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IAI Actuarial Core Principles · Business Economics · How competitive markets operate

Demand is P = 120 - 2Q and supply is P = 30 + Q (P in rupees). The government imposes a per-unit tax of Rs 15 on sellers. What is the deadweight loss of the tax?

The deadweight loss is Rs 37.5. The tax raises the supply curve by 15, cutting equilibrium quantity from 30 to 25. The lost trade forms a triangle with base 5 units and height Rs 15, so the loss is 0.5 x 5 x 15 = 37.5.

  1. ARs 37.5Correct
  2. BRs 75
  3. CRs 112.5
  4. DRs 225
  5. Rs 450

Explanation

Before tax: 120 - 2Q = 30 + Q gives Q = 30. With tax, the supply price is 45 + Q, so 120 - 2Q = 45 + Q gives Q = 25. Quantity falls by 5. DWL = 0.5 x 15 x 5 = 37.5. Option 2 uses the full tax revenue-type base of 15 x 25 = 375 halved, and option 1 omits the half.

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