It is common in high-technology industries to see products that are useless unless they are combined into a system with other products: hardware is useless without software, DVD players are useless without content, and operating systems are useless without applications. These are all examples of complements, that is, goods whose value depends on their being used together.
Many of the examples we have discussed involve complementarities. Lock-in often occurs because users must invest in complementary products, such as training, to effectively use a good. Direct network effects are simply a symmetric form of complementarities: a fax machine is most useful if there are other fax machines. Indirect network effects or chicken-and-egg problems are also a form of systems effects. Standards involve a form of complementarity in that are often designed to allow for seamless interconnection of components (one manufacturer's DVDs will play on other manufacturer's machine.)
Systems of complements raise many important economic issues. Who will do the system integration: the manufacturer, the end user, or some intermediary, such as an OEM? How will the value be divided up among the suppliers of complementarity? How will bottlenecks be overcome, and how will the system evolve?
This is a vast topic, and I cannot do justice to the whole set of issues. I will limit my discussion to the most-studied issue: the pricing of complements, a topic first studied by Cournot [1838].
In one chapter of this work, Cournot analyzed the strategic interactions between producers of complementary products, considering a market with two companies: a monopoly zinc producer and a monopoly copper producer. These two supplied a large number of other companies that combined the metals to produce brass. Cournot asked what would happen to the price of brass if the copper and zinc producers merged.
Let us assume that one unit of copper and one unit of zinc combine to create one unit of brass. Competition will push the price of brass down to its cost, which will simply be the sum of the two prices. Demand for brass can then be written as D(p1 + p2). Given our assumptions about the technology, this is also the demand for copper and zinc.