Which method for calculating elasticity uses the values of the average price and average quantity

What Is Arc Elasticity?

Arc elasticity is the elasticity of one variable with respect to another between two given points. It is used when there is no general function to define the relationship between the two variables.

Arc elasticity is also defined as the elasticity between two points on a curve. The concept is used in both mathematics and economics.

The Formula for the Arc Price Elasticity of Demand Is


P E d = % Change in Qty % Change in Price PE_d = \dfrac{\text{\% Change in Qty}}{\text{\% Change in Price}} PEd=% Change in Price% Change in Qty

How to Calculate the Arc Price Elasticity of Demand

If the price of a product decreases from $10 to $8, leading to an increase in quantity demanded from 40 to 60 units, then the price elasticity of demand can be calculated as:

  • % change in quantity demanded = (Qd2 – Qd1) / Qd1 = (60 – 40) / 40 = 0.5
  • % change in price = (P2 – P1) / P1 = (8 – 10) / 10 = -0.2
  • Thus, PEd= 0.5 / -0.2 = 2.5

Since we’re concerned with the absolute values in price elasticity, the negative sign is ignored. You can conclude that the price elasticity of this good, when the price decreases from $10 to $8, is 2.5.

What Does Arc Elasticity Tell You?

In economics, there are two possible ways of calculating elasticity of demand—price (or point) elasticity of demand and arc elasticity of demand. The arc price elasticity of demand measures the responsiveness of quantity demanded to a price. It takes the elasticity of demand at a particular point on the demand curve, or between two points on the curve.

Key Takeaways

  • In the concept of arc elasticity, elasticity is measured over the arc of the demand curve on a graph.
  • Arc elasticity calculations give the elasticity using the midpoint between two points.
  • The arc elasticity is more useful for larger price changes and gives the same elasticity outcome whether price falls or rises.

Arc Elasticity of Demand

One of the problems with the price elasticity of demand formula is that it gives different values depending on whether price rises or falls. If you were to use different start and end points in our example above—that is, if you assume the price increased from $8 to $10—and the quantity demanded decreased from 60 to 40, the Ped will be:

  • % change in quantity demanded = (40 – 60) / 60 = -0.33
  • % change in price = (10 – 8) / 8 = 0.25
  • PEd = -0.33 / 0.25 = 1.32, which is much different from 2.5

To eliminate this problem, the arc elasticity can be used. Arc elasticity measures elasticity at the midpoint between two selected points on the demand curve by using a midpoint between the two points. The arc elasticity of demand can be calculated as:

  • Arc Ed = [(Qd2 – Qd1) / midpoint Qd] ÷ [(P2 – P1) / midpoint P]

Let’s calculate the arc elasticity following the example presented above:

  • Midpoint Qd = (Qd1 + Qd2) / 2 = (40 + 60) / 2 = 50
  • Midpoint Price = (P1 + P2) / 2 = (10 + 8) / 2 = 9
  • % change in qty demanded = (60 – 40) / 50 = 0.4
  • % change in price = (8 – 10) / 9 = -0.22
  • Arc Ed = 0.4 / -0.22 = 1.82

When you use arc elasticities you do not need to worry about which point is the starting point and which point is the ending point since the arc elasticity gives the same value for elasticity whether prices rise or fall. Therefore, the arc elasticity is more useful than the price elasticity when there is a considerable change in price.

What Is Price Elasticity of Demand?

Price elasticity of demand is a measurement of the change in the consumption of a product in relation to a change in its price. Expressed mathematically, it is:

Price Elasticity of Demand = Percentage Change in Quantity Demanded ÷ Percentage Change in Price

Economists use price elasticity to understand how supply and demand for a product change when its price changes. Like demand, supply also has an elasticity, known as price elasticity of supply. Price elasticity of supply refers to the relationship between change in supply and change in price. It’s calculated by dividing the percentage change in quantity supplied by the percentage change in price. Together, the two elasticities combine to determine what goods are produced at what prices.

Key Takeaways

  • Price elasticity of demand is a measurement of the change in consumption of a product in relation to a change in its price.
  • A good is perfectly elastic if the price elasticity is infinite (if demand changes substantially even with minimal price change).
  • If price elasticity is greater than 1, the good is elastic; if less than 1, it is inelastic.
  • If a good’s price elasticity is 0 (no amount of price change produces a change in demand), it is perfectly inelastic.
  • If price elasticity is exactly 1 (price change leads to an equal percentage change in demand), it is known as unitary elasticity.
  • The availability of a substitute for a product affects its elasticity. If there are no good substitutes and the product is necessary, demand won’t change when the price goes up, making it inelastic.

What Is Elasticity?

Understanding Price Elasticity of Demand

Economists have found that the prices of some goods are very inelastic. That is, a reduction in price does not increase demand much, and an increase in price does not hurt demand, either. For example, gasoline has little price elasticity of demand. Drivers will continue to buy as much as they have to, as will airlines, the trucking industry, and nearly every other buyer.

Other goods are much more elastic, so price changes for these goods cause substantial changes in their demand or their supply.

Not surprisingly, this concept is of great interest to marketing professionals. It could even be said that their purpose is to create inelastic demand for the products that they market. They achieve that by identifying a meaningful difference in their products from any others that are available.

