Optimal Length of Leys in an Area with Winter Damage Problems – Optimal Economic Lengths of Leys

The optimal economic life cycle of grass leys with winter damage problems in northern Norway and the threshold of winter damage before it is profitable to re-seed grasses are investigated. The loss in profit of a sub-optimal strategy compared to an optimal strategy is briefly discussed. An infinite horizon stochastic dynamic programming model including a normally distributed yield process with possibilities for discrete downward jumps is developed. The jump process reflects the sudden drop in production after winter damage. Normally the yield of ley increases the first few years after a year with downward jump, and this dynamic is included in the model. The transition probabilities used in the model are estimated with Monte Carlo simulation. Our result show that, in the case of winter damage of 50% or more compared to fields without winter damage, it is optimal to replace the ley immediately. If the winter damage is limited to 20-40% of the yield of fields without winter damage, the replacement decision depends on the age of the ley and the current yield level. It does not always pay to replace immediately mildly winter damaged fields that are still producing high yields. It does not pay to replace a ley if there has been no winter damage since establishment and if the relative yield level is ‘satisfactory’ at least until the first episode of winter damage occurs.