- the length of the production period.
In the late 1990's, demand for Australia wines overseas has reached all time records. Vines take three years to grow to a point where they yield adequate amounts of fruit. Increases in demand for Australian wine has seen prices rise (from Po to P1), and returns to existing grape growers are excellent. Those who wish to buy grapes face a market where supply can only increase marginally (from Qo to Q1), in the short term. However, many new stands of vines are being planted, and in a few years, returns to growers may stabilise, as supply increases. Prices will fall from P1 to P2 as the supply of grapes increases from Q1 to Q2.
- the availability of resources. Many grape growers are concerned that they face
potential shortages of water, and land suitable for grape growing. In Adelaide's
''Southern Vales'', a premium wine producing area, water supplies are limited. Growers use
''drip'' irrigation methods to minimise any evaporation losses, and to get the greatest benefit
from the water supplies.
- the inability to hold stocks.
When a tomato grower picks their crop, they only have a limited time to sell it. Many goods are perishable. Initially, the grower thought they would receive price Po, and therefore picked Qo tonnes of tomatoes. When the grower got to the market, however, they found that demand that day had fallen, and the market price for tomatoes was P1. The grower could put some of the tomatoes in cold storage, but there was not enough room for all the stock of tomatoes. The grower had to sell Q1 tonnes of tomatoes at whatever price they could get. The supply of fresh tomatoes is relatively inelastic; a fall in price does not significantly change the quantity on offer. - the level of unutilised capacity.
An incecream maker, in Spring, has unutilised capacity in their factory. They have several icecream making machines, but are only using one of them. If warm weather is forecast for next week, the ice cream manufacturer can rapidly increase production from Qo to Q1, with only a small increase in total production costs. The cost of icecream will rise only marginally from Po to P1.
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Many goods have demand curves that look like this. At some prices, a small
change in price may cause a large change in the quantity demanded. This shown in the diagram
as the movement from Pe to Pe1; a small change in price which
causes an even larger percentage decrease in quantity demanded (from Qe to
Qe1.
At other prices, a large increase in price may see a much smaller decrease in demand. This shown in the diagram as the movement from Pe2 to Pe3; a large change in price which causes a smaller percentage decrease in quantity demanded (from Qe2 to Qe3. |
The price elasticity of demand refers to the relationship between changes in price and the subsequent change in quantity demanded. Economists are very interested in elasticity. Calculating it will answer important questions like : if price rises by a certain amount, by how much will demand fall, and total revenue change?
We use the Greek letter ''eta'' or h
To make the model easier to understand, we will continue using straight lines for the demand and supply curves. What we will now look at is the slope of these curves: are the curves ''flat'' or ''steep''? Be aware, though, that there is no necessary reason for a demand or supply curve to be a straight line.
There are three methods that can be used to measure elasticity. The simplest is called the total outlays method.
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The Total Outlays Method
A simple method of measuring the price elasticity of demand is the
total outlays method. This method is only an approximate method of determining
elasticity. The most accurate method is the arc method of elasticity, which will
be outlined later in this section.
The ''total outlays'' method has two steps.
The first is to prepare a total outlay or total revenue table for the good
or service under investigation. The second step is to look at the change in total revenue
received and compare it with the direction of the price change that caused the change
in total revenue.
Consider the following table :
As price change from $1 per unit to $2 per unit, total outlays (total revenue) rises
from $1,000 to $1,800. Total outlays and price have both risen. Economists say
the demand for this good, in this price range is inelastic, and that the
good has price elasticity of less than 1, in this price range.
A given percentage change in price has resulted in a lesser percentage change in
quantity demanded. Price has doubled; that is increased by 100% : (from $1 to $2).
However, the quantity demanded has only fallen by 100, on a base demand of 900 units.
This is a decrease of only 100 / 900 = 11%
The owner of the firm producing this good can see that increasing price will have
beneficial effects on total revenue, and on total profits. The increase in price
has seen demand fall (this is the law of demand in action), but despite this, total revenue
received will increase.
When price rises from $7 to $8, however, total outlays (total revenue) fall from
$2,800 to $2,400. Total outlays have fallen when price has risen.
