 ## Elasticity 101 - Everything you Need to Know for CFA Level 1

Elasticity is a vital economic concept, and it's one the CFA Level 1 curriculum spends considerable time defining. Elasticity helps us understand how variable demand is in response to prices, which gives us a great deal of insight about market dynamics, the impact of taxes, and for the purposes of the exam, also indicates whether a specific good is elastic, inelastic or a substitute/complementary good.

All in all, the concept itself is foundational and you should expect the CFA Level 1 exam to test it directly.

## What is Elasticity?

Elasticity is a measure of responsiveness between one variable and another. It is defined as the percentage change in a dependent variable caused by a percentage change in a dependent variable. The greater the elasticity the greater the responsiveness between the variables.

There are three basic varieties of elasticities which we need to be aware of, all of which drive at understanding the sensitivity of consumers to changes in price.

• Price Elasticity of Demand
• Income Elasticity of Demand
• Cross-Price Elasticity

Let's cover each in turn.

### (Own) Price Elasticity of Demand

Own price elasticity measures the percentage change in quantity demanded in response to a percentage change in price. The own price elasticity will always be negative: When the quantity demanded is very responsive to a price change we say that demand is elastic. When it is not very responsive, we say demand is inelastic.

Let’s look at what perfectly elastic (any change in price results in zero quantity demanded) and perfectly inelastic demand (same quantity demanded no matter what the price change) looks like. These are the two on the right: As you can see slope for a perfectly inelastic demand curve is 0, the slope for a perfectly elastic demand curve is infinity.

### Determinants of Elasticity

How do you tell if a good is elastic or inelastic (something you will probably have to do on the CFA Exam)?

You should understand that the relative elasticity of a good varies based on how much we need it. Things like shoes or food or basic services have relatively inelastic demand. We're going to buy shoes no matter how high the price goes because we can't do without. Luxury goods that we can more easily go without, however, have more elastic demand. If the price of a new plasma TV skyrockets chances are we won't buy it (or we'll buy an LCD TV). This highlights another determinant of elasticity which is that if a good has many substitutes it will have more elastic demand.

Formally, elasticity depends on:

• Time Period
• # & Closeness of Substitutes
• Percentage of Income
• Luxury vs. Necessity

Let's capture how each relationship impacts elasticity.

### Elasticity and the Demand Curve

Elasticity changes as we move along the demand curve.

This is a significant and testable concept for the CFA Level 1 exam. You will need to know where Total Revenue is maximized and which parts of the demand curve have elastic/inelastic demand.

As we move along a linear demand curve we can actually see that elasticity changes, moving from more elastic to relatively inelastic. In other words, in the upper part of the demand curve the absolute value of elasticity is > -1 (i.e. the % change in quantity demanded is greater than the percentage change in price). At the midpoint it equals – 1, i.e. it is unit elastic. Finally on the lower half of the demand curve it is less (in absolute value) than -1. ### Elasticity, Market Structure, and Total Revenue

From the perspective of a supplier, the elasticity of demand is an important consideration when considering the impact of a price increase on total revenue, where we define total revenue as (Q x P).

At relatively high prices (the upper half of the demand curve) where demand is elastic, total revenue will increase (decrease) when prices decrease (increase) since the percentage growth in quantity demanded will outweigh the percentage decline in price.

On the lower half of the demand curve where we have inelastic demand the opposite is true. Total revenue will increase when the price is increased as the change in quantity demanded will be less than the percentage change in price.

The midpoint of the demand curve, where we have unit elastic demand, represents the point of maximum total revenue.

Increasing prices from here moves us into elastic demand where the change in quantity demanded will outweigh the price increase and a decrease in price moves us into the area of inelastic demand where the percentage decrease in price will outweigh the resultant gain in quantity demanded.

### Income Elasticity of Demand

Be prepared for a question testing your understanding of normal and inferior goods.

So far we've been talking about the elasticity of demand as it relates to the price of the underlying good itself. But that is not the only type of elasticity (or at least, not the only way to represent and understand elasticity).

We capture the actual measurement of how sensitive the change in quantity demanded is to shifts in income using the income elasticity of demand.

The basic principle is the same except we substitute income into the denominator instad of using a good's price: #### Normal and Inferior Goods

Most goods, called normal goods, have a positive income elasticity—as incomes rise we want to purchase more. Graphically this would be shown as a shift of the demand curve up and to the right.

However there are goods where quantity demanded decreases as income rises (they will have a negative elasticity). These are called inferior goods.

Can you think of an example of an inferior good? How about spam? Generally spam is purchased to eat if you can’t afford meat. As your income rises you would shift your consumption and decrease the amount of spam you buy.

### Cross-Price Elasticity

Cross-price elasticity measures the how much the quantity demanded of one good changes in response to the price change of another good. We measure cross-price elasticity against either a substitute or complement. Cross-price elasticity is negative for complementary goods. That is, as the price of a complement (Y) increase the demand for Good X will decrease. Cross-price elasticity is positive for substitute goods. As the price of Substitute B increases demand for good A will increase.

Be prepared for CFA L1 exam questions asking you to identify a good is complementary or a subtsitute for another good based exclusively on cross-price elasticity.

### Summary – Elasticity for the CFA Level 1 Exam

Elasticity is the ratio of the percentage change of one variable to the percentage change of another. The three elasticities from our original demand curve equation relate to the price of the good, the level of income, and the price of related goods (substitutes and complements) respectively.

• If Own Price Elasticity > 1 demand is elastic, if it is < 1 demand is inelastic
If Income Elasticity is > 0 the good is a normal good, if it is < 0 it is an inferior good
If the Cross Price elasticity is > 0 the related good is a substitute, if it is < 0 it is a complement