Working time reduction and employment in a finite world

We study the consequences of a working time reduction (WTR hereafter) in an exogenous growth model with unemployment (due to efficiency wage considerations) and a renewable natural resource. The resource is an essential input whose marginal productivity is bounded by physical laws. In the laissez-faire equilibrium, firms set headcount employment, working time and a wage level which affects workers' effort. We show that if a WTR always decreases the total number of worked hours, its impact on the number of (un)employed crucially depends on the relative scarcity of the resource. If the ressource inflow is unlimited, the economy converges toward a balanced growth path and a WTR lowers the levels of output, employment and wages along this path, without affecting their growth rate. When the resource inflow is finite, the economy converges toward a stationary state. In this case, a WTR increases the stationary level of hourly wages and employment if the resource is scarce enough (which is for instance the case if the labour and capital saving technical progress is unbounded). Furthermore, the long-term elasticity of employment (resp., of the hourly wage) to the cut in hours is larger (resp., smaller) when the resource is scarcer. The transitory dynamics toward the stationary state is studied numerically. As far as the impact of a WTR on employment and wage are concerned, this analysis confirms the results put forward for the stationary state.