Author:  Lori Alden

 

Wong’s Theater is losing money, but Ernesto thinks he knows how to make it profitable again:   lower ticket prices.

You may be wondering how lowering the ticket price could help the Drive-In become more profitable.  If Wong's Drive-In is losing money, shouldn't Mr. Wong raise ticket prices?

While raising prices is sometimes a good way to increase profits, it doesn’t always work.  If Mr. Wong raises the ticket price, he'll sell fewer tickets.  The higher price might cause his revenue to go up, but selling fewer tickets might cause it to go down.  To be sure about the effect of a change of price on a firm's revenue, we have to look more closely at the demand curve─in particular, its elasticity.

Elasticity measures the responsiveness of something to a change in something else.  For example, snow cone sales tend to be very responsive to changes in the temperature outside, so we can say that snow cone sales are elastic with respect to temperature.  Dog food sales, however, hardly respond at all to changes in temperature.  Dog food sales are therefore inelastic with respect to temperature.

Economists are especially interested in how the quantity demanded of a good responds to changes in its price.  This kind of elasticity is called the price elasticity of demand.  Take Dr. Kenisha Maddox’s demand for bridge crossings, for example.  Dr. Maddox lives across the bridge from City Hospital , where she works five days a week.  The price (or toll) for crossing the bridge into the city is $3, and there is no price for the return crossing.  At that price, Dr. Maddox crosses the bridge into the city five times a week.

Dr. Maddox would also cross the bridge into the city five times a week if the price were $1, or $10, or even $25.  Her demand for bridge crossings into the city isn’t very responsive to changes in the price, so we say that her demand is inelastic with respect to price.  More generally, we say that demand is price inelastic if a change in price results in a smaller percentage change in quantity demanded.

Next consider the demand for gasoline at Oakdale's Arco station, as shown below.  Arco currently charges $2.50 per gallon and sells 15,000 gallons per day.  The Shell station across the street charges the same price and sells about the same number of gallons.  Now suppose that Arco raised its price to $2.75, but Shell didn't.  (Remember, if Shell raised its price, too, then Arco's demand curve would shift to the right.  When measuring elasticity, we are interested in how quantity demanded responds to a change in price, other things being equal.)  How would consumers respond?

Since Arco's gas is very similar to the gas at the Shell station across the street, few customers would continue buying gas there if the price was that much higher.  Quantity demanded would fall off by quite a bit, say to 1,000 gallons a day.  Since the change in price caused a larger percentage change in quantity demanded, we say that the demand for Arco gas in Oakdale is price elastic.

 

Elasticity and Revenue

1.  Price inelastic demand

Economists are interested in the price elasticity of demand curves because it tells them how changes in price affect the revenue received by producers.  Recall that revenue is equal to the price times the quantity sold of a good. 

A demand curve for coffee is shown below.  Notice that when the price goes from $1 to $2 (a large percentage increase), the quantity falls from 10 billion pounds per year to 8 billion pounds per year (a small percentage decrease).  Since the quantity demanded isn’t very responsive to a large percentage increase in price, demand is price inelastic.  Assume that the price is initially $1 a pound and the quantity is 10 billion pounds, as shown at point A.  At that equilibrium, the revenue received by coffee growers would be $1 times 10 billion pounds, or $10 billion.

Now suppose that the coffee-growing regions worldwide have a bad winter and frost destroys much of the coffee crop.  This would cause the supply curve to shift from S to S' and move the equilibrium to point B.  At B, the price is $2 and the quantity is 8 billion.  The revenue, then, becomes $2 times 8 billion, or $16 billion.

You may want to read the last two paragraphs again, for they lead to a remarkable conclusion.  If frost destroys part of the coffee crop, then the revenue received by coffee growers will actually go up.  In fact, Brazil , which used to produce the vast majority of the world’s coffee, used to deliberately destroy part of its crops during those years in which it was not lucky enough to experience frost. 

The reason an increase in price caused an increase in revenue for coffee is that its demand is price inelastic.  In this example, as the table below shows, the increase in price had a greater effect on revenue than the decrease in quantity demanded. If the price goes up by a larger percentage than the quantity goes down, then the product of the two, revenue, will increase. 

 

 

Price
(per pound)

Quantity 
(billions of pounds per year)

Revenue
(billions per year)

Point A

$1

10

$10

Point B

$2

8

$16

The table also shows what would happen if the price of coffee were to fall from $2 to $1.  The quantity demanded would increase from 8 billion pounds to 10 billion pounds, and revenue would decrease, from $16 billion to $10 billion. 

