Butter mountains, milk lakes and optimal price limiters

It is known that simple price limiters may have unexpected consequences in irregular commodity price fluctuations between bull and bear markets and complicated impacts on the size of buffer stocks. In particular, imposing a lower price boundary may lead to a huge buffer stock, e.g. to a 'butter mountain' or a 'milk lake' and this is a real problem for regulators since storage costs may become impossible to finance over time. The relation between price limiters and the size of buffer stocks is nontrivial and there may exist some optimal price limiters which require only weak market interventions and thus provide a rather inexpensive option to regulate commodity markets. In this article, we use a simple commodity market model to explore the relation between price limiters and the average growth rate of the buffer stocks. It is found that these optimal price limiter levels are simply the minimum values of unstable periodic orbits of the underlying deterministic system.