Final answer:
The deadweight loss of a tax on producers is higher when supply is inelastic because producers cannot easily change their production levels, and higher when demand is elastic because consumers significantly reduce their quantity demanded.
Step-by-step explanation:
The deadweight loss of a tax on producers is higher when supply is inelastic, and the deadweight loss of a tax is higher when demand is elastic. This is because the deadweight loss, which is the loss of economic efficiency when the equilibrium outcome is not achieved, is affected by the elasticity of both supply and demand. Tax incidence and the resulting deadweight loss depend on how the burden of a tax is distributed between consumers and producers, which in turn depends on the relative elasticities of demand and supply.
When supply is inelastic, producers are less responsive to changes in price due to a tax, meaning the quantity supplied does not decrease significantly with an increase in price, which leads to a higher deadweight loss. On the other hand, when demand is elastic, consumers are very responsive to changes in price; thus, when a tax increases the price, the quantity demanded drops significantly, creating a larger deadweight loss. It's important to note that when either supply or demand is perfectly inelastic or perfectly elastic, the deadweight loss can be zero or infinite respectively. However, in real-world scenarios, we usually deal with less extreme elasticity situations.