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IAI Actuarial Core Principles · Business Economics · Impact of advertising on sales and demand

A bank's linear demand for its personal loans is Q = 1,000 - 20P, where P is the interest rate in percent and Q is loans in thousands. An advertising campaign changes demand to Q = 1,200 - 20P. The bank's rate stays at 25%. Which statement is correct?

Quantity rises from 500 to 700 and absolute price elasticity at a 25 percent rate falls from 1.00 to 0.71. The parallel rightward shift keeps the slope at 20 but raises quantity, and point elasticity equals slope times price divided by quantity.

  1. AQuantity rises from 500 to 700 and price elasticity (absolute) at 25% falls from 1.00 to 0.71Correct
  2. BQuantity rises from 500 to 700 and price elasticity at 25% is unchanged at 1.00
  3. CQuantity rises from 500 to 700 and price elasticity at 25% rises from 0.71 to 1.00
  4. DQuantity rises from 500 to 600 and elasticity falls from 1.00 to 0.83
  5. Quantity is unchanged because price is unchanged

Explanation

Before: Q = 1,000 - 500 = 500; elasticity = 20 x 25/500 = 1.00. After: Q = 1,200 - 500 = 700; elasticity = 20 x 25/700 = 0.71. The parallel shift keeps the slope but lowers point elasticity as the quantity rises. Claiming unchanged elasticity ignores the change in quantity.

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