An optimal tax policy is given using Pontryagin s maximum principle.

Choosing the maximum periodic biomass yield as the manage- ment objective,we investigate the optimal harvesting policies for periodic Gompertz ecosystem with impulsive harvest.

In this paper, we investigate the optimal harvesting problem for a class of linear time-dependent population system with diffusion,prove the existence of the optimal harvesting control, and obtain the necessary condition of optimality and the uniqueness of the optimal control.

Global dynamic state and optimal harvesting effort are obtained.

Theory of optimal taxations mainly deals with the optimal designing of the tax system,while the theory of tax evasion chiefly focuses on the optimal implementation of the government.

An optimal taxation policy is obtained by Pontryagin s maximum prin- ciple.

Providing the government does eventhing to maximize social welfare,how it deals with the optimal taxation issue is discussed in this paper.

Through comparing three situations,in which the optimal order quantity,optimal revenues and supplier\'s wholesale price will be different,it concludes that both supply chain efficiency and purchase price of PEM owner are lowest.