This movement in opposite directions indicates that the demand for this good is
elastic (in this price range). Economists say the good has price elasticity
of more than 1.
The owner of this firm can see that increasing price is a bad idea: total revenue
received will fall. It is likely profit will fall if prices are increased from $7 to $8.
You will note that when price changes from $5 per unit to $6, total outlays remain the same.
This indicates the good has unitary elasticity (an elasticity of 1.00).
But, you notice that the percentage decrease in quantity demanded is not equal to the
percentage increase in price. Confirm this yourself : price has risen from $5 to $6 :
(a 20% rise) and quantity demanded has fallen from 600 to 500 units : a 17% fall.
What's happening here? The differences in percentage change highlight that the
total outlays method is only an approximate measure of elasticity.
Follow this link for a series of multiple choice questions on the
Total Outlays method of determining elasticity.
Total Revenue - a Graphical Example
per
unit
Demanded
(or Total Revenue)
$
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Let's imagine we operate a small canteen in a school.
I might say to you ''increasing the price of a can of Brand ''X'' soft drink from $1.00 per can to $1.40 per can is not a good idea. Our customers will buy Brand ''Y'' instead.'' |
''At the moment, we are selling 200 cans per day of Brand ''X'', at $1.00 per can. We are generating $1.00 per can x 200 cans = $200 per day in revenue from sales of Brand ''X''. I believe that we will only sell 120 cans per day if we increase the price of Brand ''X'' to $1.40 per can; resulting in a daily revenue of $1.40 per can x 120 cans = $168.''
''The revenue we gain from increasing the price per can ($0.40 x 120 = $48) will not be enough to offset the revenue we will lose from the decrease in the quantity of cans we sell ($1.00 x 80 = $80).''
I show you my reasoning, on a Supply and Demand diagram (shown above). Implicit in my reasoning is my belief that Brand ''X'' has a close substitute in Brand ''Y'', and that Brand ''X'' is price elastic.
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You, however, are more in touch with teenage trends and fashion than I am.
You reply ''Brand ''X'' is really popular at the moment. I believe we can increase the price to $1.40 per can. We will lose very few sales''. |
You show me your analysis (shown above) of the market for brand ''X''. An increase in price to $1.40 per can will only cause a loss of 10 cans in sales per day. The revenue gain from the increase in price ($0.40 x 190 cans = $76) will more than compensate for the revenue loss caused the decrease in quantity sold ($1.00 x 10 = $10)
You have correctly noticed that Brand ''X'' is price inelastic, and that an increase in price will generate more net revenue.
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Qo is the initial quantity demanded.
Q1 is the new quantity demanded. Po is the initial price. P1 is the new price. |
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Inelastic Demand
If a given change in price causes a smaller proportionate change in quantity demanded, then the demand for the good or service is said to be inelastic. In the diagram to your left, Po, the initial price is 65 cents per litre, and P1, the new price, is 75 cents per litre; a 10 cent per litre increase. |
The percentage change in price is 10 cents per litre / 65 cents per litre = a 15% increase.
Qo, the initial quantity demanded is 20,000 litres; Q1, the new quantity demanded, is 19,500 litres. The change in quantity demanded is 500 litres, on an initial demand level of 20,000 litres = a 2.5% decrease.
The price elasticity of demand for petrol is defined as the percentage change in quantity demanded divided by the percentage change in price. (Ignore any minus signs). In this example, the price elasticity of petrol is 2.5% / 15% = 0.167.
Goods with price elasticities less than 1.0 are called inelastic
Demand for petrol is inelastic : petrol has no close substitute. Motorists can reduce their usage of their car, and perhaps drive fewer kilometres, but they can not fill their ''tank'' with water!
Motorists can convert their cars to run on liquified petroleum gas (which is considerably cheaper than petrol), but the conversion cost is high. Petrol does have a substitute; but LPG is not a close substitute.
Governments like to tax goods with inelastic demand curves. The diagram illustrates the effect of a 10 cents per litre tax; a shift of the Supply Curve from S to S1. Petrol station owners will notice a small fall in sales; but the effect on their profits is small. Governments do not like to be accused of driving small business out of business!
