Important Differences Between Point and Arc Elasticity

Recently updated on August 20th, 2023 at 11:52 am

Point Elasticity

Point elasticity is a measure of the responsiveness of the quantity demanded or supplied of a good or service to a change in one of its own price, with all other determinants of demand or supply held constant. It is defined as the percentage change in quantity demanded or supplied divided by the percentage change in price. The elasticity of demand or supply at a specific point on the demand or supply curve is called the point elasticity. It is used to measure the sensitivity of consumers or producers to changes in price, and can be used to make predictions about how changes in price will affect the quantity of a good or service demanded or supplied.

Examples of Point Elasticity

  • Luxury goods: Luxury goods such as designer handbags, watches and jewelry have a high point elasticity of demand. A small increase in price would result in a large decrease in the quantity demanded, as consumers are willing to pay a premium price for these items but are also sensitive to price changes.
  • Necessities: Necessities such as food and medicine have a low point elasticity of demand. A small increase in price would result in a small decrease in the quantity demanded, as consumers are less sensitive to price changes for items they need to purchase regardless of the cost.
  • Complementary goods: Goods that are often used together, such as a car and gasoline, have a high point elasticity of demand. An increase in the price of gasoline would result in a decrease in the quantity of gasoline demanded and a decrease in the quantity of cars demanded.
  • Substitute goods: Goods that can be used as a replacement for each other, such as coffee and tea, have a high point elasticity of demand. An increase in the price of coffee would result in an increase in the quantity of tea demanded and a decrease in the quantity of coffee demanded.
  • Agricultural goods: Agricultural goods such as wheat, rice, corn etc have a low point elasticity of demand. The reason for this is that these goods are necessities for human consumption and consumers have limited options for substitution.

Formula of Point Elasticity

The formula for point elasticity of demand is:

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)

Alternatively, the point elasticity of supply formula is :

Elasticity = (% Change in Quantity Supplied) / (% Change in Price)

It’s important to note that the elasticity is not a constant number but it varies along the demand or supply curve. Elasticity can be positive or negative, depending on whether the quantity demanded or supplied increases or decreases as the price changes. If the elasticity is greater than 1, the good is considered elastic, meaning that changes in price have a large effect on quantity demanded or supplied. If the elasticity is less than 1, the good is considered inelastic, meaning that changes in price have a small effect on quantity demanded or supplied. And if the elasticity is equal to 1, the good is considered unit elastic, meaning that changes in price have the same effect on quantity demanded or supplied.

Types of Point Elasticity

There are several types of point elasticity, including:

  1. Price Elasticity of Demand (PED): This measures the responsiveness of the quantity demanded of a good or service to a change in its own price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
  2. Income Elasticity of Demand (YED): This measures the responsiveness of the quantity demanded of a good or service to a change in consumer income. It is calculated as the percentage change in quantity demanded divided by the percentage change in income.
  3. Cross-Price Elasticity of Demand (XPED): This measures the responsiveness of the quantity demanded of one good or service to a change in the price of another good or service. It is calculated as the percentage change in quantity demanded of the first good or service divided by the percentage change in price of the second good or service.
  4. Price Elasticity of Supply (PES): This measures the responsiveness of the quantity supplied of a good or service to a change in its own price. It is calculated as the percentage change in quantity supplied divided by the percentage change in price.
  5. Time Elasticity of Supply (TES): This measures the responsiveness of the quantity supplied of a good or service to a change in time. It is calculated as the percentage change in quantity supplied over a period of time divided by the percentage change in time.
  6. Arc Elasticity: It is a measure of the responsiveness of the quantity demanded or supplied to a change in price, but it’s calculated by taking the average of the elasticity over the interval of the change in price.

Objectives of Point Elasticity

The main objectives of using point elasticity in economics are:

  • To measure the responsiveness of consumers and producers to changes in price: Point elasticity helps to determine how sensitive consumers and producers are to changes in price, and can be used to make predictions about how changes in price will affect the quantity of a good or service demanded or supplied.
  • To analyze the impact of price changes on revenue: Point elasticity can be used to analyze the impact of price changes on a firm’s revenue. For example, a firm may choose to raise prices if demand for its product is elastic, as an increase in price will lead to a proportionately larger increase in revenue.
  • To identify the factors affecting demand and supply: Point elasticity can be used to identify the factors that are affecting the demand or supply of a good or service. For example, if the elasticity of demand for a good is high, it suggests that there are many close substitutes available and that consumers are sensitive to price changes.
  • To make pricing decisions: Businesses can use the concept of point elasticity to make pricing decisions. A business that sells a product with a high elasticity of demand would not want to raise its prices because it would lose many customers. In contrast, a business that sells a product with a low elasticity of demand would be able to raise prices without losing many customers.
  • To predict changes in the market: Point elasticity can be used to predict changes in the market, such as how changes in price will affect the quantity of a good or service demanded or supplied, and how changes in consumer preferences will affect the demand for a good or service.

Arc Elasticity

Arc elasticity is a measure of the responsiveness of the quantity demanded or supplied to a change in price, but it’s calculated by taking the average of the elasticity over the interval of the change in price, rather than at a specific point on the demand or supply curve.

