Liquidity and the Simple Io of Stock Exchanges

It is usually thought that network externalities, which are inherent to liquidity, make it desirable to concentrate transactions in one stock exchange. This paper shows that when the value of liquidity stems from the ability to potentially reach as many traders as possible, the market is integrated when every broker meets every other broker in at least one exchange. Thus, fragmentation is not about trades being executed in different exchanges but of connectedness among brokers.An implication of this distinction is that in an integrated market the network externality created by liquidity becomes pecuniary and the optimal number of exchanges depends only on the shape of the (physical) technology to execute trades - whether it exhibits increasing, constant or decreasing returns to scale - as in any standard industry.We characterize the planner's allocation and compare it with that reached by a monopoly. It is shown that when exchanges are natural monopolies a particular ownership structure of the exchange and allocation of voting rights over the exchange fee achieve the planner's optimum.With decreasing returns to scale the Walrasian allocation is efficient, provided that the market is integrated. Nevertheless, with few exchanges the price-taking assumption is suspect. If exchanges are not price takers, there are many other equilibria, all of them inefficient. Moreover, there are reasons to doubt that the market will become integrated. Fragmentation softens price competition between exchanges and may help a monopolist exchange to erect a barrier to entry even when he has no cost advantage