If demand is perfectly inelastic, a tax imposed will be borne entirely by the consumer. Perfectly inelastic demand means that the quantity demanded does not change at all in response to a change in price. In this case, the consumers are not able to substitute the taxed product for another product, so they will have to pay the entire amount of the tax. The producer will not bear any of the tax burden because they cannot pass on any of the tax to the consumers through price increases, as the consumers are already willing to pay the original price for the same quantity of the product.
For example, if a government imposes a tax on insulin (a life-saving drug for people with diabetes), and the demand for insulin is perfectly inelastic, the consumers will continue to buy the same amount of insulin at the same price, even with the tax. Therefore, the entire burden of the tax will fall on the consumers, who will have to pay more for the same amount of insulin. The producer will not be affected because they can still sell the same amount of insulin at the same price, as the demand is perfectly inelastic.