If the government imposes an excise tax in a market in which the demand curve is perfectly inelastic, the burden of the tax will fall completely on consumers and the deadweight loss will equal zero.
The deadweight loss depends on both the inelasticity of supply and demand. If either of them is perfectly inelastic, the deadweight loss will become zero.
The burden of tax can fall on consumers or on producers depending on which curve is more inelastic. If the demand curve is more inelastic, the tax burden will far more on the consumer. In the given case, the demand curve is perfectly in elastic, so the entire burden of the tax will fall on the consumer.
However, if the supply curve is more inelastic, the tax burden will fall more on the producer.
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