Income Elasticity of Demand Formula

For example, let's assume that you've been working hard for the past year, and as a result, your income has increased from $50,000 to $75,000 in a year. When your income has increased, you increase the number of clothes you buy in a year from 30 units to 60 units. What is your income elasticity of demand when it comes to clothes?

To find that out, we need to calculate the percentage change in income and the percentage change in quantity demanded.

When your income increases from $50,000 to $75,000, the percentage change in income is equal to:

\(\%\Delta\hbox{Income} =\frac{75000-50000}{50000} = \frac{25000}{50000}=0.5\times100=50\%\)

The percentage change in quantity demanded is equal to:

\(\%\Delta\hbox{Quantity} =\frac{60-30}{30} = \frac{30}{30}=1\times100=100\%\)

The income elasticity of demand is equal to:

\(\hbox{Income elasticity of demand}=\frac{\%\Delta\hbox{Quantity demanded}}{\%\Delta\hbox{Income}} = \frac{100\%}{50\%}=2\)

Your income elasticity of demand for clothes is equal to 2. That means that when your income increases by one unit, you will end up increasing the quantity demanded that particular good by twice as much.

For example, the number of burgers one consumes when their income rises will most likely drop. Instead, they will consume more healthy and expensive food.

Consider Anna, who has an annual salary of $40,000. She works as a financial analyst in New York City. Anna loves chocolates, and in a year, she consumes 1000 chocolate bars.

Anna is a hardworking analyst, and as a result, she gets promoted the following year. Anna's salary goes from $40,000 to $44,000. In the same year, Anna increased chocolate bars consumption from 1000 to 1300. Calculate Anna's income elasticity of demand for chocolates.

To calculate the income elasticity of demand for chocolates, we have to calculate the percentage change in quantity demanded and the percentage change in income.

The percentage change in quantity demanded is:

\(\%\Delta\hbox{Quantity} =\frac{1300-1000}{1000} = \frac{300}{1000}=0.3\times100=30\%\)

The percentage change in income:

\(\%\Delta\hbox{Income} =\frac{44000-40000}{40000} = \frac{4000}{40000}=0.1\times100=10\%\)

The income elasticity of demand for chocolate bars is:

\(\hbox{Income elasticity of demand}=\frac{\%\Delta\hbox{Quantity demanded}}{\%\Delta\hbox{Income}} = \frac{30\%}{10\%}=3\)

That means that 1% increase in Anna's income will lead to a 3% increase in the consumption of chocolate bars.

Let's consider another example. George is a software engineer who just started working at a company in San Francisco. George makes $100,000 in a year. As George lives in San Francisco, where the living expenses are high, he has to consume a lot of fast food. In a year, George consumes 500 burgers.

The following year, George gets a rise in income from $100,000 to $150,000. As a result, George can afford more expensive food, such as dinners at Steakhouses. Therefore, George's consumption of burgers drops to 250 burgers in a year.

What is the income elasticity of demand for burgers?

To calculate the income elasticity of demand for burgers, let's calculate the percentage change in quantity demanded and the percentage change in George's income.

\(\%\Delta\hbox{Quantity} =\frac{250-500}{500} = \frac{-250}{500}=-0.5\times100=-50\%\)

\(\%\Delta\hbox{Income} =\frac{150000-100000}{100000} = \frac{50000}{100000}=0.5\times100=50\%\)

Income elasticity of demand is equal to:

\(\hbox{Income elasticity of demand}=\frac{\%\Delta\hbox{Quantity demanded}}{\%\Delta\hbox{Income}} = \frac{-50\%}{50\%}=-1\)

That means that when George's income increases by 1%, the amount of burgers he eats will decline by 1%.

Calculate the income elasticity of demand using the midpoint method of a person who experiences an increase in income from $30,000 to $40,000 and changes the number of jackets he buys in a year from 5 to 7.

Let's calculate the midpoint quantity and midpoint income first.

\( Q_m = \frac{Q_1 + Q_2}{2}=\frac{7+5}{2}=6 \)

\( I_m = \frac{I_1 + I_2}{2}=\frac{30000+40000}{2}=35000 \)

Using the income midpoint elasticity of demand formula:

\(\hbox{Midpoint income elasticity of demand}=\frac{\frac{Q_2 - Q_1}{Q_m}}{\frac{I_2 - I_1}{I_m}}\)

\(\hbox{Midpoint income elasticity of demand}=\frac{\frac{7 - 5}{6}}{\frac{40000 - 30000}{35000}}\)

\(\hbox{Midpoint income elasticity of demand}=\frac{\frac{2}{6}}{\frac{10000}{35000}}\)

\(\hbox{Midpoint income elasticity of demand}=\frac{70000}{60000}\)

\(\hbox{Midpoint income elasticity of demand}=1.16\)