Optimal growth with labour market frictions

In this paper, I develop an optimal growth model with labour market frictions in which recruiting efforts are measured in terms of labour instead of output. Specifically, I build an intertemporal framework à la Ramsey in which labour has to be alternatively employed in the production of goods or in the recruitment of workers. Within this setting, assuming that capital is paid according to its marginal productivity, I show that (i) capital measured along its intensive margin may converge towards its stationary value in a non-monotonic manner; (ii) Pareto optimal allocations typical of a centralized economy can also be achieved in a decentralized environment in which the prevailing wage is indexed to the labour market tightness indicator; (iii) the consistency of the wage that implements efficient allocations with the competitiveness of the market for goods relies on vanishing values of the discount rate.