Elasticity

I.          Introduction

In a free market, and after enough time passes and information is exchanged to reach equilibrium, supply equals demand for both price and quantity sold.  That is one of the beauties of free enterprise.  It is efficient, productive and generates little economic waste.  If every good and service stayed at equilibrium, then we could end the course right now.

But we are not so fortunate.  Prices do change daily.  During your next few trips to the supermarket, notice how much the prices fluctuate.  This is because both supply and demand are always changing.  Supply changes due to problems or improvements in manufacturing and shipping.  Labor costs change over time, which also affects supply.  Demand is constantly fluctuating also.  Every day people lose or change jobs, which affects their buying decisions.  The changing of the seasons also affects demand, as do alterations in personal tastes.

Five to ten years ago there was tremendous demand for Beanie Babies, driving up the price.  Now there is far less demand, so the price has fallen.  The same could be said about any fad.

Greed also plays a role.  The suppliers of goods and services would like to increase their prices without losing sales, so that they can make more money.  Before Wal-Mart made price-cutting so popular, it was routine for suppliers to increase their prices every year.  Everyone expected it.

Imagine yourself as president of a company that makes widgets, and you are having a meeting to discuss your product.  Inevitably an employee suggests increasing the price on the widget so that the company will make more money.  People who have never studied economics think that increasing the price will always result in increased revenue from sales (Price x Quantity sold).

But suppose you have an employee who had taken this economics course in your meeting.  He or she points out that an increase in price will reduce the demand, because the demand curve is usually downward sloping.  You will sell fewer goods if you raise the price.

You then ask, “how much fewer sales?”  If sales decline by a smaller percentage than the price increased, then overall revenue (Price times quantity sold) will increase.  If, however, sales decline by a larger percentage than the price increased, then overall revenue will decline.

II.        Price Elasticity of Demand

The “price elasticity” of demand is the percentage change in quantity demanded divided by the percentage change in price.  It is usually negative but the sign is dropped so that price elasticity is always a positive number.

More simply, price elasticity is responsiveness to changes in price.  Think of a rubber band.  How easily can you stretch it any point?  The issue is the same for the public’s response to a change in price.  Will the public pay the higher price without complaint, or will they tend to refuse?

Let’s take an example.  Suppose the local NFL (football) team wants to make even more profit than it does already.  The owner decides to increase the ticket prices by 20% for next season.  Student Mary Rose calls this a silly game and so she persuaded her father not to renew the family’s season tickets at the higher price.  How many other season ticket holders will decide not renew?

Because watching football is an obsession for many fans, most are likely to pay the higher prices.  Maybe only 5% will choose not to renew.  The quantity demanded changed little despite a large increase in price.  This means the elasticity of demand is low.  To be precise, it is the percentage change in quantity demanded divided by the percentage change in price: -5%/20% = -1/4.  The sign is dropped so the elasticity is expressed as “1/4”.  This low elasticity encourages the supplier (the football team owner) to repeatedly increase the price.  Low inelasticity is described as an “inelastic demand” by economists.

How much more revenue does the team make by increasing the price?  Revenue is price times quantity.  If its original price was P and its original quantity Q, then initial revenue is PxQ, or PQ.  After the price increase, the revenue is (1.20 x P) x (.95 x Q) = 1.14PQ.  Revenue has thus increase 14% simply by increasing the price.  Nice business, if you don’t mind the silliness of watching it!

Let’s take another example.  Suppose that airlines increase the price on their flights from New York to Florida from an average of $300 per seat to $500 per seat.  That is a 67% increase.  What would that do to the tourist traffic to Florida from New York?  It only takes a day and a half to drive to Florida, which incurs gas charges of less than $100 and a hotel charge of perhaps $80.  Tourists would likely drive rather than pay the higher fares.  The demand for these higher-priced tickets could fall by 75%, assuming that business travel is only a small percentage of that traffic.

What is the price elasticity of this demand?  The percent change in quantity demanded is -75% (3/4) and the percent change in price is 67% (2/3), so the elasticity is -3/4 divided by 2/3 = -9/8.  The sign is dropped so the elasticity is expressed as 9/8.  It is greater than 1, and thus is described as having an “elastic demand” rather than an “inelastic demand,” which is less than 1.  (If it equaled 1, then it would be called “unit elasticity of demand.”)

