The effect of a tax on the market causes the supply curve for the commodity to shift up, with the magnitude of the vertical shift being equal to the per unit tax levied on the commodity. After the tax, at any given product level, there is a wedge between the price received by the supplier of the commodity, which is indicated by the original supply curve, and the price paid by the consumer, which is indicated by the new supply curve. The deadweight loss from the imposition of the tax is the loss in consumer surplus (CS) and producer surplus (PS) that is not accounted for by the increase in tax revenue accruing to the government.

We are told that the supply curve in all four markets is identical and that it is a constant price-elasticity supply curve. We can assume, for example, that it has constant price elasticity of 1, which is a straight line from the origin with a particular slope. We are considering four demand curves passing through the same initial equilibrium point. The first in Market A is a horizontal curve, with infinite price elasticity. The slope of the demand curve then declines in three steps through a value of 3 in Market B and 0.25 in Market C, with the final stage being a vertical demand curve, which has zero price elasticity, in Market D.

Consider first Market A with the horizontal demand curve. When the supply curve shifts up vertically by the amount of the tax, equilibrium price remains the same but quantity demanded declines. There is no loss in CS because with a horizontal demand curve there is no CS. There is, however, a loss in PS that is not made up by government tax revenue collected. The loss is the triangle formed above the original supply curve between the constant equilibrium price, the new equilibrium quantity and the old equilibrium quantity.

Consider now Markets B and C as the demand curve becomes steeper in two stages. We now get both an increase in equilibrium price and a decrease in equilibrium quantity as a result of the upward shift in the supply curve from the imposition of the tax. With the slope of the demand curve being greater in Market C, the increase in price will be larger there than in Market B and the decrease in quantity smaller. Since tax is only collected on yachts actually sold, there is a deadweight loss in both cases involving both lost CS and lost PS. Decreased CS will be a larger portion of overall deadweight loss for market C than for Market B. As the demand curve becomes steeper, however, the overall deadweight loss will be decreasing and tax revenue collections will become an increasing share of lost CS plus PS.

In the final case, Market D, the demand curve is vertical. Now as a result of the tax and the upward shift in the supply curve, only equilibrium price changes. The loss in surplus is the largest of the four cases, being equal to the per unit tax times the constant equilibrium quantity. However, because of the vertical demand curve, the burden is borne totally by consumers in increased price; there is no reduction in PS. Moreover, the loss in CS is precisely offset by increased government revenue so there is no deadweight loss in this case. So, it is in Market D that the deadweight loss will be the smallest.