If the absolute value of the price elasticity of demand for good X is 0.5, then a 10% decrease in the price of good X will result in which of the following?

Question

BlackTom AI · Accepted Answer

First, restating the scenario: the absolute value of the price elasticity of demand for good X is 0.5, which means demand is inelastic. A 10% decrease in price is given, and we examine its effects on quantity demanded and revenue.
Option 1: 'A 5% decrease in the quantity demanded of Good X' This is clearly incorrect because a decrease in price, all else equal, leads to an increase—not a decrease—in quantity demanded when there is any positive slope in the demand curve. With elasticity inelastic (|E| = 0.5), the quantity demanded will rise, albeit by a smaller percentage than the price fall.
Option 2: 'A 5% increase in revenues from the sale of Good X' This confuses the quantity effect with total revenue. While quantity demanded increases by 5% (since elasticity is 0.5 and price falls 10%), total revenue does not necessarily rise by 5%. Because demand is inelastic, a price drop reduces revenue overall, so revenue is not increasing by 5%.
Option 3: 'A 5% increase in the quantity demanded of Good X' This matches the elasticity calculation: percentage change in quantity demanded = elasticity × percentage change in price = 0.5 × (−10%) = −5% for price and +5% for quantity. The sign convention shows quantity rises by 5% when price falls by 10%, which is consistent with the definition of elasticity for a downward price movement.
Option 4: 'A 10% decrease in revenues from the sale of Good X' This statement concerns revenue, and the magnitude could be plausible given inelastic demand, but the exact percentage requires combining price and quantity effects. With a 10% price drop and a 5% quantity increase, total revenue changes by −10% + 5% = −5%. So the revenue decrease is 5%, not 10%. Therefore this option overstates the revenue decline.
Option 5: 'A 10% increase in revenues from the sale of Good X' This is inconsistent with the inelastic demand scenario and the computed revenue effect, which shows revenue falling, not rising, when price falls by 10% and quantity rises by only 5%.
In summary, the key ideas are: an elastic value less than 1 means price decreases reduce total revenue, the quantity increases by half the percentage change in price when elasticity is 0.5, and the net revenue effect combines both changes. The only option that correctly reflects the direction of the quantity change is the 5% increase in quantity demanded, while revenue would actually fall by 5% under these numbers.

If the absolute value of the price elasticity of demand for good X is 0.5, then a 10% decrease in the price of good X will result in which of the following?单项选择题

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