A demand function is given by the equation Q=107-4P. Suppose the price is P=12. At this price,...

Question:

A demand function is given by the equation Q=107-4P. Suppose the price is P=12. At this price, find the price elasticity of demand. USE THE POINT SLOPE METHOD to find this elasticity. Hint: You'll have to find the quantity at this price as well. Round your answer to the nearest tenth.

Price Elasticity of Demand:

When the price elasticity of demand is larger than one in absolute terms, demand is elastic. When facing elastic demand, a firm can increase total revenue by lowering price.

Answer and Explanation:

Using the point slope method, the price elasticity, we first compute the quantity demanded at the price P = 13, which is:

  • Q = 107 - 4 * 12
  • Q = 59

Then the price elasticity of demand is:

  • {eq}\dfrac{dQ}{dP}\dfrac{P}{Q} = (-4) * \dfrac{12}{59}\\ = -0.81 {/eq}

That is, the price elasticity of demand is -0.81.


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