The deadweight loss from a tax is likely to be smallest when

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The question asks when the deadweight loss from a tax is smallest, which hinges on how responsive buyers and sellers are to price changes.
Option 1: 'supply is inelastic and demand is elastic.' If either side is highly inelastic, the quantity traded falls less, but with one elastic and one inelastic side, the tax still distorts quantity noticeably because the more elastic side bears less of the tax burden, leading to a sizable reduction in both producer and consumer surplus depending on elasticities. Overall, deadweight loss tends to be larger when one side is elastic, so this combination is not minimizing DWL.
Option 2: 'supply is inelastic and demand is inelastic.' When both sides are inelastic, quantity demanded and supplied don't respond much to price changes, so the tax causes only a small reduction in quantity from the equilibrium. With minimal quantity change, the lost gains from trade (deadweight loss) are relatively small compared to other configurations. This pairing is associated with the smallest deadweight loss.
Option 3: 'supply is elastic and demand is inelastic.' Here the supply side being elastic means producers are highly responsive to price changes, leading to a larger drop in quantity when a tax raises price for buyers. Since one side is highly responsive, the overall distortion in quantity is amplified, increasing deadweight loss.
Option 4: 'supply is elastic and demand is elastic.' When both sides are highly responsive to price changes, the imposition of a tax causes a sizable decrease in traded quantity, producing a relatively large deadweight loss. Elastic interactions on both sides typically worsen inefficiency.
In summary, the core intuition is that DWL grows with the degree of responsiveness (elasticity) on the sides of the market. If both sides are inelastic, the market moves less in response to the tax, minimizing the distortion in quantity and thus the deadweight loss. Conversely, any elasticity on either side tends to increase DWL, and elasticity on both sides compounds that effect.

ECON1-TTh Chapter 8 Assignment

The deadweight loss from a tax is likely to be smallest when

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