Consider a perfectly competitive market with market supply $Q ^ { s } = - 2 + P$ and market demand $Q ^ { d } = 30 - P$. Suppose the government imposes an excise tax of $\$ 4$ per unit on this market.
What is the deadweight loss from this tax?
A) 2
B) 4
C) 6
D) 8

Question

Quizplus · Accepted Answer

To find the deadweight loss (DWL) from the tax, we first need to determine the equilibrium price and quantity without the tax, and then find the new equilibrium with the tax. Without the tax, setting $Q^s = Q^d$ gives:$$-2 + P = 30 - P$$Solving for $P$ gives $P = 16$, and thus $Q = 30 - 16 = 14$.With a \$4 tax, the supply curve shifts up by 4 units, so the new supply equation becomes $Q^s = -2 + P - 4$, or $Q^s = -6 + P$. Setting the new $Q^s$ equal to $Q^d$ gives:$$-6 + P = 30 - P$$Solving for $P$ gives $P = 18$, but this is the price paid by consumers. The price received by producers is $P - 4 = 14$, and the quantity traded is $Q = 30 - 18 = 12$.The deadweight loss is the loss in total surplus, represented by the triangle formed between the original and new quantity and the original supply and demand curves. The base of the triangle is the difference in quantity (14 - 12 = 2), and the height is the tax (\$4). The area of this triangle, which represents the DWL, is:$$\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 4 = 4$$

Consider a Perfectly Competitive Market with Market Supply Qs=−2+PQ ^ { s } = - 2 + PQs=−2+P

Consider a Perfectly Competitive Market with Market Supply $Q ^ { s } = - 2 + P$