Suppose the price elasticity of demand for a good is . How will the expenditure on the good be affected if there is a 10% increase in the price of the good?
The price elasticity of demand is -0.2, which means the absolute value of elasticity is less than 1. Therefore, the demand for the good is price inelastic.
When price increases by 10%, the quantity demanded decreases by 2% (calculated as: percentage change in quantity = elasticity × percentage change in price = - = -2%). Since the percentage decline in quantity (2%) is less than the percentage increase in price (10%), the good is price inelastic.
According to the relationship between elasticity and expenditure, when demand is price inelastic, the expenditure on the good changes in the same direction as the price change. Therefore, with a 10% increase in price, the total expenditure on the good will increase.
Explanation
The textbook establishes that for price inelastic goods (where |elasticity| < 1), expenditure changes in the same direction as the price change. This is because the percentage change in quantity is less than the percentage change in price. With elasticity of -0.2 and a 10% price increase, quantity falls by only 2%, making demand inelastic. Hence, expenditure increases when price increases.
Solution Steps
Step 1: Identify that elasticity = -0.2 means |e_D| < 1, so demand is price inelastic.
Step 2: Calculate percentage change in quantity = elasticity × percentage change in price = -% = -2%.
Step 3: Apply the rule: for inelastic demand, expenditure changes in the same direction as price change.
Step 4: Conclude that since price increases and demand is inelastic, total expenditure will increase.