This letter studies the economical dispatch problems (EDPs) in islanded microgrid from three aspects: a) whether the global optimal dispatch (GOD) can be achieved through a decentralized manner in a system; (b) if yes, how to achieve the GOD; (c) otherwise, how to obtain a suboptimal alternative. As a result, we arrive a criterion that GOD can be achieved in decentralized manners if and only if optimal solution functions (OSFs) are all strictly monotonically increasing. If a system meets this criterion, a decentralized droop method is proposed to help the system achieve GOD. Otherwise, a modified decentralized method is presented to guarantee the suboptimal dispatch. Both simulation and experiments are performed to validate the proposed methods.