What does it mean to a company if its goods have “elastic demand”?  It means the company should be cautious in raising prices.  Look at what happens to the revenue to the airlines due to the elastic demand for seats on their planes.  The initial revenue was price times quantity, which is PxQ, or PQ.  The revenue after the pricing change is (5/3)(P)(1/4)(Q) = (5/12)PQ.  Its revenue fell to 5/12 of its initial revenue due to the price increase.  The airlines lost over half of its revenue by increasing its price!  Uh oh, that requires laying off many employees, reporting losses to the investors, and firing the persons responsible for that price increase.

In that prior example, however, consider price increases on the same route that are due only to increases in fuel costs.  Will they have the same elasticity?  (No, because the alternative of traveling by car increases in cost by a similar amount.  However, some people will simply stay at home rather than travel.)

Take a straight line demand curve and consider what the shape the total revenue has as a function of price.  It has the shape of a semi-oval opening downward: it starts at zero revenue (when quantity is 0) and ends at zero revenue (when price is 0).

III.       Income Elasticity

Once you grasp the price elasticity of demand, you’ll see that you can describe the elasticity (or responsiveness) of many other variables in economics.

Income, like someone’s salary, affects the demand for goods.  Many more Mercedes-Benz luxury cars are likely to sell when average income is high than when it is low, for example.  So economists find it useful to describe “income elasticity of demand,” which is the percentage change in quantity demanded divided by the percentage change in income.

Most goods sell more when the income of buyers increases.  We all tend to go to restaurants more often, buy new clothes more often, and pay more for goods and services when we are making more money.  When our income declines, we cut back on our purchases.

In the first Lecture, we discussed the difference between goods we need (e.g., food) and goods we want (e.g., restaurant food).  The goods that we need are “necessities”; the goods we merely want are “luxury goods.”  Necessities are income inelastic, because they are needed and purchased whether our income is high or low.  Whether we have a good year or a bad one in terms of income, we still buy things like daily food, basic clothing, and heating at home.  In contrast, luxury goods are income elastic.  People do not buy as many yachts and luxury cars and homes when times are tough.

Here are some useful definitions.  A “normal” good is one for which demand increases when income increases.  Nearly all goods are “normal” goods.  Income goes up, then more of it is purchased.  Occasionally a good can be found that is “inferior”, such that demand actually decreases when income increases.  Can you think of one?  (Margarine is an example.  Can you explain why?)  So when the income elasticity is positive, then the good is “normal”.  When the income elasticity is negative, then the good is “inferior”.

A “necessity” is a good that has a positive income elasticity that is less than 1.  A “luxury” good is a good that has an income elasticity greater than 1.

IV.       Calculating Elasticities

There is an ambiguity in calculating the percentage change in price or quantity.  What should be used as the denominator in deriving the percentages?  If $100 increases to $110, then the percent change could be described as $10/$100 x 100% or $10/$110 x 100%.  Above we used the initial price and quantity as the denominator, but be could have used the final price and quantity as the denominator instead.

Economists resolve this by typically using the average overall value as the denominator in calculating the elasticities.  So if the price changes from $20 to $30, the percentage change in price is $10 divided by the average of $20 and $30, which is $25.  The percentage change is thus $10/$25, which is 40%.  This is also known as the “arc elasticity” because it is a more accurate depiction of the “arc” or curve of demand.  Use this method when doing specific calculations on homework.

V.        Complements and Substitutes

A complement of a good is something that is used with it.  Compact disks (CDs) are complements of CD players.  Hole punchers are complements to three-ring binders.  Monitors are complements to desktop computers.  Gasoline is a complement to cars.  Bread is a complement to sandwich meat.

A substitute of a good is something that replaces it.  Bicycles are substitutes for mopeds.  Motorcycles are substitutes for cars.  Channel 2 is a substitute for channel 4 on television.  One non-fiction book is a substitute for another.  Chicken is a substitute for beef.

