Unit 4: Elasticity

Elasticity

Suppose you own a bicycle business and you are thinking of raising your prices.  You are naturally curious how your customers are going to react.  You know that at a higher price consumers will buy fewer bicycles.  But you are tempted by the extra money that can be made by selling your bicycles at a higher price.  What should you do?  Your decision will be based on the total revenues you collect.  What are total revenues?  Continue to read below to find out more about elasticity.

Elasticity describes the responsiveness ( in percentage terms) of the quantity demanded to changes in price.  Knowing how sensitive a product is to a change in price is important in pricing goods and services.  Elasticity is a tool that an owner of a business can use to understand how consumers will change their behavior when you, as a business owner, change the price of a product.  There are five categories of price elasticity.  The categories of perfectly elastic and perfectly inelastic lean towards being more theoretical.  There are few real world examples for those two categories.

Categories of Elasticity

1.  Perfectly Elastic:  A price change causes Q demanded to change by an indefinitely larger percentage- a small decrease in price would cause buyers to increase buying from zero to all they desired.

2.  Elastic:  A given % change in price results in a larger % change in Q demanded.  The elasticity coefficient is greater than 1 but less than infinity.  For example, if a business reduces the price of televisions by 20%, and the demand for these cheaper televisions increases by 50%, this demonstrates that the televisions are elastic.

3.  Unitary Elastic:  A given % change in price results in an equal % change in Q demanded-  The elasticity coefficient always equals 1.   For example, if a business reduces the price of coffee makers by 20%, and the demand for these cheaper coffee makers increases by 20%, this demonstrates that the coffee makers are unitary elastic.

4.  Inelastic:  a given % change in price results in a smaller % change in quantity demanded.  The elasticity coefficient is greater than 0 but less than 1.  For example, if a business reduces the price of sandwich bag by 20%, and the demand for these cheaper sandwich bags increases by only 10%, this demonstrates that the sandwich bags are inelastic.

5.  Perfectly Inelastic:  A given % change in price results in no % change in Q demanded.  This usually occurs with necessities such as life saving drugs like insulin.

 

Elasticity and Total Revenue

Elasticity can also be understood by its relationship to total revenues.  Total revenues refers to the total number of dollars a firm earns from the sale of a good or service.  It is calculated by multiplying price times quantity (price x quantity).  In other words, elasticity deals with income (money that goes into the cash register) not with profits.  Elasticity tells the seller what happens to total revenue as the price of a product increases or decreases.

For elastic demand, the change in total revenue is in the opposite direction of price.  In other words, if the price of a product is decreased, total revenue increases.  Sales increase because consumers like lower prices (law of demand). If the price of a product is raised, then sales will decrease because consumers will look for lower priced substitute goods, which means total revenue will decrease.

For inelastic demand the change in total revenue is in the same direction.  In other words, if the price of a product is decreased, the change in total revenue also decreases. Also, if the price of a product increases, total revenues will increase (brand loyalty, lack of substitutes).

With respect to total revenues, unitary demand is unaffected by changes in price.

Characteristics that Affect Elasticity of Demand

There are factors that influence why a good or service is elastic, inelastic or unitary.  those factors are discussed below.

A)  Nature of the product.   Necessities tend to be inelastic, such as salt, and luxuries, such as stereos, tend to be elastic.

B)  Durability of the product.   Durable goods such as cars and TV’s tend to be elastic and non-durable goods, such as garbage bags,  tend to be inelastic.

C)   Size of the expenditure.   Small expenditures tend to be inelastic, and large expenditures are elastic.  Other things remaining the same, the greater the proportion of income spent on a good, the more elastic is the demand for it.  For example, if there is a sale on an expensive item such as automobiles (or if the interest rates are low, such as 0%), then there will be a large number of people who will seek to purchase a new car.  On the other hand,  if the good represents a small fraction of your income, such as butter, then the elasticity will be low, since most people can still afford to buy as much butter as they need as before the price increase.

D)  Substitute goods.    Substitute goods tend to be elastic.  For example, metals have substitutes such as plastics, so the demand for metals is elastic.  The question to ask here is, can people easily find a substitute when the price of a good or service goes up?  If the answer is yes, then the price elasticity will be elastic.

