# Elasticity and its application

Elasticity and its application
Cours Introduction to microeconomics

Lectures

Elasticity, a measure of how much buyers and sellers respond to changes in market conditions, allows us to analyse supply and demand with greater precision.

# The elasticity of demand

To measure how much consumers respond to changes, economists use the concept of elasticity.

## The price elasticity of demand and its determinants

The law of demand states that a fall in the price of a good raises the quantity demanded. The price elasticity of demand measures how much the quantity demanded responds to a change in price. Demand for a good is said to be elastic if the quantity demanded responds substantially to changes in the price. Demand is said to be inelastic if the quantity demanded responds only slightly to changes in the price.

We can state some general rules about what determines the price elasticity of demand:

• Goods with close substitutes tend to have more elastic demand because it is easier for consumers to switch from that good to others.
• Necessities tend to have inelastic demands, whereas luxuries have elastic demands
• The elasticity of demand in any market depends on how we draw the boundaries of the market. Narrowly defined markets tend to have more elastic demand than broadly defined markets, because it is easier to find close substitutes of narrowly defined goods.
• Goods tend to have more elastic demand over longer time horizons.

## Computing the price elasticity of demand

Economists compute the price elasticity of demand as the percentage change in the quantity demanded divided by the percentage change in the price that is:

${\displaystyle \epsilon _{p}^{d}={{\rm {\%\ change\ in\ quantity\ demanded}} \over {\rm {\%\ change\ in\ price}}}}$.

Because the quantity demanded of a good is negatively related to its price, the percentage change in quantity will always have the opposite sign to the percentage change in price. A larger price elasticity implies a greater responsiveness of quantity demanded to price.

## The Midpoint method: A better way to calculate percentage changes and elasticities

If you try calculating the price of demand between two points on a demand curve, you will quickly notice an annoying problem: the elasticity from point A to point B seems different from the elasticity from point B to point A. One way to avoid this problem is to use the midpoint method for calculating elasticities.

We can express the midpoint method with the following formula for the price elasticity of demand between two points denoted (${\displaystyle Q_{1}P_{1}}$) and (${\displaystyle Q_{2}P_{2}}$).

${\displaystyle \epsilon _{p}^{d}={\frac {\frac {q_{1}^{d}-q_{0}^{d}}{\frac {q_{1}^{d}+q_{0}^{d}}{2}}}{\frac {p_{1}-p_{0}}{\frac {p_{1}+p_{0}}{2}}}}}$

## The variety of demand curves

Economists classify curves according to their elasticity. Demand is elastic when the elasticity is greater than 1. Demand is inelastic when the elasticity is less than 1. If the elasticity is exactly 1, demand is said to have unit elasticity.

The flatter the demand curve that passes through a given point, the greater the price elasticity of demand. The steeper the demand curve that passes through a given point, the smaller the price elasticity of demand.

## Total Revenue and the price elasticity of demand

When studying changes in supply or demand in a market, one variable we often want to study is total revenue, the amount paid by buyers and received by sellers of the good. In any market, total revenue is P x Q, the price of a good times the quantity of the good sold.

How does total revenue change as one moves along the demand curve? The answer depends on the price elasticity of demand. If demand is inelastic then an increase in the price causes an increase in total revenue. We obtain the opposite result if demand is elastic: an increase in the price causes a decrease in total revenue.

We can state some general rules:

• When demand is inelastic (price elasticity less than 1), price and total revenue move in the same direction
• When demand is inelastic (price elasticity greater than 1) price and total revenue move in opposite directions.
• If demand is unit elastic (price elasticity exactly equal to 1) total revenue remains constant when the price changes.

## Elasticity and total revenue along a linear demand curve

Although some demand curves have an elasticity that is the same along the entire curve, that is not always the case. Even though the slope of a linear demand curve is constant, the elasticity is not.

## Other demand elasticities

In addition to the price elasticity of demand, economists also use other elasticities to describe the behavior of buyers in a market. The income elasticity of demand measures how the quantity demanded changes as consumers’ income changes. It is calculated as the percentage change in quantity demanded divided by the percentage change in income:

${\displaystyle \epsilon _{y}^{d}={{\rm {\%\ change\ in\ the\ quantity\ demanded}} \over {\rm {\%\ in\ income}}}={\frac {\frac {\Delta q^{d}}{q^{d}}}{\frac {\Delta y}{y}}}={\frac {\Delta q^{d}}{\Delta y}}\times {\frac {y}{q^{d}}}={\frac {\partial q^{d}}{\partial y}}\times {\frac {y}{q^{d}}}}$.

Necessities tend to have small income elasticities. Luxuries tend to have a large income elasticities.

The cross-price elasticity of demand measures how the quantity demanded of one good changes as the price of another good changes. It is calculated as the percentage in quantity demanded of good 1 divided by the percentage change in the price of good 2. That is:

${\displaystyle \epsilon _{p\neq i}^{d}={{\rm {\%\ change\ in\ quantity\ demanded\ of\ good\ 1}} \over {\rm {\%\ change\ in\ the\ price\ of\ good\ 2}}}={\frac {\frac {\Delta q^{d}}{q^{d}}}{\frac {\Delta p_{\neq i}}{p_{\neq i}}}}={\frac {\Delta q^{d}}{\Delta {p_{\neq i}}}}\times {\frac {p_{\neq i}}{q^{d}}}={\frac {\partial q^{d}}{\partial {p_{\neq i}}}}\times {\frac {p_{\neq i}}{q^{d}}}}$.

Whether the cross-price elasticity is a positive or negative number depends on whether the two goods are substitutes or complements.

# Elasticity of supply

## The price elasticity of supply and its determinants

The price elasticity of supply measures how much the quantity supplied responds to changes in the price. Supply of a good is said to be elastic if the quantity supplied responds substantially to changes in the price. Supply is said to be inelastic if the quantity supplied responds only slightly to changes in the price.

## Computing the price elasticity of supply

Economists compute the price elasticity of supply as the percentage change in the quantity supplied divided by the percentage change in the price. That is:

${\displaystyle \epsilon _{p}^{s}={{\rm {\%\ change\ in\ quantity\ supplied}} \over {\rm {\%\ change\ in\ price}}}={\frac {\frac {\Delta q^{s}}{q^{s}}}{\frac {\Delta p}{p}}}={\frac {\Delta q^{s}}{\Delta p}}\times {\frac {p}{q^{s}}}={\frac {\partial q^{s}}{\partial p}}\times {\frac {p}{q^{s}}}}$.

## Variety of supply curves

Because the price elasticity of supply measures the responsiveness of quantity supplied to the price, it is reflected in the appearance of the supply curve. In the extreme case of a zero elasticity supply is perfectly inelastic and the supply curve is vertical. In this case, the quantity supplied is the same regardless of the price. As the elasticity rises, the supply curve gets flatter, which shows that the quantity supplied responds more to changes in the price. At the opposite extreme supply is perfectly elastic. This occurs as the price elasticity of supply approaches infinity and the supply curve becomes horizontal, meaning that very small changes in the price lead to very large changes in the quantity supplied.