This video explains what subadditivity is. We start with economies of scale for one firm, and then analyse what happens when a second firm enters the market.
Subadditivity is an important concept because it is often used to justify imperfect competition, the classic nemesis of neo-classicists. The only real way to justify less than perfect competition is the kind of sector that lends itself to natural monopolies. Natural monopolies are those where barriers to entry are so high that it is worth making the investment only once, and where one producer will operate more efficiently than two. Traditionally, natural monopolies are state-run, generally in energy or communication sectors, although current trends are leaning towards privatisation.
When a large investment is required in order to begin production, these costs must naturally be passed on to the consumer. What differentiates natural monopolies is that generally, once the investment is made, marginal costs are infinitely small. In these cases, if there is only one company in the market, prices for consumers may actually be lower than if there are rivals, because of the way average costs drop with additional users.
So what exactly is the difference between subadditivity and economies of scale? Subadditivity is a more generic concept which encompasses economies of scale. We say subadditivity exists when the costs function (including initial investment) for the sum of all units at a given level of production is actually smaller than the sum of the various cost functions (given multiple companies) at the same given level.
This is why subadditivity is considered a necessary but insufficient condition for a natural monopoly to be considered optimal, whereas if economies of scale exist, this is a sufficient but not necessary condition for a natural monopoly to be sustainable.
Learn more by reading the dictionary entry.