Question

consider the deadweight loss generated in each of the following cases: no tax, a tax of $8 per pack, and a tax of $16 per pack. on the following graph, use the black curve (plus symbols) to illustrate the deadweight loss in these cases. (hint: remember that the area of a triangle is equal to 1/2 x base x height. in the case of a deadweight loss triangle found on the graph input tool, the base is the amount of the tax and the height is the reduction in quantity caused by the tax.) as the tax per pack increases, deadweight loss _

Explanation:

Step1: Recall dead - weight loss formula

The formula for the area of a triangle is $A=\frac{1}{2}\times base\times height$. In the context of dead - weight loss, the base is the tax amount and the height is the reduction in quantity due to the tax.

Step2: Analyze no - tax case

When there is no tax ($t = 0$), the base of the dead - weight loss triangle is $0$. Using the area formula $A=\frac{1}{2}\times0\times h=0$. So the dead - weight loss is $0$.

Step3: Analyze $t = 8$ case

Let's assume we know the reduction in quantity $\Delta Q_1$ due to the $\$8$ tax. The dead - weight loss $DWL_1=\frac{1}{2}\times8\times\Delta Q_1 = 4\Delta Q_1$.

Step4: Analyze $t = 16$ case

Let's assume the reduction in quantity due to the $\$16$ tax is $\Delta Q_2$. The dead - weight loss $DWL_2=\frac{1}{2}\times16\times\Delta Q_2=8\Delta Q_2$.
As the tax per pack increases, the dead - weight loss increases. This is because the base of the dead - weight loss triangle (the tax amount) is increasing, and assuming the height (reduction in quantity) is non - zero and often increases with the tax amount as well, the area of the dead - weight loss triangle (dead - weight loss) increases.

Answer:

Increases