Elasticity

If the price of a good increases or decreases, would you buy more or less of that good? In actuality, it depends.

For example, if the price of gas increases, I am still going to buy the same amount of gas as I did before. If the price of prescription medicine increases, one would probably still buy the same amount because it is a necessity.

However... if the price of ice cream were to increase 3 fold, I would buy a lot less. I don't need ice cream to live my life!

This concept is known as price elasticity...

Price elasticity measures how responsive quantity demanded and quantity supplied are to a change in price. 

There's two different types of price elasticity we'll be working with: (1) Price Elasticity of Demand and (2) Price Elasticity of Supply!

Price Elasticity of Demand 

In the examples above involving gas, medicine, and ice cream, we were dealing with price elasticity of demand.

Price Elasticity of Demand measures the responsiveness of quantity demanded to a change in the price of a good or service. 

To see this in action, let’s look at the market for skateboards.

Question: The price of skateboards is $50 dollars. At this price, 100 skateboards are demanded. If the price increases to $75 dollars, the demand falls to 80 skateboards. What's the price elasticity of demand?

If we wanted to calculate the price elasticity of demand (E_d) of this demand curve, we'd use the formula below:

E_d = percentage change in quantity demanded / percent change in price 

This formula shows how much quantity demanded changes when the price is changed. Let's start by calculating the percentage change in quantity demanded, which we can compute with the following formula (to essentially determine the percentage change between Q₁ and Q₂):

E_d = [ (Q₂ - Q₁) / ((Q₁ + Q₂) / 2) ] / percent change in price 

Based on the question, Q₁ is 100...

Question: The price of skateboards is $50 dollars. At this price, 100 skateboards are demanded. If the price increases to $75 dollars, the demand falls to 80 skateboards. What's the price elasticity of demand?

E_d = [ (Q₂ - 100) / ((100 + Q₂) / 2) ] / percent change in price 

...and Q₂ is 80.

Question: The price of skateboards is $50 dollars. At this price, 100 skateboards are demanded. If the price increases to $75 dollars, the demand falls to 80 skateboards. What's the price elasticity of demand?

E_d = [ (80 - 100) / ((100 + 80) / 2) ] / percent change in price 

Now, let's move onto percent change in price. To compute this, we're going to use the exact same percentage change formula, except this time for price (P) instead of quantity (Q)!

E_d = [ (80 - 100) / ((100 + 80) / 2) ] / [ (P₂ - P₁) / ((P₁ + P₂) / 2) ]

Based on the question, P₁ is $50...

Question: The price of skateboards is $50 dollars. At this price, 100 skateboards are demanded. If the price increases to $75 dollars, the demand falls to 80 skateboards. What's the price elasticity of demand?

E_d = [ (80 - 100) / ((100 + 80) / 2) ] / [ (P₂ - 50) / ((50 + P₂) / 2) ]

...and P₂ is $75.

Question: The price of skateboards is $50 dollars. At this price, 100 skateboards are demanded. If the price increases to $75 dollars, the demand falls to 80 skateboards. What's the price elasticity of demand?

E_d = [ (80 - 100) / ((100 + 80) / 2) ] / [ (75 - 50) / ((50 + 75) / 2) ]

When we solve this out, we get a price elasticity of demand of -0.776.

E_d = [ (80 - 100) / ((100 + 80) / 2) ] / [ (75 - 50) / ((50 + 75) / 2) ] = (-20 / 90) / (25 / 87.5) = -0.222 / 0.286 = -0.776

So... what does this mean?

Why is it always negative?

Simply put, it's because...

Because of law of demand (meaning that the demand curve is downward sloping), price elasticity of demand will always be negative.

Elastic vs. inelastic vs. unit elastic

Elasticity, as stated above, measures responsiveness to quantity demanded based on price of a good or service.

Elasticity can fit into 3 types...

-1 < E_d < 0 means that E_d is inelastic. This means that quantity demanded is less reactive to changes in price.
E_d < -1 means that E_d is elastic. This means that quantity demanded is more reactive to changes in price.
E_d = -1 means that E_d is unit elastic. This means that quantity demanded is equally reactive to changes in price.

In our case, since we have an E_d value of -0.776, that means our demand of skateboards is inelastic! The quantity demanded of skateboards is less reactive to changes in price of the skateboards!

What determines Price Elasticity of Demand?

Let's dig into each of them below!

Type of good

If a good is a necessity, then it is inelastic. Think about the gas or medicine example. If the price goes up or down demand stays the same because people will buy it no matter what.

If a good is a luxury, then it is elastic. For example, ice cream is a luxury so if the price goes up, the quantity demanded will change.

Substitutes

If a good has lots of substitutes, then it is elastic. For example, if Colgate toothpaste increases their prices, then the quantity demanded for Colgate toothpaste will go down because people will switch to substitute brands. 

If a good has few substitutes, then it is inelastic. For example, in Oxford, OH there are very private gyms. If the off-campus gym I go to increases their prices, I don’t have another option so the quantity demanded for my gym will stay constant if the price changes. 

