Answer) The tax burden is inversely related to the elasticity. Since the elasticity of demand is inelastic. The entire tax burden falls upon the consumer. The producer doesn't pay tax on the production of the cigrette. Whereas the consumer borne the entire tax burden. This is the best example of an indirect tax.
Answer 2) No, there exist a dead weight loss. Which indicates a loss for the society. As the entire loss of the consumer is captured by the producer. When the demand is inelastic, there is no dead weight loss.
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