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IAI Actuarial Core Principles · Business Economics · Production, costs, revenue and profit in price and output decisions

A firm sells at a single price and faces a linear downward-sloping demand curve. At its current output the price elasticity of demand (absolute value) is 0.8. Which statement about the firm's position is correct if it wants to maximise profit and has positive marginal cost?

The firm should raise price and cut output. With elasticity below one, marginal revenue is negative, so reducing output increases total revenue and also reduces costs. Profit maximisation with positive marginal cost requires operating on the elastic part of the demand curve.

  1. AIt is at the profit maximum because demand is inelastic
  2. BIt should cut output, because marginal revenue is positive
  3. CIt should raise price and cut output, because marginal revenue is negative and cutting output saves cost while raising revenueCorrect
  4. DIt should lower price to increase total revenue
  5. It should leave output unchanged because MR equals MC when elasticity is below one

Explanation

MR = P(1 − 1/|e|), which is negative when |e| < 1. Cutting output then raises revenue and also lowers cost, so profit rises. A profit-maximiser with positive MC must operate where MR is positive, i.e. on the elastic part of demand. Lowering price would reduce revenue further.

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