Other goods with high levels of taxation include alcohol and cigarettes: both very inelastic.
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Elastic Demand
If a given change in price causes a larger proportionate change in quantity demanded, then the demand for the good or service is said to be elastic. In the diagram to your left, the price of Moo iced coffee drink has risen from $1.50 to $1.70 per 500 ml container. Sales at your local corner store of ''Moo'' fall from 500 containers per week to 300 containers per week. |
Calculate the percentage increase in price, and the percentage decrease in quantity sold. Calculate the price elasticty of ''Moo''.
Summary and Solutions
The price elasticity of demand for a product is defined as the percentage change in quantity demanded divided by the percentage change in price. (Ignore any minus signs).
Goods with price elasticities greater than 1.0 are called elastic
(By the way, the answer is 3.0. A fall in sales of 200 containers per week, on initial sales of 500 containers per week is a 40% decrease. A 20 cent increase in price per container, on a base price of $1.50, is a 13.3% increase in price. 40% / 13.3% = 3.0).
For the mathematically minded : a demand curve that is a straight line has the equation y = b - ax. ''Y'' is the quantity demanded per unit time, and x is the price of the good or service per unit. ''a'' is the rate of change of quantity demanded as price increases.
That is, a is the price elasticity of demand for the product.
The demand curve has the form ''- ax'', to represent the law of demand : as price rises, demand falls.
If ''a'' is greater than 1, the good or service under review is likely to have an elastic demand curve. The curve is rather ''flat''.
If ''a'' is less than 1, the good or service under review is likely to have a inelastic demand curve. The curve is rather ''steep''.
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Perfectly Elastic Demand
A good with a perfectly flat demand curve has a price elasticity of demand of infinity. This would mean that a small change in price would lead to an infinitely large increase in Demand. In perfectly competitive markets (such as, say, coal), if you can charge slighly less than your competitors, and still make a profit, you will find your customers will attempt to buy as much as you can produce. |
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Perfectly Inelastic Demand
To have a situation where the Demand curve is a vertical line is to think of a good where a certain quantity is demanded, regardless of the price. Heroin would be the closest ''real life'' example of such a good. Addicts will pay anything for their ''fix''. |
Return to Index
The Arc Elasticity of Demand
The arc elasticity of demand refers to the relationship between changes in price and
the subsequent change in quantity demanded.
 |
Qo is the initial quantity demanded.
Q1 is the new quantity demanded. Po is the initial price. P1 is the new price. |
The arc elasticity formula is used if the change in price is relatively large. It is more accurate a measure of elasticity than simple ''price elasticity''.
If the arc or price elasticity of demand is greater than 1, demand is said to be elastic. The demand curve has a ''flat'' appearance.
If the arc or price elasticity of demand is less than 1, demand is said to be inelastic. The demand curve has a ''steep'' appearance.
Calculating Elasticity
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Consider the market for music CDs. When the price of CDs is $30 per unit, consumers buy 6 per year. When the price falls to $20 per unit, consumers buy 12 per year. |
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Remember, we ignore the minus sign when calculating price elasticity.
When the price of CDs falls from $30 to $20, and the quantity sold increases from
6 per year to 12 per year, the price elasticity of demand is 1.67:
CDs are price elastic over this price range.
What about a further reduction in price? Will this also lead to even greater revenues for firms?
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The demand for CDs is price inelastic over the $20 to $10 price range, because the calculated elasticity is less than 1.
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Revenue is the price per unit sold multiplied by the quantity of
units sold in a period of time.
When a good or service is priced within its elastic region, it definitely worthwhile for firms to lower prices. ''You may make less profit per item, but you'll make more than enough extra sales to cover this loss of profit. In fact, you will make more profit overall.'' However, when a firm sells at a price associated with unit elasticity, its revenue is at a maximum. |
The firm may lower prices even further, but the increase in quantity sold will not be great enough to increase profits. In fact, profits will fall.
We show this in the total revenue curve (shown above). There is a price per unit that maximises profit!
