Wage-vacancy contracts and multiplicity of equilibria in a directed search model of the labour market

y 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 wage-vacancy 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 wage-vacancy 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.