8. eggs have a supply curve that is linear and upward sloping and a demand curve that is linear and downward…
8. eggs have a supply curve that is linear and upward sloping and a demand curve that is linear and downward sloping. if a 2 - cent - per - egg tax is increased to 3 cents, the deadweight loss of the tax\nanswer\n a. increases by less than 50 percent and may even decline.\n b. increases by exactly 50 percent.\n c. increases by more than 50 percent.\n d. depends on whether supply or demand is more elastic.
Answer
Explanation:
Step1: Recall dead - weight loss formula
The dead - weight loss of a tax ($DWL$) is given by the formula $DWL=\frac{1}{2}t\times\Delta Q$, where $t$ is the tax per unit and $\Delta Q$ is the change in quantity due to the tax. When the tax rate changes, assuming the elasticities of supply and demand remain relatively constant in the short - run, the dead - weight loss is approximately proportional to the square of the tax rate.
Step2: Analyze the percentage change
Let the initial tax be $t_1 = 2$ cents and the new tax be $t_2=3$ cents. The percentage increase in the tax rate is $\frac{t_2 - t_1}{t_1}\times100=\frac{3 - 2}{2}\times100 = 50%$. But since $DWL\propto t^{2}$, if we consider the ratio of the new dead - weight loss $DWL_2$ to the old dead - weight loss $DWL_1$, $\frac{DWL_2}{DWL_1}=\frac{t_2^{2}}{t_1^{2}}=\frac{3^{2}}{2^{2}}=\frac{9}{4}=2.25$. The percentage increase in the dead - weight loss is $\frac{DWL_2 - DWL_1}{DWL_1}\times100=( \frac{9}{4}-1)\times100 = 125%$. So the dead - weight loss increases by more than 50 percent.
Answer:
c. increases by more than 50 percent.