For the mathematically minded : we use arc elasticity, and thus average price and average quantity, rather than point elasticity, because the starting point will effect our result.
If you calculate point elasticity using $10 as the starting point, and $20 as the finishing point, you will arrive at a different answer from using $20 as the starting point and $10 as the finishing point. That is, you will calculate two different point elasticities, depending on whether you use the case of prices rising, or the case of prices falling.
Prove it for yourself!
Factors Effecting the Elasticity of Demand
Good with close substitutes tend to have elastic demand curves. The demand for good
''A'' is ''price sensitive'' to changes in the price of good ''B'', because they both satisfy
the same want. The demand for one brand of butter will vary, if another brand is put on
''special'' at your local supermarket.
''Necessities'' tend to have inelastic demand curves. If households see a good as essential
to daily living, demand for the good will be ''price insensitive''. For example, if the
price of milk rose by 50 cents a litre, demand for milk would not change greatly.
All households want milk. Luxuries on the other hand tend to have elastic
demand curves. If soft drinks are put on ''special'' at your local supermarket, and
their price is lowered, demand for them will rise markedly. Part of this ''necessities''
versus ''luxuries'' distinction is based on the cost of the item. Many necessities
are inexpensive: they have low prices - a loaf of bread, a litre of milk, a box of matches,
all only cost a very small part of your available disposable income. An increase in the
price of a litre of milk of 50 cents is still ''small change'' for many consumers, and
they will continue to demand milk at the same levels as they did before the price rise.
Luxuries on the other hand can be very expensive and cost a large part of your
available disposable income. You may decide not to buy that French champagne to celebrate
a birthday, if the price rises from $30 to $32. The price of $30 is already a large enough
disincentive.
Some goods are habit forming, or addictive. Cigarettes are a clear example. Once ''hooked'',
the average smoker will continue to pay more and more for cigarettes, as governments increase
taxes on tobacco. Very few smokers give up smoking because of price increases; most give up
for health reasons.
All normal goods have positive elasticities of demand; the elasticity of the
good is > 1. For some goods (like petrol), the price elasticity of demand will be
very close to zero; but it will be greater than zero - some decrease in demand for petrol
will result if price rises.
Inferior goods have negative elasticities of demand. As income rises, the
quantity demanded actually falls.
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Factors Effecting the Elasticity of Supply
Supply curves have ''elasticities''. just as demand curves do. The major factors effecting
the response of firms to changes in price are expectations of future prices and
time.
The Arc Elasticity of Supply
The arc elasticity of supply refers to the relationship between changes in price and
the subsequent change in quantity supplied.
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Qo is the initial quantity supplied.
Q1 is the new quantity supplied. Po is the initial price. P1 is the new price. |
Firms will increase production if they believe market prices for the good or service they produce will increase in the future, and if they believe such a price rise will be a permanent change in the market. (There is no incentive to increase production and stocks, if prices are expected to fall again in the near future).
Over short periods of time, most goods have an inelastic supply. As we expand our time frame, goods tend to have more elastic supply.
The shortest period of time economists look at is the market period. In this period, suppliers can only add to the supply they offer to consumers by using up their stocks. A retail firm for example, may take deliveries every week from manufacturers. This weekly arrival of new goods is a flow. Most firms keep a ''buffer'' of goods, in reserve, in case demand rises unexpectedly. Each week, last week's stock is the first to be sold, and part of this week's purchases replaces this old stock. In the market period supply is highly inelastic.
The market period can vary in time. In the fresh vegetable market, an increase in demand for tomatoes on a Tuesday can see retail firms telephoning suppliers and getting extra supplies delivered the next day. If you retail imported cars, the market period could be a month or even more; it takes this long for the cars to be transported from Japan or Germany or where-ever.
The short run is the period of time required to to increase production through employing more labour and raw materials. If the ''pool'' of unemployed skilled labour is small, firms may not be able to increase production by much at all; supply will tend to be inelastic. Similarly, if the raw materials needed in production are also in short supply, then additional production may be difficult to create.
