The present paper has two aims. The first one concerns primarily an issue of method. I set up and analyse an explicitly stochastic model of the optimal behaviour of a firm, which recruits from a search labour market. The second aim of my paper concerns very much an issue of substance in economics. I show that when the firm is not allowed to decrease its money wage, its optimal response to lower unemployment is to increase its wage, if a plausible (and testable) condition with regard to its expected horizon is met. Hence search theory predicts the existence of a micro Phillips relation under plausible assumptions.