On the optimality of a normal forest with multiple land classes

Abstract

We analyze a discrete time forestry model with nonlinear utility and any number of forest age and land classes. It is shown that under discounting, this model possesses a cyclical stationary state instead of an even flow of timber. The cycle length in timber flow equals the least common multiple of the rotation lengths of the various land classes. The cycle structure is dependent on the initial age-class allocation. As the discount factor approaches unity, the cyclicality in total timber harvest vanishes, but the forest age-class structure may not approach a normal forest in any land class. An aggregate even timber flow is associated with a normal forest in each land class only if there does not exist any pair of land classes with rotation periods having a common divisor greater than one.