Market Power and Separating Equilibrium in Job Market Signaling

The job market signaling model in Spence~(1973) deals with a situation of asymmetric information. Workers vary in their productivity. A worker is privately informed of his productivity but the firms are not informed. Spence~(1973) shows that in competitive markets, costly education may signal productivity -- workers of different productivities take up education to varying degrees, thereby resulting in a separating equilibrium where firms can infer a worker's productivity from his education choice. The importance of a separating equilibrium is that it resolves the informational asymmetry. In this paper, I enquire into the relationship between the firm's market power in the labour market (the market that is the source of asymmetric information) and the existence of separating equilibria. I show that a separating equilibrium exists, and therefore the informational asymmetry may be resolved, if and only if the market power of the firm in the labour market is not above a particular threshold