The idea of the 'natural' rate of unemployment has been with us since Friedman (i 968). This can be interpreted simply as an assertion of the long-run homogeneity of the Walrasian or flexible-price IS-LM system in prices (see e.g. Sargent (I979), p. 325). Over the last ten years, however, attempts have been made to model the 'natural' rate explicitly, following the original Friedman/Phelps idea that it could be thought of as the equilibrium rate of unemployment in a search framework. Although the main focus of attention, especially on the empirical side, has been on the determinants of the equilibrium rate and changes in this rate (see Johnson and Layard, I 984) it was soon recognised that in a search environment the equilibrium rate may not be efficient. This point was made by Tobin (I972), among others, who said: 'The external effects are the familiar ones of congestion theory. A worker deciding to join a queue or stay in one considers the probabilities of getting a job, but not the effects of his decision on the probabilities that others face... external effects also occur in the decisions of employers whether to fill a vacancy with the applicant at hand or to wait for someone more qualified.' Recent papers by Diamond and Pissarides (see Diamond, I 98 I, I 982; Pissarides, I983, I984) have attempted to model these external effects in a stochastic matching model that can be described briefly as follows. There are a number of jobs and workers, who are paired by a stochastic matching process. The number of jobs (or workers) may be fixed or determined by free-entry conditions. Once a job and worker are paired, the productivity of the match is determined by random draw, and the partners must decide whether to accept or reject it. There are potentially three margins of decision-making in this type of model; the decision to enter (or exit) the market, the choice of lowest acceptable (reservation) productivity, and the choice of search or advertising intensity. It has been shown that individual decision-making at each of these three margins may be socially inefficient. What these inefficiencies have in common, as Pissarides (i 983) makes clear, is that they are all due to external effects that work through the matching technology; that is, when individuals choose to enter a market, accept a match, or search more intensively, they ignore the impact of their decisions on the matching probabilities of other agents in the market. One important limitation of the Diamond-Pissarides model is that both firms and workers are assumed homogeneous. We show in this paper that if this