** CPEoD = (% Change in Quantity Demand for Good X)/(% Change in Price for Good Y)**

### Calculating the Cross-Price Elasticity of Demand

You're given the question: "With the following data, calculate the cross-price elasticity of demand for good X when the price of good Y changes from $9.00 to $10.00." Using the chart on the bottom of the page, we'll answer this question.We know that the original price of Y is $9 and the new price of Y is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. From the chart we see that the quantity demanded of X when the price of Y is $9 is 150 and when the price is $10 is 190. Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=190. You should have these four figures written down:

**Price(OLD)=9
Price(NEW)=10
QDemand(OLD)=150
QDemand(NEW)=190**

To calculate the cross-price elasticity, we need to calculate the percentage change in quantity demanded and the percentage change in price. We'll calculate these one at a time.

### Calculating the Percentage Change in Quantity Demanded of Good X

The formula used to calculate the percentage change in quantity demanded is:
**[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)**

By filling in the values we wrote down, we get:

**[190 - 150] / 150 = (40/150) = 0.2667**

So we note that **% Change in Quantity Demanded = 0.2667** (This in decimal terms. In percentage terms this would be 26.67%).

### Calculating the Percentage Change in Price of Good Y

The formula used to calculate the percentage change in price is:
**[Price(NEW) - Price(OLD)] / Price(OLD)**

We fill in the values and get:

**[10 - 9] / 9 = (1/9) = 0.1111**

We have our percentage changes, so we can complete the final step of calculating the cross-price elasticity of demand.

### Final Step of Calculating the Cross-Price Elasticity of Demand

We go back to our formula of:
** CPEoD = (% Change in Quantity Demanded of Good X)/(% Change in Price of Good Y)**

We can now get this value by using the figures we calculated earlier.

** CPEoD = (0.2667)/(0.1111) = 2.4005**

We conclude that the cross-price elasticity of demand for X when the price of Y increases from $9 to $10 is 2.4005.

### How Do We Interpret the Cross-Price Elasticity of Demand?

The cross-price elasticity of demand is used to see how sensitive the demand for a good is to a price change of another good. A high positive cross-price elasticity tells us that if the price of one good goes up, the demand for the other good goes up as well. A negative tells us just the opposite, that an increase in the price of one good causes a drop in the demand for the other good. A small value (either negative or positive) tells us that there is little relation between the two goods.Often an assignment or a test will ask you a follow up question such as "Are the two goods complements or substitutes?". To answer that question, you use the following rule of thumb:

- If CPEoD > 0 then the two goods are substitutes
- If CPEoD =0 then the two goods are independent (no relationship between the two goods
- If CPEoD < 0 then the two goods are complements

If you'd like to ask a question about elasticity, microeconomics, macroeconomics or any other topic or comment on this story, please use the feedback form.