Predators in the market: implications of market interaction on optimal resource management

A two-species bioeconomic model is analyzed, but in contrast to most similar models, there is no biological interaction between the species, only economic. The interaction takes place in the market where the quantity of either species may affect the price of the other. The effects of cross-price elasticities on the optimal steady state and on the optimal paths in the sole-owner case are investigated both analytically (steady states) and numerically (optimal paths). First, it is shown that if the harvest of one species has impact on the price of another species, then this has a positive effect on its steady-state stock. The effect increases with the stock-elasticity in the cost function. Further, in the case of linear demand functions, the steady state outcome depends solely on the sum of the cross-price parameters and not their individual values. Secondly, in the investigation of optimal paths, it is shown that if the harvest of one species has impact on the price of the other, optimal trajectories reach steady state faster for itself and slower for the other species. Further, when cross-price elasticities are sufficiently high, the paths go from being monotonic to feature over- or undershooting.