Questions: Relationship between tax revenues, deadweight loss, and demand elasticity The government is considering levying a tax of 30 per unit on suppliers of either jeans or allergy medication. The supply curve for each of these two goods is identical, as you can see on each of the following graphs. The demand for jeans is shown by DJ (on the first graph), and the demand for allergy medication is shown by DA (on the second graph). Suppose the government taxes jeans. The following graph shows the annual supply and demand for this good. It also shows the supply curve (S + Tax) shifted up by the amount of the proposed tax (30 per pair). On the following graph, use the green rectangle (triangle symbols) to shade the area that represents tax revenue for jeans. Then use the black triangle (plus symbols) to shade the area that represents the deadweight loss associated with the tax.

Relationship between tax revenues, deadweight loss, and demand elasticity

The government is considering levying a tax of 30 per unit on suppliers of either jeans or allergy medication. The supply curve for each of these two goods is identical, as you can see on each of the following graphs. The demand for jeans is shown by DJ (on the first graph), and the demand for allergy medication is shown by DA (on the second graph).

Suppose the government taxes jeans. The following graph shows the annual supply and demand for this good. It also shows the supply curve (S + Tax) shifted up by the amount of the proposed tax (30 per pair).

On the following graph, use the green rectangle (triangle symbols) to shade the area that represents tax revenue for jeans. Then use the black triangle (plus symbols) to shade the area that represents the deadweight loss associated with the tax.

Transcript text: Relationship between tax revenues, deadweight loss, and demand elasticity The government is considering levying a tax of $\$ 30$ per unit on suppliers of either jeans or allergy medication. The supply curve for each of these two goods is identical, as you can see on each of the following graphs. The demand for jeans is shown by $D_{J}$ (on the first graph), and the demand for allergy medication is shown by $\mathrm{D}_{\mathrm{A}}$ (on the second graph). Suppose the government taxes jeans. The following graph shows the annual supply and demand for this good. It also shows the supply curve ( S + Tax) shifted up by the amount of the proposed tax ( $\$ 30$ per pair). On the following graph, use the green rectangle (triangle symbols) to shade the area that represents tax revenue for jeans. Then use the black triangle (plus symbols) to shade the area that represents the deadweight loss associated with the tax.

Solution

Solution Steps

Step 1: Understanding the Problem

The government is considering a $30 per unit tax on suppliers of jeans. The supply curve shifts up by the tax amount, and we need to identify the tax revenue and deadweight loss on the graph.

Step 2: Identifying the Supply and Demand Curves

The graph shows the original supply curve (Supply) and the new supply curve after the tax (S+Tax). The demand curve is labeled as $ D_j $.

Step 3: Determining the Equilibrium Points

Identify the initial equilibrium point where the original supply curve intersects the demand curve. Then, identify the new equilibrium point where the new supply curve (S+Tax) intersects the demand curve.

Step 4: Calculating Tax Revenue

Tax revenue is represented by the area of the rectangle formed by the new equilibrium quantity and the vertical distance between the original supply curve and the new supply curve (which is the tax amount, $30).

Step 5: Calculating Deadweight Loss

Deadweight loss is represented by the area of the triangle formed between the original supply curve, the new supply curve, and the demand curve. This area represents the loss in total surplus due to the tax.