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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business

For the demand function q = 500/p (p > 0), what is the point price elasticity of demand (in absolute value) at any price?

For q equal to 500 divided by p, the derivative is minus 500 over p squared. Multiplying by p over q, which is p squared over 500, gives an absolute value of 1. The demand curve is a rectangular hyperbola with unit elasticity at every price.

  1. AEqual to p
  2. BEqual to 1Correct
  3. CEqual to 500
  4. DEqual to 0

Explanation

dq/dp = −500/p². Elasticity = |(−500/p²)·(p/q)| = (500/p²)·p·(p/500) = 1. So demand has unit elasticity at every price. Choosing 500 confuses the constant with elasticity.

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