Time horizon

If the time horizon for purchasing a good is long, then the good will be elastic. If you have a lot of time to purchase a good, you can find substitutes if the price changes. 

If the time horizon for purchasing a good is short, then the good is inelastic because people don’t have a lot of time to find substitutes. 

Market

If the definition of the market is narrow (e.i. A specific brand), then the good is elastic. For example, the market for Colgate toothpaste is elastic because there are plenty of substitutes available.

If the definition of the market is broad (e.i. product), then the good is inelastic. For example, if the market is for toothpaste as a whole, then there are not any substitutes for cleaning teeth and people cannot switch products. 

Product expenditure

If the share of product expenditure in your budget is small, then the good is inelastic. For example, chewing gum takes up a tiny portion of someone’s income so if the price of gum increases, then people will not change how much they buy.

If the share of product expenditure in your budget is large, then the good is elastic. For example, if the price of cars significantly increases, the amount of cars that are purchased changes because it takes a great portion of someone’s income. 

Price Elasticity of Supply

Like Price Elasticity of Demand measures responsiveness of quantity demanded to the price of the good...

Price Elasticity of Supply measures the responsiveness of quantity supplied to a change in the price of a good.

In economics situations, price elasticity of supply is a function of how easily producers can adjust manufacturing or the amount they offer to sell. 

The equation is very similar to the price elasticity of demand equation:

E_s = percentage change in quantity supplied / percent change in price

For example, with the following situation...

Question: The price of skateboards is $50 dollars. At this price, 50 skateboards are supplied. If the price increases to $75 dollars, the demand falls to 80 skateboards. What's the price elasticity of supply?

...we'd plug the following variables into the price elasticity of supply equation...

E_d = [ (Q₂ - Q₁) / ((Q₁ + Q₂) / 2) ] / [ (P₂ - P₁) / ((P₁ + P₂) / 2) ]
E_d = [ (80 - 50) / ((80 + 50) / 2) ] / [ (75 - 50) / ((50 + 75) / 2) ]

...and obtain the following price elasticity of supply.

E_d = [ (80 - 50) / ((80 + 50) / 2) ] / [ (75 - 50) / ((50 + 75) / 2) ] = (30 / 65) / (25 / 87.5) = 0.462 / 0.286 = 1.615

So... what does this mean?

Why is it always positive?

Simply put, it's because...

Because of law of supply (meaning that the supply curve is upward sloping), price elasticity of supply will always be positive.

Elastic vs. inelastic vs. unit elastic

Elasticity, as stated above, measures responsiveness to quantity supplied based on price of a good or service.

Elasticity can fit into 3 types...

0 < E_s < 1 means that E_s is inelastic. This means that quantity supplied is less reactive to changes in price.
E_s > 1 means that E_s is elastic. This means that quantity supplied is more reactive to changes in price.
E_s = 1 means that E_s is unit elastic. This means that quantity supplied is equally reactive to changes in price.

In our case, since we have an E_s value of 1.615, that means our supply of skateboards is elastic! The quantity demanded of skateboards is more reactive to changes in price of the skateboards!

What Determines Price Elasticity of Supply?

Let's dig into each of them below!

Time Horizon 

The more time a producer has to respond to price, the more elastic production will be.

For example, if manufacturers of shoes expect the price to increase next year, they have a full year to improve the manufacturing capabilities to met the expected change in price.

Production capacity

If already at full capacity then production will be inelastic.

We saw plenty of examples of this during the COVID pandemic because production capacities were kept very high so producers could not respond to changes in price.

Inventories 

Large inventories allow for suppliers to be elastic while small inventories cause the price elasticity to be inelastic. This is because producers can sell stored items if price increases. 

Income elasticity of demand and types of goods

There's one last type of elasticity we'll touch on: Income elasticity of demand.

Income elasticity of demand measures the responsiveness of demand to a change in income.

In other words, when a person’s income changes, how do their purchasing habits change? Well... it depends on what type of goods they are purchasing. 

Normal goods

A normal good is a good where an increase in income causes an increase in demand. They have an income elasticity greater than 0.

For example, let’s say that your salary increases by $40,000 a year. Now that you have this extra money, your demand for normal goods increases. Examples of normal goods would be regular clothing, foods.

Within normal goods, there's two categories of goods: necessities and luxury goods.

Necessities

A necessity is a good where an increase in income causes a smaller percentage increase in demand. They have an income elasticity between 0 and 1.

A good example of a necessity good is water. If your income increases, you're probably not going to increase your water consumption by a large percentage as before.

Luxury goods

A luxury good is a good where an increase in income causes a bigger percentage increase in demand. They have an income elasticity greater than 1.

For example, if your income doubled you would be likely to buy luxury clothing or a sports car. 

Inferior goods

An inferior good is a good where an increase in income causes a fall in demand. They have an income elasticity less than 0.

For example, if someone can only afford plastic plates and ramen noodles, their demand for those goods would decrease if their income increases.