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

Demand is P = 120 - 2Q and supply is P = 20 + 3Q (P in rupees, Q in units). The government imposes a per-unit tax of Rs 25 on sellers. What is the deadweight loss of the tax?

The deadweight loss is Rs 62.50. The tax reduces quantity from 20 to 15 units, a fall of 5. The loss is a triangle with base 5 and height equal to the Rs 25 tax wedge, so 0.5 x 25 x 5 equals 62.5.

  1. ARs 62.50Correct
  2. BRs 125
  3. CRs 187.50
  4. DRs 250
  5. Rs 31.25

Explanation

Pre-tax equilibrium: 120 - 2Q = 20 + 3Q gives Q = 20. With the tax, supply becomes P = 45 + 3Q, so 120 - 2Q = 45 + 3Q gives Q = 15. Quantity falls by 5. Deadweight loss = 0.5 x 25 x 5 = 62.5. Option B forgets the 0.5 factor of the triangle.

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