In this paper, an explicit micro scenario is developed which yields a well-defined aggregate job matching function. In particular, a stochastic model of job-matching behavior is constructed in which the system steady state is shown to be approximated by an exponential-type matching function, as the population becomes large. This steady-state approximation is first derived for fixed levels of both wages and search intensities, where it is shown (without using a free-entry condition) that there exists a unique equilibrium. It is then shown that if job searchers are allowed to choose their search intensities optimally, this model is again consistent with a unique steady state. Finally, the assumption of a fixed wage is relaxed, and an optimal 'offer wage' is derived for employers.