Final answer:
The deadweight loss of a tax is higher when supply is elastic because producers are more responsive to changes in price and adjust their quantity supplied more significantly. Inelastic supply results in a smaller reduction in quantity supplied and thus a smaller deadweight loss.
Step-by-step explanation:
The deadweight loss of a tax on producers is higher when the supply is elastic. This occurs because elastic supply means that producers are more sensitive to changes in price due to the tax and are more likely to reduce the quantity supplied, leading to a greater loss of efficiency in the market. Conversely, if the supply is inelastic, producers are less responsive to price changes, and thus the quantity supplied does not decrease as much, resulting in a smaller deadweight loss.
It is also important to consider tax incidence, which refers to how the burden of a tax is distributed between buyers and sellers. The distribution of this burden depends on the relative price elasticities of supply and demand. When supply is more inelastic than demand, producers bear a larger share of the tax burden. This increases the cost of production, leading to a decrease in supply and potential deadweight loss.