Demand Elasticity
The law of demand states that as the price decreases, the quantity demanded increases, but does not say by how much. Demand elasticity is the change in quantity demanded per change in a demand determinant. Although there are several demand determinants, such as consumer preferences, the main determinant with which demand elasticity is measured is the change in price. Businesses are particularly interested in price elasticity, since it measures by how much total revenue changes with the price. A higher or lower price may result in more or less revenue depending on the elasticity of demand for a particular product. Demand elasticity can also determine how much a product or service is taxed, since a higher tax rate will result in higher revenue if the demand is inelastic or lower revenue if demand is elastic.
The price elasticity of demand is equal to the percentage change in quantity demanded divided by the percentage change in price.
Price Elasticity of Demand  =  Quantity Change Percentage Price Change Percentage 
If a large change in price results in little change in the quantity demanded, then demand is considered inelastic. If a small change in price results in large changes in the quantity demanded, then demand is considered elastic. If the price change percentage is equal, though opposite, to the percentage change in quantity, then the product is said to have unit elasticity.
If demand elasticity  < 1  then demand is  inelastic 
= 1  unit elastic  
> 1  elastic 
Graphs of Perfectly Elastic and Perfectly Inelastic Demand
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 Perfectly Inelastic Demand(Graph #2):

Although the elasticity of the product varies because of many factors, several factors are more important, including the necessity of the product, the availability of good substitutes, and the time period in which elasticity is measured.
Products that have good substitutes tend to have a high elasticity of demand, since if the price of one substitute increases, buyers can switch to another substitute. More closely related substitutes will have higher demand elasticity. Thus, margarine and butter are closely related enough so that increases in the price of either margarine or butter, will increase the demand for the other product. Meats, fruits, and vegetables are 3 categories of food in which, although not closely related, nonetheless, are close substitutes. So if the price of cantaloupes increases, then consumers will tend to purchase more watermelons or honeydew melons. If pork increases, then people will buy more ham, beef, or some other meat.
Related to close substitutes is how broadly the categories are defined — the broader the category, the less likely there will be close substitutes. So, the demand for a broad category such as food or clothing would be very inelastic, while the demand for strawberries would be very elastic, since many other fruits can be chosen instead.
Another category of goods that would tend to be inelastic are complementary goods in which the demand is derived from the demand of another product. For instance, many different types of cars can be purchased, but once one is bought, then there will be demand for gasoline and oil, which have no close substitutes.
Since the elasticity of demand most often depends on being able to substitute one good for another, the elasticity over a longer time period will tend to be greater than over a shorter time period, because it will give people more time to find substitutes. For instance, when the price of gasoline increases, people will pay the increased price, since no substitutes exist for gasoline and people loathe changing their habits, such as by driving less. Over time, if gasoline remains expensive, then people will start buying more fuelefficient vehicles, lowering the demand for gasoline.
Demand Elasticity Comparison Over the Short Term and Long Term
Inelastic Demand (Graph #1):
 Elastic Demand(Graph #2):

Calculating Price Elasticity of Demand
Since revenue is affected, businesses want to know how much the quantity will change with the changing price. Hence the price elasticity of demand is generally calculated by dividing the percentage change in quantity by the price change percentage. However, because price and demand are inversely related, the elasticity ratio will be negative, but since only the absolute value of the elasticity is considered important, the convention has been to show price elasticity as a positive number.
However, a problem arises when using a ratio of percentage changes, in that the actual percentage will depend on the initial pricedemand point. For instance, if the price of cantaloupes drops from $4 to $2, that is a decrease of 50%. But if cantaloupe prices subsequently increases from $2 to $4, then that will be an increase of 100%, even though the absolute change in price is the same.
This problem is solved by adopting a midpoint convention, where the change in price or quantity is divided by the average of the 2 prices and quantities.
Midpoint Quantity = (Q_{1} + Q_{2}) / 2
Midpoint Price = (P_{1} + P_{2}) / 2
Price Elasticity of Demand  =  (Q_{2}  Q_{1}) / Midpoint Quantity (P_{2}  P_{1}) / Midpoint Price 
So if the price of cantaloupes declines from $4 to $2 and the quantity sold increases from 50 to 100 cantaloupes, then calculating the elasticity using the midpoint convention will yield:
Elasticity of Cantaloupes  =  (50  100) / 75 ($4  $2) / $3  =  50 / 75 $2 / $3  =  67% 67% 
=  Absolute Value of 1  =  1  =  Unit Elasticity 
CrossPrice Demand Elasticity
The crossprice elasticity of demand measures the change of one good by the percentage change in the price of another good, usually a close substitute. Here, the sign of the elasticity is more important, since it can be either positive or negative. When comparing close substitutes, the cross price elasticity of demand is generally positive, so if the price of bananas increases, the demand for other fruits will increase. If the compared products are complements, in which one is used with the other, then an increase in the price of one will decrease the quantity demanded of the other. So if the price of tennis rackets increases, then the demand for tennis balls will decline.
Elasticity of Other Demand Determinants
Although prices are the most important demand determinant, other determinants can affect the demand for a product, such as changes in consumers' preferences. One important demand determinant is income. The demand for normal goods increases with income. Although most goods are considered normal goods, some products are considered inferior products, where the demand for those products decreases as income increases. In other words, richer people buy better stuff. Income elasticity is generally measured with regard to normal goods, where the percentage change in demand quantity is divided by the percentage change in income.
Income Elasticity of Demand  =  Quantity Change Percentage Income Change Percentage 
How Total Revenue Is Changed by the Price Elasticity of Demand
A business selling a product will want to know the price elasticity of demand for the product, since total revenue can be maximized by knowing the price elasticity of its demand.
Total Revenue = Price × Quantity Sold
When the price changes, the change in quantity sold may either increase or decrease the total revenue, depending on the elasticity of the product.
When demand is inelastic, total revenue changes in the same direction as prices, since the price change more than compensates for the change in quantity, which is represented by a steep demand curve. Hence, raising prices increases revenue.
Elastic demand is more sensitive to price, so small changes in price results in larger changes in quantities, changing revenue in the opposite direction to prices. Hence, increasing prices decreases revenue.
If revenue remains the same when prices change, then demand is considered unit elastic.
Example — The Interrelationship of Prices, Revenue, and Elasticity
Using the above example, total revenue for selling 50 cantaloupes at $4 apiece was $200. What happens to revenue if the price of cantaloupes is decreased from $4 to $2?
 Demand is inelastic, if the quantity increases to 75 cantaloupes, yielding lesser revenue of 75 × 2 = $150.
 Demand is unit elastic, if the quantity increases to 100 cantaloupes, yielding the same revenue of 100 × 2 = $200
 Demand is elastic, if the quantity increases to 125 cantaloupes, yielding increased revenue of 125 × $2 = $250.
Because elasticity depends on percentage changes between 2 variables, elasticity will change depending on the 2 prices being compared, even if the demand curve is linear.