Income Elasticity of Demand Formula

Imagine that the past year you have been working quite hard, and as a result, your boss told you that you got a 10% increase in income. Until then, you were skipping many dinners at steakhouses with friends and colleagues. Instead, you consumed more burgers and more affordable food. When your income changes, would you consume the same amount of burgers? What about dinners at steakhouses? Most probably, you will. But by how much? To find that out, you'll have to use the income elasticity of demand formula.

Income Elasticity of Demand Formula Income Elasticity of Demand Formula

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    The income elasticity of demand formula will show how much you will change the consumption of steaks and burgers, but not only. The income elasticity of demand formula is an important tool that shows how individuals change their consumption whenever there is a change in income. Why don't you read on and find out how to calculate it using the income elasticity of demand formula?

    Income Elasticity of Demand Definition

    The income elasticity of demand definition shows the change in the quantity of a good consumed in response to a change in income. The income elasticity of demand is important to show the value individuals attach to certain goods.

    The income elasticity of demand measures how much there is a change in the quantity consumed of a particular good when the income of an individual changes.

    Check out our article on the elasticity of demand to find out all there is about demand elasticity!

    The income elasticity of demand shows the relationship that exists between an individual's income and the quantity of a specific good they consume.

    This relationship could be positive, meaning that with an increase in income, the individual will increase the consumption of that good.

    On the other hand, the relationship between income and quantity demanded could also be negative, meaning that with an increase in income, the individual lowers the consumption of that particular good.

    As income elasticity of demand reveals the response to changes in income in terms of quantity demanded, the higher the income elasticity of demand, the higher will be the change in the amount consumed.

    Formula for Calculating Income Elasticity of Demand

    The formula for calculating income elasticity of demand is as follows:

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

    Using this formula, one can calculate the change in quantity demanded when there is a change in income.

    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.

    Another critical thing to consider when it comes to income elasticity of demand is the type of good for which we are considering the income elasticity of demand. There are normal goods and inferior goods.

    Normal goods are those goods whose quantity demanded increases with an increase in the income of an individual.

    The income elasticity of demand for normal goods is always positive.

    Income Elasticity of Demand Formula Normal Good StudySmarterFig. 1 - Normal good

    Figure 1 shows the relationship between income and quantity demanded for a normal good.

    Notice that with an increase in income, the quantity demanded of that good increases as well.

    Inferior goods are goods that experience a decrease in quantity demanded when the income of an individual increases.

    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.

    Income Elasticity of Demand Formula Inferior Good StudySmarterFig. 2 - Inferior good

    Figure 2 shows the relationship between income and quantity demanded for an inferior good.

    Notice that with a rise in income, the quantity demanded of that good drops.

    The income elasticity of demand for inferior goods is always negative.

    Income Elasticity of Demand Calculation Example

    Let's go over an income elasticity of demand calculation example together!

    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%.

    Income Elasticity of Demand Midpoint Formula

    The income elasticity of demand midpoint formula is used to calculate the change in quantity demanded of a good when there is a change in income.

    The income elasticity of demand midpoint formula is used to calculate the income elasticity of demand between two points.

    The midpoint formula to calculate the income elasticity of demand is as follows.

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

    Where:

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

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

    \( Q_m \) and \( I_m \) are the midpoint quantity demanded and midpoint income respectively.

    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:

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

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

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

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

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

    If you want to learn more about the midpoint method, check out our article!

    Income Elasticity of Demand vs Price Elasticity of Demand

    The main difference between income elasticity of demand vs price elasticity of demand is that income elasticity of demand shows the change in quantity consumed in response to an income change. On the other hand, price elasticity of demand shows the change in quantity consumed in response to a price change.

    Price elasticity of demand shows the percentage change in quantity demanded in response to a price change.

    Check out our article to find out more about the price elasticity of demand!

    The formula to calculate the price elasticity of demand is as follows:

    \(\hbox{Price elasticity of demand}=\frac{\%\Delta\hbox{Quantity demanded}}{\%\Delta\hbox{Price}}\)

    The formula to calculate the income elasticity of demand is:

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

    Notice that the main difference between the income elasticity of demand and the price elasticity of demand in terms of their formula is that instead of income, you have price.

    Income Elasticity of Demand Formula - Key takeaways

    • The income elasticity of demand measures how much there is a change in the quantity consumed of a particular good when the income of an individual changes.
    • The formula for calculating income elasticity of demand is:\[\hbox{Income elasticity of demand}=\frac{\%\Delta\hbox{Quantity demanded}}{\%\Delta\hbox{Income}}\]
    • \(\hbox{Midpoint income elasticity of demand}=\frac{\frac{Q_2 - Q_1}{Q_m}}{\frac{I_2 - I_1}{I_m}}\)
    • Price elasticity of demand shows the percentage change in quantity demanded in response to a price change.
    Frequently Asked Questions about Income Elasticity of Demand Formula

    How do you calculate income elasticity of demand?

    The income elasticity of demand is calculated by taking the percentage change in quantity demanded and dividing it by the percentage change in income.

    How do you calculate price elasticity and income elasticity?

    The price elasticity of demand is calculated by taking the percentage change in quantity demanded and dividing it by the percentage change in price.

    The income elasticity of demand is calculated by taking the percentage change in quantity demanded and dividing it by the percentage change in income.

    What is the midpoint formula for income elasticity of demand?

    The midpoint formula for income elasticity of demand:

    [(Q2-Q1)/Qm]/[(I2-I1)/Im)]

    What is the income elasticity of demand for inferior goods?

    The income elasticity of demand for inferior goods is negative.

    Why is income elasticity of demand important?

    Income elasticity of demand is important because it shows how much customers value a good.

    Test your knowledge with multiple choice flashcards

    The income elasticity of demand shows the relationship that exists between an individual's income and the ___ of a specific good they consume.

    When an increase in income leads to higher consumption of a certain good, the relationship between income and quantity demanded is ___.

    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 over 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? 

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