Introduction

In “The Economic Implications of Learning by Doing,” Professor Arrow (1962) emphasizes that inefficiencies arise if doing generates external effects on the learning of others. That such externalities are pervasive seems obvious. Communication between individuals takes place through the usual channels, and communication between firms occurs when individuals move from one firm to another, or when learning by one firm is transferred to the supplier of a capital good and then embodied in the equipment purchased by another.

In the presence of externalities in learning, inefficiencies arise because for each firm the private benefits of experience are less than the social benefits, leading to underproduction even with perfectly competitive markets. This is why subsidies to “infant” industries may be called for. In fact, the free-rider problem is more severe the greater the number of firms, so there is no presumption that entry is socially beneficial – even with constant returns to scale in production and no cost of entry. Thus, second best policies may include those – like patents – that restrict entry.

The analysis of any such policies requires an understanding of how firms compete in industries where learning occurs. A model of such competition, based on the framework of differential games, is studied below.

The dynamics of a single industry are examined under the assumption that spillovers in learning are complete, that is, that learning is industry-wide.