E)  Complementary goods.   Complementary goods tend to be inelastic.  For example, if the price of coffee decreases,  it will probably not affect the amount of sugar you buy to put in your coffee.

F)  Time.  If you give people longer to change their behavior, they will be able to make larger adjustments.  Here is where habit enters the picture.  Because habits are slow to break, a change in price is not likely to have a large immediate impact on demand.  If you give people a chance to adjust, however, they may very well be able to ‘break’ their habits and thus we could expect a larger response to the price change in the long-run.   Elasticity can also be affected in the short-run.   For example, if a store held a one day sale,  price elasticity would be high, because people would shift their buying to the sale day believing the opportunity for savings to be temporary.  On the other hand, if consumers believe the price cut will be permanent, the price elasticity will be smaller, since there is no advantage to buying sooner rather than later.

The amount of time one has to respond to a price change affects the size of that response. For most goods, in the short run, buyers tend to purchase nearly the same quantity as before a price change. So in the short run, demand tends to be price inelastic. But given time, buyers can alter their consumption behavior and look for hard to find substitutes. So in the long run, demand tends to be price elastic. Take an increase in the price of gasoline for example. If you do not learn about the price increase until you pull up to the pump (and you believe gas prices have increased at all gas stations) you will likely top off your tank as usual. But given time, you can find ways to drive your car shorter distances, buy a car that gets better gas mileage, or even move so that you live closer to where you work. So in the long run, you will be much more responsive to a price increase than you can be in the short run.

Think of elastic and inelastic goods this way.  People will get in their car and drive to a store to buy a product that is elastic, such as a new bedroom set.  The reason for this is that the potential savings is large.  They probably will not run out to the store if the price change is on an inelastic good, such as sandwich bags.  Goods and services that are elastic have many substitutes and are quite sensitive to price changes.  Goods and services that are inelastic are not sensitive to price changes and we don’t see much of a change in quantity demanded.

Characteristics of Elastic and Inelastic Goods.

Elastic                                         Inelastic

durable                                        non-durable

expensive                                    inexpensive

luxuries                                        necessities

substitute goods                        complementary goods

 

 Midpoint Formula For Price Elasticity of Demand

As was described earlier, elasticity measures the responsiveness of the quantity demanded to changes in price. There is a mathematical formula used to calculate elasticity. That formula is discussed below.

Many students have a math phobia, especially when it relates to subject matter outside of the field of mathematics. The midpoint formula should not cause too much math anxiety. If you look at the formula below, most of what you are doing is adding and dividing. The purpose of the formula is to discover the responsiveness in quantity demanded to a change in price. The midpoint formula is preferable when calculating the price elasticity of demand because it gives the same answer regardless of the direction of the change.

 

The Midpoint Formula

Price per candy bar Q demanded per week Total Revenue Elasticity Coefficient
.40 3 $1.20
.35 4 $1.40
.30 5 $1.50
.25 6 $1.50
.20 7 $1.40
.15 8 $1.20

 

The formula for elasticity of demand is in the yellow box below:

 

where:

Q1 = initial or old quantity

Q2 = final or new quantity

P1 = initial or old price

P2 = final or new price

 

When you have completed your math, the absolute value removes any negative sign.

 

The example below is using is using the numbers for moving from 3 candy bars to 4 candy bars (the price change of going from 40 cents to 35 cents) from the table above.

( change from 3 to 4 candy bars)

___1____=       1

(3+ 4) / 2         3.5  =                .2857

_______ 

(Q1 + Q2) / 2)

.05 (change from 40 cents to 35 cents)

(.40 + .35) / 2   =    .05

(P1 + P2) / 2 )        .375    =     .133

What you get after you do the math from the numbers above is in the left hand column of numbers below. After you do the math at that step you get the numbers to the right of the first equal sign. When you do the math at that step, you get the final answer to the right of the second equal sign (2.1433) The answer means the price change is elastic since the number is greater than one. In other words, you have 1 ÷ 3.5 which equals .2857   Underneath the division sign, you then have .05 ÷ .375 which equals .133 Next you divide .2857 by .133 which gives you 2.1433

1       = .2857         .2857 =      2.1433

3.5                            .133

.05    = .133

.375

To figure out the remaining price elasticities from the candy bar table above, simply substitute the new numbers from the next price change. For the next price change, in parenthesis for quantity demanded you would put 4 and 5, and in parenthesis for price you would put .35 and .30.

