# 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 = the percentage change in quantity demanded divided by the percentage change in price.

 Demand Quantity Change % Price = ÷ Elasticity 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.

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

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 tend to have a high elasticity of demand, since if the price increases, buyers can switch to a cheaper substitute. More closely related substitutes will 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 — 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, since people must eat or clothe themselves, 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, long-run elasticity will exceed short-run elasticity, 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 fuel-efficient vehicles or electric vehicles, lowering the demand for gasoline. Demand Elasticity Comparison Over the Short Run and the Long Run

## 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 price-demand 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 = (Q1 + Q2) / 2

Midpoint Price = (P1 + P2) / 2

 Demand (Q2 - Q1) / Midpoint Quantity Price = ÷ Elasticity (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 (50 - 100) / 75 -50 / 75 -67% of = ÷ = ÷ = ÷ Cantaloupes (\$4 - \$2) / \$3 \$2 / \$3 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 Quantity Change % Income = ÷ Elasticity 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 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.

## Elasticity, Revenue, and Exports

The relationship between demand elasticity and revenue is different 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 in the same way as it would under a domestic currency, with higher prices leading to lower demand, and vice versa. However, the amount of 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 in relation 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 the following initial facts:

• Initial exchange rate: \$1 = £1
• Quantity of American exports: 100 American widgets
• Price of American widget in the UK: £200
• Price received by exporter for each American widget: \$200 (= £200 × \$1/£1)
• American exporter's revenue: \$20,000 = \$200 × £1/\$1 ×100

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:

• New exchange rate: \$2 = £1
• Elasticity of American export: 1 (unit elasticity)
• Quantity of exports: 200 American widgets
• (double because of the lower price in the UK)
• New lower price of American widget in the UK: £100
• Price received by exporter for each American widget: still \$200 (= £100 × \$2/£1)
• American exporters revenue: \$40,000 = British Price × Exchange Rate × Quantity = £100 × \$2/£1 × 200

While depreciation of the currency certainly benefits exporters, whether or not it will benefit the country will depend on the elasticities of demand for both imports and exports. Many times, countries will try to increase their export revenue and increase the price of imports 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 a depreciation of the currency will increase or decrease net exports, which is the difference between export revenue and import expenses:

Net Exports = Exports – Imports

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

|PEDX| + |PEDM| > 1

• |PEDX| = absolute value of the price elasticity of demand for exports
• |PEDM| = absolute value of the price elasticity of demand for imports

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