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IAI Actuarial Core Principles · Business Economics · Relationship between the government and the individual firm

A monopolist faces linear demand P = 100 - Q and has constant marginal cost of Rs 20. The government imposes a lump-sum tax of Rs 500 per period. What happens to the profit-maximising price and output, and why?

Price and output are unchanged at Rs 60 and 40 units. A lump-sum tax is a fixed cost that does not alter marginal cost or marginal revenue, so the profit-maximising point stays the same; only profit falls, from Rs 1,600 to Rs 1,100.

  1. APrice rises and output falls, because the tax raises marginal cost
  2. BPrice and output are unchanged, because a lump-sum tax does not alter marginal cost or marginal revenueCorrect
  3. CPrice falls and output rises, to spread the tax
  4. DOutput falls to zero because profit is reduced
  5. Price rises by Rs 500 divided by output

Explanation

MR=100-2Q equals MC=20 gives Q=40 and P=60. Profit before tax is 40x40=1,600; after the lump sum it is 1,100, still positive. The tax is a fixed cost so MC and the optimum are unchanged in the short run.

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