The difference is that there is a bigger size of the deadweight loss when demand and supply are elastic in nature, while deadweight loss is smaller when demand is supply are inelastic. It happens due to the reason of degree of adjustment due to the rise in price. For example, when demand and supply is elastic, the with increase in tax, demand and supply creases more as they opt for the other alternatives. It creates dead weight loss due to the increase in price due to the tax. But, it does not happen the same when demand and supply are inelastic. Here, the size of the adjustment is smaller and DWL is smaller as well.
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