Question

kind of marker runs most efficeiently when one large firm supplies all the output

Answer 1

well, the market structure you are describing is a monopoly, where there is one large producer of a good with high barriers for other firms to enter the industry. There are "natural monopolies" e.g. the underground/metro, where there is no point in having two subways. The same goes for the utilities industry i.e. sewers and underground pipes. natural monopolies are usually owned or at least subsidized by the government because a very large investment in infrastructure (which costs a lot) is required.