Wagevacancy contracts and multiplicity of equilibria in a directed search model of the labour market

This paper studies a directed search model of the labour market, which is standard in all aspects except two. First, we allow firms to post wagevacancy contracts advertising the number of workers they would pay as well as the payment all will receive. Second, we consider two cases: one where workers are risk neutral and one where workers are risk averse, both in finite and large economies. Our paper shows that when firms post wagevacancy contracts, whether workers are modelled as risk neutral or risk averse matters: the types of symmetric equilibria and the nature of multiplicity of equilibria are different. Somewhat surprisingly, when there are finite numbers of risk-neutral workers and firms, we obtain a finite number of symmetric equilibria, but when workers are risk averse, we obtain a continuum of equilibria. Furthermore, our paper sounds a cautionary note on using large economies as an approximation of finite economies: when workers are risk neutral, the nature of equilibrium is preserved going from a finite to a large economy, but the nature of equilibrium is different when workers are risk averse.