Final answer:
Statement a is incorrect as taxes can raise revenue without causing deadweight loss in cases of perfectly inelastic demand or supply. Statement b is mostly true, since if there's no taxable transaction, there can't be a tax-imposed deadweight loss, although economic activity may still suffer.
Step-by-step explanation:
Evaluating the two statements concerning taxation and deadweight loss, we find that:
Statement a
A tax that has no deadweight loss cannot raise any revenue for the government. This statement is incorrect. It is possible for a tax to raise revenue without causing deadweight loss, particularly in the case of a perfectly inelastic supply or demand where the quantity bought or sold does not change despite the tax. An example would be the taxation of a life-saving drug that has no substitutes; people will pay the tax without altering their purchasing behavior.
Statement b
A tax that raises no revenue for the government cannot have any deadweight loss. This statement is mostly true. If a tax does not raise any revenue, typically because it has led to a cessation of the taxed activity, then there is no transaction on which to impose a tax, and therefore no deadweight loss from a tax. However, there may still be deadweight loss in terms of forgone economic activity.
The concept discussed is related to Revenue: The Economics of Taxation, where the connection between taxation, government revenue, and economic behavior is analyzed. Notably, the Laffer curve demonstrates that there is an optimal tax rate which maximizes revenue without overburdening taxpayers, hinting that excessive taxation can indeed reduce total revenue.