If the quantity demanded of a product changes greatly in response to changes in its price, it is elastic. That is, the demand point for the product is stretched far from its prior point. If the quantity purchased shows a small change after a change in its price, it is inelastic. The quantity didn’t stretch much from its prior point. 

Factors That Affect Price Elasticity of Demand

Availability of Substitutes

The more easily a shopper can substitute one product for another, the more the price will fall. For example, in a world in which people like coffee and tea equally, if the price of coffee goes up, people will have no problem switching to tea, and the demand for coffee will fall. This is because coffee and tea are considered good substitutes for each other.

Urgency

The more discretionary a purchase is, the more its quantity of demand will fall in response to price increases. That is, the product demand has greater elasticity.

Say you are considering buying a new washing machine, but the current one still works; it’s just old and outdated. If the price of a new washing machine goes up, you’re likely to forgo that immediate purchase and wait until prices go down or the current machine breaks down.

The less discretionary a product is, the less its quantity demanded will fall. Inelastic examples include luxury items that people buy for their brand names. Addictive products are quite inelastic, as are required add-on products, such as inkjet printer cartridges.

One thing all these products have in common is that they lack good substitutes. If you really want an Apple iPad, then a Kindle Fire won’t do. Addicts are not dissuaded by higher prices, and only HP ink will work in HP printers (unless you disable HP cartridge protection).

Duration of Price Change

The length of time that the price change lasts also matters. Demand response to price fluctuations is different for a one-day sale than for a price change that lasts for a season or a year.

Clarity of time sensitivity is vital to understanding the price elasticity of demand and for comparing it with different products. Consumers may accept a seasonal price fluctuation rather than change their habits.

Types of Price Elasticity of Demand

Price elasticity of demand can be categorized according to the number calculated by dividing the percentage change in quantity demanded by the percentage change in price. These categories include the following:

Types of Price Elasticity of Demand
If the percentage change in quantity demanded divided by the percentage change in price equals: It is known as: Which means:
Infinity Perfectly elastic Changes in price result in demand declining to zero
Greater than 1 Elastic Changes in price yield a significant change in demand
1 Unitary Changes in price yield equivalent (percentage) changes in demand
Less than 1 Inelastic Changes in price yield an insignificant change in demand
0 Perfectly inelastic Changes in price yield no change in demand

Data: Khan Academy

Example of Price Elasticity of Demand

As a rule of thumb, if the quantity of a product demanded or purchased changes more than the price changes, then the product is considered to be elastic (for example, the price goes up by 5%, but the demand falls by 10%).

If the change in quantity purchased is the same as the price change (say, 10% ÷ 10% = 1), then the product is said to have unit (or unitary) price elasticity.

Finally, if the quantity purchased changes less than the price (say, -5% demanded for a +10% change in price), then the product is deemed inelastic.

To calculate the elasticity of demand, consider this example: Suppose that the price of apples falls by 6% from $1.99 a bushel to $1.87 a bushel. In response, grocery shoppers increase their apple purchases by 20%. The elasticity of apples is thus: 0.20 ÷ 0.06 = 3.33. The demand for apples is quite elastic.

What is price elasticity of demand?

Price elasticity of demand is the ratio of the percentage change in quantity demanded of a product to the percentage change in price. Economists employ it to understand how supply and demand change when a product’s price changes.

What makes a product elastic?

If a price change for a product causes a substantial change in either its supply or its demand, it is considered elastic. Generally, it means that there are acceptable substitutes for the product. Examples would be cookies, luxury automobiles, and coffee.

What makes a product inelastic?

If a price change for a product doesn’t lead to much, if any, change in its supply or demand, it is considered inelastic. Generally, it means that the product is considered to be a necessity or a luxury item for addictive constituents. Examples would be gasoline, milk, and iPhones.

What is the importance of price elasticity of demand?

Knowing the price elasticity of demand of a good allows someone selling that good to make informed decisions about pricing strategies. This metric provides sellers with information about consumer pricing sensitivity. It is also key for makers of goods to determine manufacturing plans, as well as for governments to assess how to impose taxes on goods.

Which method for calculating elasticity uses the values of the average price and average quantity Group of answer choices?

The midpoint method for calculating price elasticity of demand​ is: the change in quantity divided by the average of the initial and final quantities divided by the change in price divided by the average of the initial and final prices.

What are the two methods for calculating elasticity of demand?

In economics, there are two possible ways of calculating elasticity of demand—price (or point) elasticity of demand and arc elasticity of demand. The arc price elasticity of demand measures the responsiveness of quantity demanded to a price.

What is the formula to calculate elasticity of demand for two quantities and two prices?

Using the formula as mentioned above, the calculation of price elasticity of demand can be done as: Price Elasticity of Demand = Percentage change in quantity / Percentage change in price. Price Elasticity of Demand = -15% ÷ 60% Price Elasticity of Demand = -1/4 or -0.25.

How do you calculate price elasticity of supply using the point method?

The point approach computes the percentage change in quantity supplied by dividing the change in quantity supplied by the initial quantity, and the percentage change in price by dividing the change in price by the initial price. Thus, the formula for the point elasticity approach is [(Qs2 – Qs1)/Qs1] / [(P2 – P1)/P1].