If the government can regulate and control bitcoin, of course the bitcoin can improve the economy of a country. Many benefits if that happens, no administrative costs are required, although there is still transaction fees, and of course taxes from bitcoin transactions can improve the economy of a country.
If that happens to bitcoin, then the government also could benefits on this.
Not only bitcoin can improved our economy but it could contribute a lot if it will happen that the government have take a share on it. But if not, then bitcoin have nothing to share with, that's why more countries are legalized this in order to earned some benefits.