The paper considers a two stage capacity and production planning model under uncertainty. The optimal second stage production policy falls into three cases: When capacity is slack the firm will produce with the cost minimizing production rate and adjust the production time to meet its output target. When the capacity constraint is binding, the firm will first adjust the production rate and then again produce with a constant production rate but employ overtime to meet the output target.
The optimal capacity choice of the first stage is determined by the trade off between the sunk costs of slack labor and the expected opportunity costs of adjusting the production rate and employing overtime in the case of a binding capacity constraint.
The key item determining the firm’s labor demand is the overtime premium. The amount of contracted labor strictly increases with the overtime premium and the expected overtime strictly decreases. Since then latter effect dominates the former for small overtime premia, the firm’s labor demand is first decreasing and then increasing with the overtime premium.
A reduction of overtime premia can be Pareto improving because it does not only lead to substantial cost savings but also an increasing labor demand.