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

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

The deadweight loss is Rs 75. The tax cuts quantity from 70 to 60 units, a fall of 10, and the wedge between buyer and seller prices is Rs 15, so the loss triangle is half of 15 times 10.

  1. ARs 112.50Correct
  2. BRs 225
  3. CRs 337.50
  4. DRs 450
  5. Rs 75

Explanation

Original equilibrium: 120 - P = 2P - 30 gives P = 50, Q = 70. With tax, seller price Ps and buyer price Pb = Ps + 15: 120 - (Ps+15) = 2Ps - 30 gives 135 = 3Ps, Ps = 45, Q = 60. Quantity falls by 10. DWL = 0.5 x 15 x 10 = Rs 75. Recheck: Qd = 120 - 60 = 60 and Qs = 90 - 30 = 60, so Q = 60 and DWL = Rs 75. The key is therefore Rs 75.

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