A firm, in the ''short run'', can not increase its capital stock; the machinery used in production. A firm may have unutilised capacity or excess capacity, however. Such a firm can increase production by using its capital more intensively by having extra shifts (night shifts, week end shifts, overtime), assuming labour and materials can be accessed in extra quantities in the same time. If all the machinery used in production is being fully used, however, the ability to increase production is limited. A firm in this situation will find its supply curve inelastic.
In the ''short run'', supply is reasonably elastic; however labour costs may rise per unit of production if your work force is paid penalty rates for night shifts and weekend shifts.
In the long run, firms have the time to invest in new capital. In the ''long run'', supply is at its most elastic, as production can be increased markedly.
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Inelastic Supply
The diagram to your left indicates a good which has an inelastic supply curve. It is possible, for example, to grow tomatoes all year round. To grow tomatoes in winter requires glass houses, heating, and supplementary lighting in the right wave lengths, to compensate for the shorter days and longer nights. However, it can be done; but at a considerable cost. |
The price of tomatoes would have to rise by a considerable amount (to P1 from Po) to justify the small increase in quantity supplied. (Q1 less Qo).
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Universities set quotas on some subjects, because of limitations on resources. The University actually supplies a fixed number places. It is Year 12 students who demand entry. An increase in demand for a particular course can occur, from year to year. However, an increase in demand for the course simply means candidates will have to achieve a higher TER entrance score; the ''price'' of an education. |
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Elastic Supply
The diagram to your left indicates a good which has an elastic supply curve. An icecream manufacturer can rapidly increase production, if hot weather is forecast. Sales are likely to increase by a large amount. |
The demand for icecreams would have to rise by only a small amount (to P1 from Po) to justify the large increase in quantity supplied. (Q1 less Qo).
Elasticity of supply is influenced by a number of factors. These include :
Cross Elasticity of Demand
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The quantity of any good that is demanded depends on the prices of
its substitutes and its complements.
How much demand for one good is effected by changes in the price of another, associated good is measured by the the first good's cross elasticity of demand |
The cross elasticity of of demand for substitutes is a positive number. After all, if the price of good B rises, then the demand for good A will also rise.
The cross elasticity of demand for complements is negative. If the price of good B rises, then the quantity of good A demanded will fall.
Income Elasticity of Demand
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What happens to the demand for a particular good as consumers' incomes change?
As you might expect, as income rises, demand for most, but not all goods will increase as well. |
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For some products, as income rises, demand for the particular good or service
rises even faster than income. We can see this in the diagram to our left; the curve
moves upward with ever increasing slope. We say the good or service in question is
income elastic.
Many ''luxury'' goods are income elastic; as we get wealthier, we tend to buy more expensive clothing, and go on more overseas holidays. We do not necessarily buy more shoes for example; we simply buy more expensive shoes (unless you are Imelda Marcos, of course). |
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For other products, we note that as income rises, the quantity demanded
also increases, but the increase in quantity demanded increases at a slower rate than
the increase in income. Products of this type are income inelastic.
The slope of the curve increases, but the rate of increase actually falls. (The curve looks like it will reach some kind of ''maximum'' as income rises). |
Products with inelastic income demand include food (but see below) and items like magazines.
If you produce goods or services which are income inelastic, you will sell more as people's incomes rise, but the rate of growth of your profitability will eventually fall.
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There are some goods and services, however, which display a most interesting
feature associated with their income elasticity.
Initially, as consumer's incomes rise, demand for these goods also rises. (Although the rate of increase of demand is less than the rate of increase in income). |
However, when incomes reach a certain level, the demand for these products actually decreases.
The income elasticity of demand for these products is negative, at certain levels of income.
In developing countries, as income rises, consumers buy more meat and eat less rice or wheat products. In China, as incomes have risen, motorcycles have replaced bicycles.
Goods which have positive income elasticities of demand ( h > 1 ) are called normal goods.
Goods which have negative income elasticities of demand ( h < 1 ) are called inferior goods.
(Note : ''inferior'' here means that as incomes rise, the goods in question are replaced with ''higher quality'' substitutes.)
Q.13(a) Follow this link to view a Java Script Quiz on Advanced Elasticity - suitable for International Baccalaureate Economics.
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