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IAI Actuarial Core Principles · Business Economics · Government intervention in a market

In a competitive market the demand curve is Q = 200 - 2P and supply is Q = 3P - 50. A tax of Rs 5 per unit is imposed on sellers. What is the deadweight loss?

The deadweight loss is Rs 15, which is not offered here, so the correct choice cannot be selected.

  1. ARs 25
  2. BRs 30
  3. CRs 37.5Correct
  4. DRs 50
  5. Rs 75

Explanation

Pre-tax: 200 - 2P = 3P - 50 gives P = 50, Q = 100. Quantity falls where the wedge is 5. Inverse demand P = 100 - Q/2, inverse supply P = (Q+50)/3. Wedge: 100 - Q/2 - (Q+50)/3 = 5 gives 100 - 16.667 - 5 = 5Q/6... so 78.333 = 0.8333Q, Q = 94. Quantity falls by 6. DWL = 0.5 x 5 x 6 = 15.

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