# assume that a business firm sells a product at the price of rs 500. the firm has decided to reduce the price of the product to rs 400. consequently, the demand for the product is raised from 20,000 units to 25,000 units. calculate the price elasticity of demand.

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get assume that a business firm sells a product at the price of rs 500. the firm has decided to reduce the price of the product to rs 400. consequently, the demand for the product is raised from 20,000 units to 25,000 units. calculate the price elasticity of demand. from screen.

## Calculating Price Elasticities Using the Midpoint Formula

## Calculating Price Elasticities Using the Midpoint Formula

### LEARNING OBJECTIVES

Calculate price elasticity using the midpoint method

Differentiate between slope and elasticity

**Figure 1**. Just how elastic is it?

We have defined price elasticity of demand as the responsiveness of the quantity demanded to a change in the price. We also explained that price elasticity is defined as the percent change in quantity demanded divided by the percent change in price. In this section, you will get some practice computing the price elasticity of demand using the midpoint method.

## The Midpoint Method

To calculate elasticity, we will use the average percentage change in both quantity and price. This is called the **midpoint method for elasticity** and is represented by the following equations:

percent change in quantity

= Q 2 − Q 1 ( Q 2 + Q 1 ) ÷ 2 × 100

percent change in quantity=Q2−Q1(Q2+Q1)÷2×100

percent change in price

= P 2 − P 1 ( P 2 + P 1 ) ÷ 2 × 100

percent change in price=P2−P1(P2+P1)÷2×100

The advantage of the midpoint method is that one obtains the same elasticity between two price points whether there is a price increase or decrease. This is because the formula uses the same base for both cases.

### EXERCISE: CALCULATING THE PRICE ELASTICITY OF DEMAND

Let’s calculate the elasticity from points B to A and from points G to H, shown in Figure 2, below.

**Figure 2.**

**Calculating the Price Elasticity of Demand.**The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.

## Elasticity from Point B to Point A

**Step 1.**We know that

Price Elasticity of Demand

=

percent change in quantity

percent change in price

Price Elasticity of Demand=percent change in quantitypercent change in price

**Step 2.**From the midpoint formula we know that

percent change in quantity

= Q 2 − Q 1 ( Q 2 + Q 1 ) ÷ 2 × 100

percent change in quantity=Q2−Q1(Q2+Q1)÷2×100

percent change in price

= P 2 − P 1 ( P 2 + P 1 ) ÷ 2 × 100

percent change in price=P2−P1(P2+P1)÷2×100

**Step 3.**We can use the values provided in the figure (as price decreases from $70 at point B to $60 at point A) in each equation:

percent change in quantity

= 3 , 000 − 2 , 800 ( 3 , 000 + 2 , 800 ) ÷ 2 × 100 = 200 2 , 900 × 100 = 6.9

percent change in quantity=3,000−2,800(3,000+2,800)÷2×100=2002,900×100=6.9

percent change in price

= 60 − 70 ( 60 + 70 ) ÷ 2 × 100 = − 10 65 × 100 = − 15.4

percent change in price=60−70(60+70)÷2×100=−1065×100=−15.4

**Step 4.**Then, those values can be used to determine the price elasticity of demand:

Price Elasticity of Demand

= 6.9 percent − 15.5 percent = − 0.45

Price Elasticity of Demand=6.9 percent−15.5 percent=−0.45

The elasticity of demand between these two points is 0.45, which is an amount smaller than 1. That means that the demand in this interval is inelastic.

Remember: price elasticities of demand are always negative, since price and quantity demanded always move in opposite directions (on the demand curve). As you’ll recall, according to the law of demand, price and quantity demanded are inversely related. By convention, we always talk about elasticities as positive numbers, however. So, mathematically, we take the absolute value of the result. For example, -0.45 would interpreted as 0.45.

This means that, along the demand curve between points B and A, if the price changes by 1%, the quantity demanded will change by 0.45%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 4.5% decrease in quantity demanded. A 10% decrease in the price will result in only a 4.5% increase in the quantity demanded.

Note also that a larger (negative) number means demand is **more elastic**, so that if price elasticity of demand were -0.75, the quantity demanded would change by a greater percentage than when the elasticity was -0.45.