Elasticity of demand can apply to complements and substitutes.  The “cross elasticity of demand” is how the quantity demanded of one good responds to a change in price of another good.  Specifically, it is measured as the percentage change in demand for one good in response to the percentage change in price for a different good.

If good A sees a 20% drop in demand based on a 20% increase in price of good B, then the cross elasticity of demand is -20%/20% = -1.  Do you think good A and B are complements or substitutes?  They are complements.  A negative cross-elasticity in demand means they are complements.  Their elasticity is in the same direction as the price elasticity of demand for the good itself.

If, however, good A sees a 20% increase in demand based on a 20% increase in price of good B, then their cross-elasticity in demand is 20%/20% = 1.  This positive value means that A and B are substitutes for each other.

Ponder that for a minute.

VI.       Addictions

The colony of Virginia survived and thrived by turning to tobacco and slavery.  Much of the economy, even today, is based on vices.  Sad but true.  The largest building west of the Mississippi, which includes all of California and many other states, is located in Las Vegas, built on gambling.  In fact, Las Vegas has far more hotel space than any other city in the United States, including even New York.

Manuel Miranda, a prominent attorney who just left the U.S. Senate staff, recently disclosed that abortion profits, not rights, are in control of the Democratic Party’s policies today.  He says that an average of $1000 in profits is made off of every abortion.

Go into a typical convenience store and you will find that they do a brisk trade in cigarettes, pornography, alcohol and lottery tickets.  Those four categories probably account for most of their profits.  The people paying for those goods are both losing money and hurting themselves.

In the “underground” (illegal) economy, drug trafficking accounts for an enormous amount of commercial activity.

What do all these economic activities have in common?  They exploit addictions.  The prices on these goods and services can be increased much more easily than on anything else.  Someone addicted to drugs is still going to try to buy it even if the price increases by 10%, 20%, 50%, or 100%.  The same can be said for gambling, pornography, alcohol and almost every other vice.  They are profitable to sellers who exploit the addiction.  Buyers lose far more than their money.

VII.             Assignment

Read and, if necessary, reread the above lecture.  Then read the Wikipedia entry and subentries for “elasticity (economics)”:  http://en.wikipedia.org/wiki/Elasticity_(economics)

Homework questions:

  1. In a free market, the responsiveness of demand to a change in price is known as its _________.
  2. Describe what an inelastic demand is, and give an example of a good having an inelastic demand.  Describe what an elastic demand is, and also give an example.
  3. Give examples of a complement and a substitute for exercise equipment.  Give examples of a complement and a substitute for the Big Mac hamburger.
  4. Describe a perfectly elastic demand curve, and a perfectly inelastic one.
  5. At what elasticity does a price change have the least effect on sales revenue?  What is the price elasticity of demand for a good that loses 20% in sales volume due to a 10% increase in price?
  6. If the demand curve is a straight line, then is the price elasticity of demand constant?  Explain.
  7. Describe what a negative income elasticity of demand means.  Give an example of a good or service (including charitable services) that might have a negative income elasticity of demand.
  8. The demand for milk is inelastic.  Suppose there was a disease that uniformly killed 20% of all cows, but did not affect demand at all (i.e., the public was not scared by the disease).  Are dairy farmers better or worse off due to the disease?  Explain.
  9. Suppose you own the New York Post, one of many newspapers in New York City.  Suppose also that the overall demand curve for the newspaper market in New York is inelastic.  Someone who took an inadequate economics course in college told you to raise the price based on the inelasticity of demand.  Is he right?

Extra credit (4 points each for questions 10 and 11; 6 points for question 12):

  1. Why do addictive goods tend to be inelastic?  How does that impact their supply?  Explain with examples.
  2. Consider the extra cost of religious education, which inevitably increases as the state increases the costs of public schools (through taxation).  Meanwhile, imagine a state lottery much larger and more popular than it is now.  Would you expect the cross-elasticity of demand for the state lottery relative to religious education to be positive or negative?  Explain.
  3. There are many wealthy charitable foundations that administer money donated a long time ago (e.g., the Henry Ford Foundation and the Packard Foundation).  Using the “invisible hand” (or lack of it), explain why these foundations almost always eventually spend the money in ways their founders would have never approved.