** IEoD = (% Change in Quantity Demanded)/(% Change in Income)**

### Calculating the Income Elasticity of Demand

On an assignment or a test, you might be asked "Given the following data, calculate the income elasticity of demand when a consumer's income changes from $40,000 to $50,000". (Your course may use the more complicated Arc Income Elasticity of Demand formula. If so you'll need to see the article on Arc Elasticity)Using the chart on the bottom of the page, I'll walk you through answering this question.The first thing we'll do is find the data we need. We know that the original income is $40,000 and the new price is $50,000 so we have Income(OLD)=$40,000 and Income(NEW)=$50,000. From the chart we see that the quantity demanded when income is $40,000 is 150 and when the price is $50,000 is 180. Since we're going from $40,000 to $50,000 we have QDemand(OLD)=150 and QDemand(NEW)=180, where "QDemand" is short for "Quantity Demanded". So you should have these four figures written down:

**Income(OLD)=40,000
Income(NEW)=50,000
QDemand(OLD)=150
QDemand(NEW)=180**

To calculate the price elasticity, we need to know what the percentage change in quantity demand is and what the percentage change in price is. It's best to calculate these one at a time.

### Calculating the Percentage Change in Quantity Demanded

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:

**[180 - 150] / 150 = (30/150) = 0.2**

So we note that **% Change in Quantity Demanded = 0.2** (We leave this in decimal terms. In percentage terms this would be 20%) and we save this figure for later. Now we need to calculate the percentage change in price.

### Calculating the Percentage Change in Income

Similar to before, the formula used to calculate the percentage change in income is:
**[Income(NEW) - Income(OLD)] / Income(OLD)**

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

**[50,000 - 40,000] / 40,000 = (10,000/40,000) = 0.25**

We have both the percentage change in quantity demand and the percentage change in income, so we can calculate the income elasticity of demand.

### Final Step of Calculating the Income Elasticity of Demand

We go back to our formula of:
** IEoD = (% Change in Quantity Demanded)/(% Change in Income)**

We can now fill in the two percentages in this equation using the figures we calculated earlier.

** IEoD = (0.20)/(0.25) = 0.8**

Unlike price elasticities, we do care about negative values, so *do not drop the negative sign if you get one*. Here we have a positive price elasticity, and we conclude that the income elasticity of demand when income increases from $40,000 to $50,000 is 0.8.

### How Do We Interpret the Income Elasticity of Demand?

Income elasticity of demand is used to see how sensitive the demand for a good is to an income change. The higher the income elasticity, the more sensitive demand for a good is to income changes. A very high income elasticity suggests that when a consumer's income goes up, consumers will buy a great deal more of that good. A very low price elasticity implies just the opposite, that changes in a consumer's income has little influence on demand.Often an assignment or a test will ask you the follow up question "Is the good a luxury good, a normal good, or an inferior good between the income range of $40,000 and $50,000?" To answer that use the following rule of thumb:

- If IEoD > 1 then the good is a Luxury Good and Income Elastic
- If IEoD < 1 and IEOD > 0 then the good is a Normal Good and Income Inelastic
- If IEoD < 0 then the good is an Inferior Good and Negative Income Inelastic

**Next: Cross-Price Elasticity of Demand**

## Data

Income | Quantity Demanded |

$20,000 | 60 |

$30,000 | 110 |

$40,000 | 150 |

$50,000 | 180 |

$60,000 | 200 |