A fall in the price of X from $12 to $8 causes an increase in the quantity of Y demanded from 900 to 1,100 units. What is the cross elasticity of demand between X and Y?

• A. 2
• B. -2
• C. -0.5
• D. 0.5

Answer: (C)

Cross elasticity of demand measures how the quantity demanded of one good responds to a price change of another good. It’s the percentage change in Qy divided by the percentage change in Px. To avoid distortions from the base, use the midpoint method for the percentage changes.

Change in Qy is 1100 − 900 = 200. The midpoint for Qy is (900 + 1100)/2 = 1000, so the percentage change in Qy is 200/1000 = 0.20 (20%).

Change in Px is 8 − 12 = −4. The midpoint for Px is (12 + 8)/2 = 10, so the percentage change in Px is −4/10 = −0.40 (−40%).

Cross elasticity = 0.20 / (−0.40) = −0.5.

The negative sign indicates X and Y are complements (a lower price of X raises demand for Y), and the magnitude 0.5 shows the response is modest. Using the midpoint method yields this value, whereas other bases would give a different percentage change and a different result.