Monopoly II: Subadditivity

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 which 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:

That is, 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. If we look at the diagram, we can see the traditional long run costs functions for two companies. We only consider economies of scale when additional units provide a lower average cost, but costs per unit begin to rise after a certain level. Subadditivity simply means that it is cheaper to produce the same production level when only company one is producing, and that the same production level is more expensive when company two joins the market.

 

This is why subadditivity is considered a necessary but insufficient conditionfor 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. The cyan demand curve, within the economy of scale region, indicates a viable natural monopoly. The red line would indicate a non sustainable natural monopoly. The black line indicates the frontier of a profit generating monopoly (which would attract competitors) and the green line indicates a viable duopoly.