# INCOME ELASTICITY OF DEMAND -MEANING AND CALCULATIONS

Income elasticity of demand is defined as the responsiveness of quantity demanded to changes in a consumer's income.

Mathematically, it is expressed as

$YED=\frac{\%∆Q}{\%∆Y}$

Where $\%∆Q$ changes in quantity demanded

$\%∆Y$ is the change in income

Some goods have a positive income elasticity of demand. That is, an increase in income would lead to an increase in the quantity demanded; a decrease in income would lead to a decrease in the quantity demanded

This kind of good is called normal goods. Houses and cars are examples of normal goods.

Others have a negative income elasticity of demand. That is, a decrease in income would lead to an increase in the quantity demanded; an increase in income would lead to a decrease in the quantity demanded.

This kind of good is called an inferior good. A second-hand car is a good example of an inferior good.

When income falls, the consumer will likely buy a second-hand car. When income rise, the consumer will likely buy a new car instead of a second-hand car.

A good is said to be luxurious or superior good if an increase in income is accompanied by a proportionally larger increase in quantity demanded.

This means the coefficient of income elasticity of demand will be greater than one.

Superior or luxurious is some sort of normal goods. They make up a large proportion of an individual income. Cars and jewelry are examples of superior or luxurious goods.

Another kind of normal good is a necessity good. As the name implies, necessity goods are goods that are considered necessary or absolute requisite to a consumer.

The consumer will likely buy them even with an income change, making necessity goods slightly insensitive to income changes.

This means a change in income will cause an insignificant change in the quantity demanded. The coefficient of necessity good is between zero and one, that is, $YED=0–1$

Necessity goods are mainly basic needs like food and houses that the consumer can not do without.

Another special case of income elasticity is neutral or sticky goods. Neutral goods are goods whose demand is not exactly affected by income changes.

That is, income changes do not affect the quantity demand. To illustrate, an asthmatic patient would buy an inhaler even if his income diminishes significantly. To this asthmatic patient, the inhaler is considered neutral good.

It is important to note that cases of neutral goods are very rare.

We have discussed the income elasticity of demand, let's solidify our knowledge of income elasticity by trying this calculation.

#### Example 1

Determine the type of goods involved if a $20\%$ increase in Joshua's income cause a $10\%$ decrease in quantity demanded.

Solution:

Recalled that

$YED=\frac{\%∆Q}{\%∆Y}$

Substituting the value in the formula

$YED=\frac{-10}{20\%}$

Note: Quantity demanded is decreasing, hence the negative sign

$YED=-0.5$

The numerical value of income elasticity of demand is negative, hence, the good is an inferior good

#### Example 2

Deborah's income just rose from €1900 per week to €2100 per week. As a result, Deborah decides to purchase $9\%$ more rice. Calculate the income elasticity of demand.

$YED=\frac{\%∆Q}{\%∆Y}$

percentage change in quantity demanded=$9\%$

Let's solve for the percentage of income using the midpoint method.

Remember $\%∆Y=\frac{Y_1-Y_0}{\frac{Y_1+Y_0}{2}}\times100$

$\%∆Y=\frac{2100-1900}{\frac{2100+1900}{2}}\times100$

$\%∆Y=\frac{200}{2000}\times100$

$\%∆Y=10\%$

Inserting the value

$YED=\frac{9}{10}$

$YED=0.9$

We have a positive income elasticity of demand, hence, rice is a normal good. More specifically, rice is a necessity good.

Remember that necessity good is a type of normal good. Hence all the necessary goods are normal so are luxury and superior goods.

#### Example 3

Daniel's income has just risen from €94,000 per year to €100,060 per week. As a result, his demand for jewelry increased from 94 to 188 pieces of jewelry. Determine

i. his income elasticity of demand for jewelry

ii. the nature of goods jewelry is to Daniel

$Q_1=188$, $Q_0=94$

$\%∆Q=\frac{Q_1-Q_0}{\frac{Q_1+Q_0}{2}}\times100$

$\%∆Q=\frac{188-94}{\frac{188+94}{2}}\times100$

$\%∆Q=\frac{94}{141}\times100$

$\%∆Q=66.67\%$Y_1=188$,$Y_0=94\%∆Y=\frac{Y_1-Y_0}{\frac{Y_1+Y_0}{2}}\times100\%∆Y=\frac{100,060-94,000}{\frac{100,60+94,000}{2}}\times100\%∆Q=\frac{6,060}{97,030}\times100\%∆Q=6.24%YED=\frac{66.7}{6.24}YED=10.7$ii. The numerical value of YED is 10.7, this is greater than 1, hence, jewelry is a luxurious good to Daniel. Related post #### Example 4 Determine the type of goods if a$10\%$decrease in Mark's income leads to a$0\%$increase in the number of inhalers demanded.$YED=\frac{\%∆Q}{\%∆Y}YED=\frac{0}{-10}YED=0\$

To Mark, inhalers is a neutral/sticky goods, because a change in income does not affect the number of inhalers demanded.

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