The only way for this cooperation to occur, and thus the only way to realize the productivity of specialization, is through exchange. If you can exchange only with those in a small village, your ability to specialize productively is extremely limited. The more limited the market, the more limited the productive potential of specialization. The link between specialization and the size of the market provides another explanation of the importance of market cooperation based on private property and voluntary exchange. Cooperation is possible without markets, at least without markets as we normally think of them.
Family members cooperate on the basis of intimate knowledge and shared concerns.
Members of small firms can work cooperatively in response to a common objective and peer pressures. The same can be said for churches, clubs, and other relatively small social organizations. The cooperation within families, firms, and social organizations can be explained as the result of exchange relationships. But such relationships, because they depend on personal association and common objectives, are limited to relatively small groups. A key to the productivity of the market is that it greatly extends the range of cooperation, and therefore greatly increases our ability to specialize productively.