Cross-Price Elasticity of Demand for Substitutes

Steps:

• Subsidy lowers price of X by 5%, so %ΔP_X = -5%.
• Cross elasticity of 0.4 is positive, indicating X and Y are substitutes.
• %ΔQ_Y = cross elasticity × %ΔP_X = 0.4 × (-5%) = -2%.
• Demand for Y decreases by 2%.

Why A is correct:

• Cross-price elasticity formula (%ΔQ_Y = E_{XY} × %ΔP_X) directly calculates a 2% decrease for substitute goods when the price of X falls.

Why the others are wrong:

• B: Applies full 5% price change without multiplying by elasticity coefficient.
• C: Reverses sign; price drop for substitute reduces Y's demand, not increases it.
• D: Misapplies both sign (should decrease) and magnitude (ignores elasticity of 0.4).

Final answer: A