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 yield 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 may increase revenue if the demand is inelastic or decrease revenue if demand is elastic.

The price elasticity of demand = the percentage change in quantity demanded divided by the percentage change in price.

Demand Price Elasticity = Quantity Change %
Price Change %

If a large change in price results in little change in the quantity demanded, then demand is inelastic. If a small change in price results in large changes in the quantity demanded, then demand is elastic. If the price change percentage is equal, though opposite, to the percentage change in quantity, then demand for the product is said to have unit elasticity.

Elasticity of Demand
If demand elasticity < 1 then demand is inelastic
= 1 unit elastic
> 1 elastic

Graphs of Perfectly Elastic and Perfectly Inelastic Demand

Graph showing the difference between perfectly elastic demand and perfectly inelastic demand.

Perfectly Elastic Demand (Graph #1):

  • Elasticity = ∞.
  • Above price Pe, there is no demand.
  • At Pe, the market demand equals the quantity provided.
  • Below Pe, the market would also demand the quantity provided.
  • A perfectly elastic demand can be best illustrated by farmers selling corn in a competitive marketplace. No farmer can sell for more than the going price since buyers can easily buy from their competitors. On the other hand, no farmers will sell for less since they can sell all that they have for the going rate.

Perfectly Inelastic Demand (Graph #2):

  • Elasticity = 0
  • At quantity Qi, the market demands whatever is provided, regardless of the price.
  • The best real-world example of perfectly inelastic demand is a cancer drug that can cure a fatal cancer. Everyone with the cancer will want the drug regardless of price, and the drug company will provide whatever amount is demanded.
Graph showing elastic demand between prices and quantity demanded.

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 with good substitutes have a high elasticity of demand since if prices increase, buyers can switch to cheaper substitutes. More closely related substitutes have higher demand elasticities. 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, though not closely related, nonetheless, are close substitutes. So if the price of cantaloupes increases, then consumers may buy more watermelons or honeydew melons. If pork increases, then people may buy more ham, beef, or some other meat.

Related to close substitutes is how broadly the categories are defined: broader categories have fewer close substitutes. So, the demand for a broad category such as food or clothing is very inelastic since people must eat or clothe themselves, while demand for strawberries is very elastic since many other fruits can be chosen instead.

Another category of inelastic goods are complementary goods where the demand is derived from the demand of another product. For instance, many types of gas-powered cars can be bought, but once one is bought, then there will be demand for gasoline and oil, which have no close substitutes.

Since the elasticity of demand mostly depends on being able to substitute one good for another, long-run elasticity will exceed short-run elasticity, because people have 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 fuel-efficient vehicles or electric vehicles, lowering the demand for gasoline.

Demand Elasticity Comparison Over the Short Run and the Long Run

Graphs showing how the elasticity of demand tends to be inelastic over the short term, but elastic over longer periods.

Inelastic Demand (Graph #1):

  • Over the short run, demand is more likely to be inelastic because of the limited options to compensate to changes in price. For instance, oil is inelastic over the short run, so when the OPEC countries decided to decrease supply, from Q1 to Q2, the price increased dramatically, rising from P1 to P2.
  • Note that the total revenue earned at price P2 = P2 × Q2, which is represented by the area bounded by P2 and Q2, and is larger than the area bounded by P1 and Q1.

Elastic Demand (Graph #2):

  • Over the long run, people have more time to compensate for changes in prices, so demand is more elastic. Continuing our oil example, people can buy more fuel-efficient vehicles, reducing demand for oil over the long run.
  • In the above graph, it is obvious that the total revenue earned at P2, represented by the rectangle bounded by P2 and Q2 is less than the original revenue earned at P1. Hence, more revenue was earned at P1, because the increase in price does not compensate for the decrease in quantity sold.

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 in using ratio-of-percentage changes, in that the percentage depends on the initial price-demand point. For instance, if the price of cantaloupes drops from $4 to $2, that decrease = 50%. But if cantaloupe prices subsequently increase from $2 to $4, then that increase = 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 = (Q1 + Q2) / 2

Midpoint Price = (P1 + P2) / 2

Price Elasticity of Demand Midpoint Formula
Demand Price Elasticity = (Q2 − Q1) / Midpoint Quantity
(P2 − P1) / 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

Cross-Price Demand Elasticity

The cross-price elasticity of demand measures the change of 1 good by the % 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 both tennis rackets and 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.

Demand Income Elasticity = Quantity Change %
Income Change %

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 oppositely 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?

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.

Elasticity, Revenue, and Exports

The relationship between demand elasticity and revenue differs for foreign sales, if the price changes are the result of changes in the foreign exchange rate between the domestic currency and the currency received from the foreign sales. If the foreign exchange rate changes, then the foreign price of the export will also change, and revenue in terms of the foreign currency will change as it would under a domestic currency, with higher prices leading to lower demand, and vice versa. However, the revenue in domestic currency that the exporter receives for each of its products remains the same after the currency conversion. So, if the foreign price of the export drops, such as would occur when the domestic currency depreciates relative to the foreign currency, then the quantity sold in the foreign market will increase, which will directly increase the revenue of the exporter regardless of the demand elasticity for the product. The opposite would occur if the foreign price increased, because the domestic currency appreciated.

How Foreign Exchange Rates and Demand Elasticity Affect Revenue from Export Sales

An American exporter exports American widgets to the UK. Now suppose that the exchange rate for American dollars ($) and British sterling pounds (£) is initially 1 to 1, or $1 = £1. Assume these initial facts:

Assume now that the US dollar has depreciated by 50%, so that $2 = £1, but the demand elasticity of the American export is 1, meaning that the quantity sold in Britain is doubled with a halving of price:

While currency depreciation benefits exporters, whether or not it will benefit the country depends on the elasticities of demand for both imports and exports. Many times, countries will increase their export revenue and increase import prices by depreciating the currency, with the hope of stimulating the domestic economy. Foreign exchange rates, and the elasticities of demand for imports in the domestic economy and for exports in the foreign countries will determine whether currency depreciation will increase or decrease net exports, the difference between export revenue and import expenses:

Net Exports = Exports − Imports

The country will benefit from currency depreciation if the absolute value of the price elasticity of demand for exports + the absolute value of the price of elasticity of demand for imports exceeds 1, called the Marshall-Lerner condition (MLC):

|PEDX| + |PEDM| > 1

If the Marshall Lerner condition is less than 1, then net exports will decline; if it equals 1, then net exports will remain unchanged.