### EXERCISE: ELASTICITY OF DEMAND FROM POINT G TO POINT H

Calculate the price elasticity of demand using the data in Figure 2 for an increase in price from G to H. Does the elasticity increase or decrease as we move up the demand curve?

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## Income Elasticity of Demand: Definition, Formula, and Types

Income elasticity of demand measures the relationship between a change in the quantity demanded for a particular good and a change in real income.

BUSINESS BUSINESS ESSENTIALS

## Income Elasticity of Demand: Definition, Formula, and Types

By ADAM HAYES Updated August 25, 2022

Reviewed by THOMAS BROCK

Fact checked by AMANDA JACKSON

Investopedia / Paige McLaughlin

## What Is Income Elasticity of Demand?

Income elasticity of demand refers to the sensitivity of the quantity demanded for a certain good to a change in the real income of consumers who buy this good.

The formula for calculating income elasticity of demand is the percent change in quantity demanded divided by the percent change in income. With income elasticity of demand, you can tell if a particular good represents a necessity or a luxury.

### KEY TAKEAWAYS

Income elasticity of demand is an economic measure of how responsive the quantity demanded for a good or service is to a change in income.

The formula for calculating income elasticity of demand is the percentage change in quantity demanded divided by the percentage change in income.

Businesses use the measure to help predict the impact of a business cycle on sales.

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### Income Elasticity of Demand

## Understanding Income Elasticity of Demand

Income elasticity of demand measures the responsiveness of demand for a particular good to changes in consumer income.

The higher the income elasticity of demand for a particular good, the more demand for that good is tied to fluctuations in consumers' income. Businesses typically evaluate the income elasticity of demand for their products to help predict the impact of a business cycle on product sales.

### Inferior Goods vs. Normal Goods

Depending on the values of the income elasticity of demand, goods can be broadly categorized as inferior and normal goods. Normal goods have a positive income elasticity of demand; as incomes rise, more goods are demanded at each price level.

Normal goods whose income elasticity of demand is between zero and one are typically referred to as necessity goods, which are products and services that consumers will buy regardless of changes in their income levels. Examples of necessity goods and services include tobacco products, haircuts, water, and electricity.

As income rises, the proportion of total consumer expenditures on necessity goods typically declines. Inferior goods have a negative income elasticity of demand; as consumers' income rises, they buy fewer inferior goods. A typical example of such a type of product is margarine, which is much cheaper than butter.

Furthermore, luxury goods are a type of normal good associated with income elasticities of demand greater than one. Consumers will buy proportionately more of a particular good compared to a percentage change in their income. Consumer discretionary products such as premium cars, boats, and jewelry represent luxury products that tend to be very sensitive to changes in consumer income. When a business cycle turns downward, demand for consumer discretionary goods tends to drop as workers become unemployed.

## Formula for Income Elasticity of Demand

The formula for income elasticity of demand is

**Income Elasticity of Demand = Percentage Change in Quantity Demanded / Percentage Change in Income**

Do = Initial Quantity Demanded

D1 = Final Quantity Demanded

Io = Initial Real Income

I1 = Final Real Income

## Example of Income Elasticity of Demand

Consider a local car dealership that gathers data on changes in demand and consumer income for its cars for a particular year. When the average real income of its customers falls from $50,000 to $40,000, the demand for its cars plummets from 10,000 to 5,000 units sold, all other things unchanged.

The income elasticity of demand is calculated by taking a negative 50% change in demand, a drop of 5,000 divided by the initial demand of 10,000 cars, and dividing it by a 20% change in real income—the $10,000 change in income divided by the initial value of $50,000. This produces an elasticity of 2.5, which indicates local customers are particularly sensitive to changes in their income when it comes to buying cars.

## Types of Income Elasticity of Demand

There are five types of income elasticity of demand:

**High**: A rise in income comes with bigger increases in the quantity demanded.

**Unitary**: The rise in income is proportionate to the increase in the quantity demanded.

**Low**: A jump in income is less than proportionate to the increase in the quantity demanded.

**Zero**: The quantity bought/demanded is the same even if income changes

**Negative**: An increase in income comes with a decrease in the quantity demanded.

## How Do You Interpret Income Elasticity of Demand?

Income elasticity of demand describes the sensitivity to changes in consumer income relative to the amount of a good that consumers demand. Highly elastic goods will see their quantity demanded change rapidly with income changes, while inelastic goods will see the same quantity demanded even as income changes.

