(Advanced analysis) The equations for the demand and supply curves for a particular product are P = 10 − 0.4 Q and P = 2 + 0.4 Q, where P is price and Q is quantity expressed in units of 100. After an excise tax is imposed on the product, the supply equation is P = 3 + 0.4 Q. The efficiency loss of this tax is

A) $62.5.
B) $125.
C) $87.5.
D) $1.

Question

Divakara Suvarna · Accepted Answer

Final Answer : A, Explanation :  The efficiency loss, or deadweight loss, is calculated as the area of the triangle formed between the original and new supply curves and the demand curve. The base of the triangle is the change in quantity (from equilibrium quantity before tax to after tax), and the height is the tax amount. The equilibrium quantity before tax is found by setting the original demand and supply equations equal: 10 - 0.4Q = 2 + 0.4Q, solving gives Q = 10 (1000 units). After tax, set the demand equation equal to the new supply equation: 10 - 0.4Q = 3 + 0.4Q, solving gives Q = 8.75 (875 units). The change in quantity is 1.25 (125 units), and the tax is $1. The deadweight loss is 0.5 * base * height = 0.5 * 1.25 * 1 = $62.5.

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