Let's summarize what we've learned so far:

If demand is inelastic with respect to price, an increase in price will result in an increase in revenue, and a decrease in price will result in a decrease in revenue.                                

Does this mean that all producers of goods with price inelastic demand curves should cut back on production or destroy their goods in order to increase their revenues?  Suppose Farmer Brown, an Oakdale wheat farmer, was to do that.  Wheat is price inelastic, as shown below. 

Farmer Brown produces 10,000 bushels of wheat per year.  But that amount is very small compared with the average total U.S. wheat production of about 2,000,000,000 bushels per year.  If Farmer Brown were to destroy her crops, then the market supply curve would hardly shift back at all.  And even if Farmer Brown was able to nudge the price up slightly, she wouldn't be able to benefit if she had no crops to sell.  Instead, other wheat farmers would gain at her expense.

It only makes sense to restrict the output of a good with price inelastic demand if a single firm, group, or country is the main supplier.  Brazil , for example, used to supply up to 90% of the world's coffee.  When Brazil destroyed some of its crops, the benefits of the higher price for coffee were confined mostly to Brazil itself.

2.  Price elastic demand

Now let's see how price changes affect revenue when demand is price elastic.  Look again at the demand curve for Oakdale Arco gas.  Notice that when the price increases from $2.50 to $2.75, the quantity demanded decreases from 15,000 gallons per day to 1,000 gallons per week.

 

The following table shows what happens to the revenue received by Oakdale's Arco station when the price of their gas goes up.  Revenue at a price of $2.50 is 15,000 gallons per week.  If the price is increased to $2.75, then the quantity demanded drops by such a large amount that revenue declines to $2,750 per week.  

 

Price
($ per gallon)

Quantity 
(gallons per week)

Revenue
(per week)

Before

$2.50

15,000

$37,500

After

$2.75

1,000

$2,750

 

Here, revenue declines when the price goes up because there is a large decrease in the quantity demanded.  Similarly, if the price were to go down, then the quantity demanded would rise by a larger percentage amount and cause revenue to increase.  In other words:

  If demand is elastic with respect to price, then an increase in price will result in a decrease in revenue, and a decrease in price will result in an increase in revenue.

Here's an easy note-taking trick that will help you keep all of this straight:

Here, a tall arrow represents a large percentage change and a short one a small change.  With inelastic demand curves, price changes elicit just small percentage changes in quantity, so the price change has a more dominant influence on revenue.  With elastic demand curves, it's the quantity change that has the stronger influence.

 

The geometry of revenue

1.  Elastic or inelastic?  The rectangle test     

There's an easy way to tell at a glance whether the demand for a good is elastic or inelastic.  Let’s look again at the demand curve for world coffee.  At point A, the price of coffee is $1.00, and the quantity demanded is 10 billion.  Revenue equals price times quantity, or $10 billion.

 

Revenue is also equal to the area of the red rectangle in the figure.  The area of a rectangle is equal to its height times its width.  Here, the height of the rectangle is $1, the price of coffee, and the width of the rectangle is 10 billion, or the quantity sold at that price.  The height times the width of the rectangle gives its area, $10 billion, which is also the revenue at point A.

When the price rises to $2, we saw that revenue increases to $16 billion, which is the price times the new quantity, 8 billion.  This new revenue also can be represented as the area of the blue rectangle.  Since the blue rectangle lying below point B is larger than the red rectangle lying below point A, we know that revenue has gone up in response to a price increase, and that demand is price inelastic.

Let’s also look again at the Oakdale Arco gas demand curve.  The revenue for the Arco station is given by the red rectangle when the price per gallon is $2.50.  When the price rises to $2.75 per gallon, revenue shrinks to the size of the blue rectangle.  Since a price increase has caused a decrease in revenue, we know that the price elasticity of demand for Arco gas is elastic.

 

Demand curves can be elastic at some prices and inelastic at others.  Consider the demand for hotdogs at Oakdale Park .  The revenue received by the firm at a price of $1.50 per hotdog is equal to the area of the red rectangle, or $4.50.  If the price is lowered to $1, then revenue increases to the area of the blue rectangle, or $5.  The demand curve is clearly elastic between the prices of $1.50 and $1.

But now lower the price still further, to $.50.  The firm's revenue drops down to the area of the orange rectangle, or $4.50.  Between the prices of $1 and $.50, the demand curve is clearly inelastic, since a drop in price causes revenue to fall.  