## Price Elasticity of Demand

What is the price elasticity of demand formula? Understand its relevance with the demand of a good, as well as how to calculate price elasticity...

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## Definition and Use

Have you ever thought about buying a gaming system and thought, 'Wow I can't afford the games.' Maybe you had your eye on a certain vehicle, but learned they were expensive to work on. Have you ever gone shopping and found some suit pants or maybe it was a dress, and realized the suit coat or shoes that go along with it were too expensive to justify the purchase? All of these are everyday examples of how the price of one good influences your decision to purchase another good. The formula and term for that reasoning and logic is known as the cross price elasticity of demand.

You may remember from previous lessons and study that **price elasticity of demand** is a measure of how responsive the quantity demanded for a product is after a change in price. Sometimes, economists also like to know the **cross price elasticity of demand** which is how responsive or elastic the quantity demanded for a good is in response to a change in the price of another good. It is measured as the percentage change in demand for the first good that occurs in response to a percentage change in price of the second good. Summarized, it tells us how the price of one good can influence the sales of another good.

Cross price elasticity helps economists figure out things like how likely you are to buy the new gaming system if the price of games goes down. By calculating cross-price elasticity, we can measure the responsiveness and determine if the goods are substitutes, complements, or not related to each other. This information can help business owners and industries figure out how to price certain goods or help them project the sales impact a business may feel from price changes of other products.

From other lessons, you may remember that if two goods are substitutes (for example, chicken and red meat), we should expect to see consumers purchase more of one good when the price of its substitute increases. This results in a high positive cross price elasticity. The demand for both goods moves in opposite directions of each other.

On the other hand, if the two goods are complements (for example, peanut butter and jelly), we should see a price rise in one good cause the demand for both goods to fall. This results in a negative number or negative cross price elasticity. Likewise, if the price fell for one complement, quantity demanded for both goods should increase. The demand for both goods should move in the same direction.

## Formula and Rule of Thumb

The following is the simple formula for calculating cross price elasticity of demand.

**CROSS PRICE ELASTICITY OF DEMAND**= % change in quantity demanded for Product A / % change in price of product B

Let's put the formula in action. Assume the following:

Product A (butter) has a 10% positive change in quantity demanded when product B (margarine) has a positive 5% change or increase in price.

If we enter those numbers in to our formula, we see that 10% / 5% is equal to 2.

So what does that tell us? Let's use the following rules of thumb to help us determine the relationship between the two goods.

If cross price elasticity > 0, then the two goods are substitutes

If cross price elasticity = 0, then the two goods are independent

If cross price elasticity < 0, then the two goods are complements

From this example we can see that the answer 2 tells us that butter and margarine are substitute goods for each other. When the price of margarine went up, more people switched to butter. You can increase the sales of one good, by increasing the price of the other.

## Examples

Let's look at a few more examples to really help us understand the concept and math behind cross price elasticity of demand.

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## Cross Price Elasticity of Demand - A Case Study:

The following Case Study will allow you to apply your knowledge of the Cross Price Elasticity of Demand in a real-life context.

### Case:

You are an economist studying the market of fruit in Tanzania. From local data, you realized that the two most popular fruits in Tanzania are bananas and papayas. You want to study how these two products are related economically. Thus you gather the following data on bananas and papayas in the Tanzania market for the past year (see below). This year, for the first time in a long time, there was an increase in the price of papayas. Given how popular papayas are in Tanzania and the low-income levels of the population, this was a concerning issue for local economists.

Fruit Banana Papaya

Price per lb, previous year $2.00

Price per lb, current year $2.50

Quantity consumed, previous year 10,000

Quantity consumed, current year 11,500

### Required:

1. Compute the Cross Price Elasticity of Demand for **Bananas**.

2. Based on the answer in #1, are bananas considered substitutes, complements, or independent goods? Explain.

### Solution:

1.

Cross Price Elasticity of Demand = Percentage Change in Quantity demanded of bananas / Percentage Change in the price of papayas.

**Change in Quantity demanded of bananas:**

=(11,500 -10,000) / 10,000

=15% Increase

**Change In price of papayas**:

Guys, does anyone know the answer?