Use the midpoint formula to see if you can figure out the numbers in the elasticity column in the graphic below:

1. Interactive Tutorial on Elasticity

2.  Extra Practice Problems for Calculating Elasticity

The price elasticity of supply bears some resemblance to the price elasticity of demand.  Price elasticity of supply measures the relationship between change in quantity supplied with a change in price.  If supply is elastic (greater than 1), then producers can increase output without a rise in cost or a time delay.  If supply is inelastic (less than 1) then producers find it difficult to change production in a given time period.

Just as there are factors that can impact elasticity of demand, there are also factors that can influence elasticity of supply. They are:

1)  Excess production capacity.  If a firm has extra production capacity, then it can increase output without an increase in costs.  In this case, supply will be elastic in response to a change in demand.

2)  Inventory of finished products.  If there are high levels of raw materials and finished products then the firm will be able to respond to a change in demand. If this occurs, it would indicate that demand is elastic. The opposite is true. If there is a shortage, then prices will increase.

3)  If the cost of a substitute factor is manageable, then the elasticity of supply is higher compared to if no substitution exists.  For example, if a bottling plant switches production from soda to beer.

4)  Time.  The longer the time period a business has to adjust its production level, the more elastic supply is.  The longer the adjustment period, the more able producers are to adapt to a price change.  The ability to increase quantity supplied in response to a higher price differs across industries. The response time is slower is industries such as oil and electricity (inelastic) than compared to home remodeling or being a food vendor (elastic).

Below is the midpoint formula for calculating the elasticity of supply.  You may notice that it looks similar to the midpoint formula for calculating elasticity of demand.

 

To sum up the concept of elasticity, elasticity measures the willingness and ability of buyers and sellers to alter their behavior in response to changes in their economic circumstances.

Application of Economics:  Elasticity and the War on Drugs

In the United States over the past few decades, there has been an ongoing “war” against the use of recreational drugs. This war on drugs has many costs, one of which is that it has made the United States have the highest percentage of its citizens imprisoned than any other developed nation.   Leaving aside the moralistic arguments found in other disciplines,  lets see how the field of economics views this social issue.

The government’s use of laws to restrict drug use has had an effect on the supply of drugs to the market.  Costs increase and those suppliers not willing to take the risk, leave the market.   The remaining suppliers are usually controlled by organized crime, with its connections, financial resources, and firepower.  The effect then of tougher enforcement of drug laws, is to make it more riskier and costly to supply drugs, which then results in the decreased supply of illegal drugs.

For drug users, on the demand side,  the drug war makes it more expensive to support their drug habits.   Because most drugs are addictive, the demand for illegal drugs tend to be inelastic.  In other words, the quantity needed by users does not drop off because of the increased risk.   In fact, because of the tougher penalties, the drug user is less worried about committing other crimes, such as theft, to support their habit.

This brings us to the question, should drugs be legalized?   What does the field of economics have to say if recreational drugs became legal?  There may be both good news and bad news.  The bad news is that drug use would probably increase due to the drop in price.   The good news would be that there would probably be less crime to obtain the money for a drug habit since prices would be lower.  Additionally,  the violent crime associated with territorial disputes would disappear if drug users could obtain drugs legally from a pharmacy.   There are some supporters of legalizing drugs who say that the state could discourage drug use by imposing a sales tax on drugs.   This might work.  But if the sales tax was too high, then it would allow a return to drug pushers and the violence that accompanies the illegal drug trade.  Legal or illegal, drugs have an economic cost to society.

Elasticity and Ride Sharing Companies Such as Uber and Lyft

Companies such as Uber and Lyft, which allow individuals to use their cars as taxis,  use elasticity to calculate prices.  During peak times these companies engage in “surge pricing”.  When market demand out-strips supply during peak times, then these companies raise their rates (prices).  The goal is to get more drivers to take to the road (increasing supply). Uber and Lyft are taking advantage of inelastic demand at busy times (you need to get to work so you pay the higher rate).

Copyright ©2007, 2014 Glenn Hoffarth All Rights Reserved

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