Answer to Question #110814 in Microeconomics for Jzen

Question

If the rise in the price of a bento box from $3 to $5 results in a rise in the demand for “Wakami” from 700 to 800 units, calculate the cross elasticity of demand between the two goods. State the relationship between both goods.

Answer 1

The cross-price elasticity of demand is computed as:$\%Change\; in\; the\; quantity\; demanded\; of\; X/\%Change\; in\; the\; price\; of\; Y$ $\%Change\; in\; the\; quantity\; demanded\; of\; X/\%Change\; in\; the\; price\; of\; Y$

$$E_{xy}=\dfrac{\text{\% Change in the quantity demanded of X}}{\text{\% Change in the price of Y}}$$

Let Wakami be good X and bento box be good Y.

If the demand for Wakami increases from 700 to 800 units as a result of increase in the price of bento box from $3 to $5, then:

$$\text{\% Change in the quantity demanded of X}= \dfrac{800 - 700}{700}\times 100 \approx 14.29\%$$

$$\text{\% Change in the price of Y}= \dfrac{\$5- \$3}{3}\times 100 \approx 66.67\%$$

Therefore:

$$E_{xy}=\dfrac{14.29\%}{66.67\%}\approx 0.214$$

The two goods are substitutes since their cross-price elasticity of demand is positive.