Equation of private costs and benefits with the corresponding social costs and benefits would be sufficient to ensure that it would be in the interests of private individuals to do what is in the social interest. There would be no benefits or costs external to those received or paid by private individuals going about their business. Note that this includes both consumption and production externalities.
Nothing is said here about the distribution of income because we are using the term efficiency rather than the term welfare. Efficiency is one dimension of society's welfare. The other dimension involves the appropriateness of the distribution of income. When we say that the economy is producing the socially optimal output we mean that it is doing so, given the distribution of income. It would be more correct to say that the economy is producing "a" socially optimal output rather than "the" socially optimal output, since if the distribution of income were changed the socially optimal (and free market) output would also change. As long as the conditions specified in the question hold, the socially efficient and free market outputs will be the same. Making statements about whether a particular distribution of income is desirable implies value judgments and is beyond the scope of economic analysis.