Question

chapter 08: aplia homework
now calculate the governments tax revenue if it sets a tax of $0, $4, $8, $10, $12, $16, or $20 per pack. (hint: to find the equilibrium quantity after the tax, adjust the \quantity\ field until the tax wedge equals the value of the per - unit tax.) using the data you generate, plot a laffer curve by using the green points (triangle symbol) to plot total tax revenue at each of those tax levels.
note: plot your points in the order in which you would like them connected. line segments will connect the points automatically.

Explanation:

Step1: Recall tax - revenue formula

Tax revenue = Tax per unit × Quantity sold.

Step2: For tax = $0 per pack

Since tax per unit = 0, Tax revenue = 0×Quantity = 0.

Step3: For other tax levels

We need to find the equilibrium quantity after the tax. This usually involves using supply - and - demand equations (not given here, but conceptually we adjust the quantity until the tax wedge equals the per - unit tax). Let's assume we have a demand function $D(p)$ and a supply function $S(p)$. After a tax $t$ is imposed, the price consumers pay is $p_d$ and the price producers receive is $p_s$ such that $p_d−p_s=t$. We find the quantity $Q$ at which this holds. Then tax revenue = $t\times Q$.
For example, if after setting a tax of $4 per pack, we find the equilibrium quantity $Q_1$, then tax revenue = $4\times Q_1$. We repeat this process for tax levels of $8, 10, 12, 16, 20$ per pack.

Step4: Plotting the Laffer curve

We take the tax per pack values on the x - axis and the corresponding total tax revenue values on the y - axis. Plot the points (0,0) for tax = $0, (4, Tax\ revenue\ at\ t = 4), (8, Tax\ revenue\ at\ t = 8), (10, Tax\ revenue\ at\ t = 10), (12, Tax\ revenue\ at\ t = 12), (16, Tax\ revenue\ at\ t = 16), (20, Tax\ revenue\ at\ t = 20)$ using the green points (triangle symbol) and connect them to form the Laffer curve.

Answer:

The tax revenues need to be calculated for each tax level ($0, 4, 8, 10, 12, 16, 20$ per pack) using the formula Tax revenue = Tax per unit×Quantity (after finding the post - tax equilibrium quantity) and then plotted to form the Laffer curve. Without specific supply and demand functions, we cannot give numerical values for the tax revenues.