The deadweight loss will be the least when both demand and supply are inelastic.
The deadweight loss depends on both the inelasticity of supply and demand. The more the demand or supply is inelastic, the less will be the deadweight loss. The relation is inversely proportional.
The reason is that the quantity bought or sold varies less with the price. There would be no deadweight loss if demand and supply are perfectly inelastic.
As deadweight loss is directly proportional to the elasticity of supply and demand so it will increase if supply and demand become elastic.
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