(Advanced analysis)Answer the question on the basis of the following information: The equations for the demand and supply curves for a particular product are P = 10 - .4Q and P = 2 + .4Q,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 + .4Q. Refer to the given information.The efficiency loss of this tax is:

Question

Quizplus · Accepted Answer

The efficiency loss (deadweight loss) of a tax is calculated using the formula for the area of a triangle: 1/2 * base * height. The base of the triangle is the difference in quantity between the pre-tax and post-tax equilibrium, and the height is the tax per unit. To find the pre-tax equilibrium, set the initial demand and supply equations equal to each other: 10 - .4Q = 2 + .4Q. Solving for Q gives Q = 10 units. The pre-tax price is found by substituting Q into either the demand or supply equation, giving P = 6. After the tax, the new supply equation is P = 3 + .4Q. Setting it equal to the demand equation to find the new equilibrium gives 10 - .4Q = 3 + .4Q, solving for Q gives Q = 8.75 units, and the new price paid by consumers is P = 6.5. The tax per unit is the difference between the price received by suppliers (3 + .4*8.75 = 6.5) and the price before the tax, which is 1.5 (6.5 - 5). The base of the triangle (change in quantity) is 1.25 units (10 - 8.75), and the height is the tax of 1.5. Therefore, the efficiency loss is 1/2 * 1.25 * 1.5 = $0.9375 or $62.50 when expressed in units of 100.

(Advanced Analysis)Answer the Question on the Basis of the Following