Suppose that over a range of prices, the price elasticity of demand varies from

Question

Suppose that over a range of prices, the price elasticity of demand varies from 15.0 to 2.5. Over another range of prices, the price elasticity of demand varies from 1.5 to 0.75. What can you say about total revenue and the total revenue curve over these two ranges of demand curve as price fall?

Explanation / Answer

Your question is somewhat confusing for me to read, but I will try my best. Remember that price elasticity of demand is dQ/dP. If |dQ/dP| > 1 then demand is price elastic, if |dQ/dP| = 0 then demand is unit elastic, and if |dQ/dP| < 1, demand is price inelastic. Keep in mind I used absolute value, and I have seen many textbooks that do not do this and use/show negatives. If you are in an elastic portion of the demand curve, then small changes in price have big effects in quantity demanded. In other words, lowering your price will raise total revenue and raising your price will lower total revenue. On the opposite end, if you are in an inelastic portion of the demand curve, changes in price don't affect quantity demanded that much. So, raising your price will actually raise total revenue and lowering your price will lower total revenue (what a good place to be!). On the point where demand is unit elastic, MR = 0, which you may use later. Short answer: along 15.0 to 2.5 + falling price means the TR curve will increase and along 1.5 to 0.75 means the TR curve will increase and then decrease (once you pass unit elasticity and go into the inelastic portion) It is so simple. 15.0-2.5 are elastic for sure. An increase price will reduce revenue. 1.5-0.75 will have two range in a linear demand curve,means elastic when price is high, and inelastic when price is low. At low price,it should increase price to raise revenue. And stop when elasticity = 1.

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