If demand is perfectly inelastic,the deadweight loss caused by a tax will be zero.

Perfectly Inelastic

Describes a situation in which the quantity demanded of a good does not change regardless of changes in its price.

Deadweight Loss

A loss of economic efficiency that can occur when the equilibrium for a good or service is not achieved or is unachievable.

Tax

A required financial fee or another kind of duty enforced on a taxpayer by government authorities, designed to raise funds for government outlays and a range of public expenses.