Which of the following statements is consistent with the elasticities given in Table 5-1, if the table shows that the price elasticity of demand for product X is -2.5 and the income elasticity of demand is 0.8?

• A. A 10% increase in the price of product X will lead to a 25% decrease in quantity demanded.
• B. A 10% increase in consumer income will decrease the quantity demanded of product X by 8%.
• C. Product X is an inferior good because its income elasticity is positive.
• D. Demand for product X is inelastic because the price elasticity is greater than -1.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the meaning of price elasticity of demand (PED). It measures the responsiveness of quantity demanded to a change in price. The formula is: \[\text{PED} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}\]
2. Step 2: Use the given price elasticity of demand for product X, which is -2.5. This means that for every 1% increase in price, the quantity demanded decreases by 2.5%. To find the effect of a 10% price increase, multiply 10% by -2.5: \[\% \Delta Q = \text{PED} \times \% \Delta P = -2.5 \times 10\%\]
3. Step 3: Understand the meaning of income elasticity of demand (YED). It measures the responsiveness of quantity demanded to a change in consumer income. The formula is: \[\text{YED} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}}\]
4. Step 4: Use the given income elasticity of demand for product X, which is 0.8. This means that for every 1% increase in income, the quantity demanded increases by 0.8%. To find the effect of a 10% increase in income, multiply 10% by 0.8: \[\% \Delta Q = \text{YED} \times \% \Delta I = 0.8 \times 10\%\]
5. Step 5: Interpret the signs and magnitudes of elasticities: - Since the price elasticity is -2.5 (less than -1), demand is elastic, not inelastic. - Since the income elasticity is positive (0.8), product X is a normal good, not an inferior good. - Use these interpretations to evaluate which statements are consistent with the elasticities given.