The rectangle test:  Draw revenue rectangles for two points on a demand curve.  If a price increase makes the revenue rectangle become larger, then the demand curve is price inelastic between those two points.  If a price increase makes the revenue rectangle smaller, then the demand curve is price elastic between those two points.

2.  Where is revenue highest?  The midpoint test

Another quick way to determine the elastic and inelastic ranges of a demand curve is to make use of the following rule: 

If a linear demand curve is drawn from the vertical axis to the horizontal axis, the demand curve is price elastic between any two points above the midpoint of that line, and price inelastic below.

  In the following figure, point X is the midpoint of a line drawn between point A and point B.  The demand curve is price elastic between any two points above X, and price inelastic below.

 

This rule gives us a quick way of figuring out how to maximize a firm's revenue.  Since the demand curve is price elastic above point X, then as we come down the demand curve towards point X, the firm's revenue is increasing as its price goes down.  But below point X, the demand curve is price inelastic.  That means the lowering the price further will decrease revenue.

X, then, marks the spot.  The point that divides the demand curve into its elastic and inelastic ranges is also the point at which the firm's revenues are greatest.

The midpoint test:  If a linear demand curve is drawn from the vertical axis to the horizontal axis, the firm's revenue is greatest at the midpoint of that line.

 

What determines elasticity?

We've seen that the demand for a good tends to become more elastic as its price goes up, and less elastic as its price goes down.  The prices of most goods, though, don't vary that much, and tend to stay either in the elastic or inelastic range.  The demand for bridge tolls, for example, is price inelastic in its normal price range, so economists usually only draw the inelastic portion of its demand curve.

The demand for goods, then, can often be classified as either price elastic or price inelastic.  You can often guess whether the demand for a good is price elastic or price inelastic by considering the good's characteristics.

1.  Substitutes

Goods that have close substitutes tend to be more price elastic than goods that do not. We saw that the demand for Arco gas is price elastic.  This is because Arco customers could switch to a substitute, Shell gas, if Arco's price went up.  On the other hand, Dr. Maddox’s demand for bridge crossings is price inelastic because there aren't any good substitutes available.

 

2.  Luxury goods

Goods that are luxuries tend to have more elastic demands than goods that are necessities.  New parents would not cut back much on milk and diaper‑rash ointment -- both necessities -- even if their prices increased by a large amount.  But they would buy fewer luxuries -- like stuffed animals -- if their prices went up. 

3.  Share of budget

If you're like most people, you don't comparison shop for pencils.  If you need a pencil, you just go to the nearest store and pay whatever it charges.  In fact, you might even pocket your change without ever having found out the price.

It's not like that with cars, though.  People will spend many days comparing different models and driving to different dealerships in search of the best deal.

The reason people comparison shop for cars, but not for pencils, is because they spend a larger portion of their budgets on them.  If someone earns $20,000 a year, a $10,000 car is a major expense and it's worthwhile to spend some time searching for a good deal.  If you shopped around for a bargain pencil you'd end up saving only a few cents.

People tend to be more sensitive to prices when making large purchases.  If car prices were to double, then car sales probably would fall sharply. A lot of people who can afford a $10,000 car wouldn't be able to afford a $20,000 car.  They would simply have to make do with their old cars or public transportation.  Demand for cars and other "big-ticket items," then, tends to be price elastic.

On the other hand, if the price of pencils were to double,  sales probably wouldn't change that much.  People would just shrug and pay the higher price.  Goods like pencils that use up just a small share of a person's budget tend to be price inelastic.

 

Should Wong’s Theater lower its prices?

 

  Here’s the demand schedule for tickets to Wong’s Theater:

 

Price per ticket

Quantity
(tickets per day)

$4

53

$3

140

$2

252

$1

344

 

  And here’s a graph of it:

 

Mr. Wong is now charging $3 per ticket.  As the following table shows, if he raised the ticket price to $4, his revenue would decrease.  The demand curve is elastic in this range.  It’s also elastic between the prices of $3 and $2, since if he lowered the price to $2 per ticket, his revenue would increase.  He should lower his price to that level.  Mr. Wong shouldn’t lower the price to $1 per ticket, though, since his revenue would decrease.  The demand curve is inelastic in that range.

Price per ticket

Quantity
(tickets per day)

Revenue
(per day)

$4

53

$212

$3

140

$420

$2

252

$504

$1

344

$344

 

    

  

 

           

          

 

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