The formula for arc elasticity of demand is:

Arc Elasticity = (ΔQ/Q) / (ΔP/P)

Where Q is the average quantity demanded over the interval of price change and P is the average price over the interval of the price change.

The formula for arc elasticity of supply is:

Arc Elasticity = (ΔQ/Q) / (ΔP/P)

Where Q is the average quantity supplied over the interval of price change and P is the average price over the interval of the price change.

The use of arc elasticity is particularly useful when the change in price is over a range rather than a single point, it also helps in avoiding any confusion caused by the nonlinearity in the demand or supply curve.

Arc elasticity is used to analyze long-term price-quantity relationship, whereas point elasticity is used to analyze short-term price-quantity relationship.

Examples of Arc Elasticity

Here are a few examples of how arc elasticity can be applied in real-world scenarios:

  • A company wants to increase the price of its product by 10% over a six-month period. During this time, the quantity demanded decreases by 5%. The arc elasticity of demand for the product is calculated as (-5/50) / (10/100) = -0.1, which means that the demand for the product is relatively inelastic over this six-month period.
  • A farmer wants to increase the price of their wheat by 20% over a year. During this time, the quantity supplied increases by 15%. The arc elasticity of supply for the wheat is calculated as (15/50) / (20/100) = 0.3, which means that the supply of wheat is relatively elastic over this one-year period.
  • A restaurant chain wants to raise the price of its menu items by 15% over the course of three months. The quantity demanded decreases by 10%. The arc elasticity of demand for the menu items is calculated as (-10/50) / (15/100) = -0.2, which means that the demand for the menu items is relatively inelastic over this three-month period.
  • A store wants to increase the price of its clothing items by 25% over a year. During this time, the quantity supplied decreases by 20%. The arc elasticity of supply for the clothing items is calculated as (-20/50) / (25/100) = -0.8, which means that the supply of clothing items is relatively inelastic over this one-year period.

Types of Arc Elasticity

Like point elasticity, there are several types of arc elasticity, including:

  1. Arc Price Elasticity of Demand (PED): This measures the responsiveness of the quantity demanded of a good or service to a change in its own price over a specific period of time. It is calculated as the average percentage change in quantity demanded over the period of time divided by the average percentage change in price over the period of time.
  2. Arc Income Elasticity of Demand (YED): This measures the responsiveness of the quantity demanded of a good or service to a change in consumer income over a specific period of time. It is calculated as the average percentage change in quantity demanded over the period of time divided by the average percentage change in income over the period of time.
  3. Arc Cross-Price Elasticity of Demand (XPED): This measures the responsiveness of the quantity demanded of one good or service to a change in the price of another good or service over a specific period of time. It is calculated as the average percentage change in quantity demanded of the first good or service over the period of time divided by the average percentage change in price of the second good or service over the period of time.
  4. Arc Price Elasticity of Supply (PES): This measures the responsiveness of the quantity supplied of a good or service to a change in its own price over a specific period of time. It is calculated as the average percentage change in quantity supplied over the period of time divided by the average percentage change in price over the period of time.
  5. Arc Time Elasticity of Supply (TES): This measures the responsiveness of the quantity supplied of a good or service to a change in time. It is calculated as the average percentage change in quantity supplied over a period of time divided by the average percentage change in time.

Comparison Between Point and Arc Elasticity

Point Elasticity

Arc Elasticity

Measures the responsiveness of demand or supply to a small change in price or income Measures the responsiveness of demand or supply to a change in price or income over a range
Only considers a specific point on the demand or supply curve          Considers the entire range of the change in price or income
Can be either positive or negative Positive for normal goods and negative for inferior goods
Can be used to estimate the impact of a small change in price or income on quantity demanded or supplied  Can be used to estimate the overall impact of a change in price or income on quantity demanded or supplied over a range

 Important Difference Between Point and Arc Elasticity

The main difference between point elasticity and arc elasticity is the way they measure the responsiveness of demand or supply to changes in price or income.

Point elasticity measures the responsiveness at a specific point on the curve, it is calculated as the percentage change in quantity demanded or supplied divided by the percentage change in price or income at that specific point.

Arc elasticity, on the other hand, measures the responsiveness over a range of changes in price or income. It is calculated as the percentage change in the quantity demanded or supplied divided by the percentage change in price or income over a range.

Another difference is that Point elasticity can be either positive or negative, while arc elasticity is positive for normal goods and negative for inferior goods.

Point elasticity is useful when small changes in price or income are being analyzed, while arc elasticity is useful when analyzing the overall impact of changes in price or income on a market.

Conclusion

In conclusion, both point and arc elasticity are used to measure the responsiveness of demand or supply to changes in price or income. However, point elasticity only considers a specific point on the curve, while arc elasticity considers the entire range of changes. Point elasticity can be either positive or negative, while arc elasticity is positive for normal goods and negative for inferior goods. In general, arc elasticity provides a more comprehensive view of the responsiveness of demand or supply and is useful for analyzing the overall impact of changes in price or income on a market.

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