## Elasticity

### Elasticity #### Key Learning Outcomes

• Explain the concept of elasticity.
• Explain price elasticity of demand (PED).
• Calculate PED from given data using the supplied formula and interpret values for PED.
• Understand the usefulness of a knowledge of PED to the consumer, producer and government.
• Explain the factors that determine the PED of a good.
• Apply a knowledge of price elasticity to determine the effect of a change in price on a firm’s revenue and profits.
• Explain cross elasticity of demand (CED).
• Calculate CED from given data using the supplied formula and interpret values for CED (substitute goods and complementary goods).
• Understand the significance of a knowledge of CED to a firm.
• Explain income elasticity of demand (YED).
• Calculate YED from given data using the supplied formula and interpret values for YED (normal goods and inferior goods).
• Apply a knowledge of income elasticity to determine the effect of a change in income on a firm’s sales.

#### Introduction:

Definition: Elasticity is a measure of responsiveness of the quantity demanded of a good to a change in some variable.

Elasticity of demand relates to the change in the quantity demanded of a good as a result of a change in something else. This something else could be

• A change in the price of the good itself (Price Elasticity of Demand).
• A change in the price of a complement or substitute good (Cross Price Elasticity of Demand).
• A change in a person’s income (Income Elasticity of Demand).

Elastic = the percentage change in quantity demanded is greater then the percentage change in price.

Examples: luxury goods, consumer durables and goods with many substitutes. Perfectly Elastic = any increase in price causes quantity demanded to fall to zero.

Example: firms that operate in perfect competition. Inelastic = the percentage change in quantity demanded is less then the percentage change in price.

Examples: necessities e.g. petrol, goods of addictive nature. Perfectly Inelastic = any change in prices results in no change in quantity demanded

Examples: goods such as life-saving medicines. Unitary Elastic = the percentage change in price is equal to the percentage change in quantity demanded. PRICE ELASTICITY OF DEMAND (PED)

The most important one is the Price Elasticity of Demand (PED).

Price Elasticity of Demand measures the responsiveness of quantity demand of a good to changes in the price of that good.

Definition: The Price Elasticity of Demand of a good is the percentage change in the quantity demanded for a good caused by the percentage change in the price of that good.

Significance of the plus (+) or minus (-) sign.

Sign = normal good (goods that obey the law of demand)
+ Sign = Giffen good (goods that do not obey the law of demand)

All goods which obey the Law of Demand have a negative price elasticity of demand.

 We know that all goods that obey the law of demand have a downward sloping demand curve, because of the inverse relationship that exists between price and quantity demanded. We know that as price goes up demand goes down and vice-versa. If ∆P↓ then ∆Q↑ and if ∆P↑ then ∆Q↓. Therefore the PED of a good that obeys the law of demand will always be negative. The PED of the good above was -1.1818 showing us that this good obeys the law of demand. We know that not all goods obey the law of demand. Giffen goods, Snobs goods and goods that are affected by consumer’s expectations can have an upward sloping demand curve. As the price of these goods goes up so does the quantity demanded.  If ∆P↓ then ∆Q↓ and if ∆P↑ then ∆Q↑.  The PED of these goods is positive.

Note

Give a definition of said good:

Normal good – goods which obey the law of demand. As price rises, quantity demanded falls and vice versa. Normal goods have a negative PED.

Giffen Good – goods of a lower quality bought by lower-income families e.g. basic food necessities such as rice and potatoes. Giffen goods have a positive price effect. More is bought as price rises and less is bought as price falls.

Significance of the size of the number.

• The size of the number in absolute terms (ignoring the sign) tells us how responsive demand for the good is to changes in its price.
• If the PED is greater than 1 then the good is said to be elastic. A change in price leads to a proportionately bigger change in demand.
• If the PED of the good is less than 1 then the demand for the good is said to be inelastic. A change in price leads to a proportionately smaller change in the demand for the good.

Explain the size of the number:
PED > 1 = Elastic
PED < 1 = Inelastic

Effect on Revenue & Sales

• An increase in the price of a normal good will lead to a decrease in quantity demanded.
• Decrease price elastic goods to increase quantity demanded and hence increase revenue.
• Increase price inelastic goods to increase quantity demanded and hence increase revenue.

Formula: P1 Original Price P2 New Price ∆P Change in Price                                          ∆P =P1 – P2 Q1 Original Quantity Demanded Q2 New Quantity Demanded ∆Q Change in Quantity Demanded               ∆Q = Q1 –Q2

Example Question: A consumer buys 60 units of a good when the price is €1.50. The price increases to €1.75 and the consumer now buys 50 units. Calculate the price elasticity of demand of this good. P1 = €1.50

P2 = €1.75

∆P = +€0.25 (positive because it increased by €0.25)

Q1 = 60 units

Q2 = 50 units

∆Q = -10 units (negative because it decreased by 10 units) Explanation:

• It is an elastic good as the PED > 1.
• This means that if the price of the good rises by 1% the quantity demanded of this good will fall by 1.18%. If the price of the good falls by 1% the quantity demanded of this good will rise by 1.18%.
• It is a normal good due to the negative sign.

Factors That Affect Price Elasticity of Demand (PED)

• THE AVAILABILITY OF CLOSE SUBSTITUTES

This is probably the most important factor influencing the elasticity of a good or service. In general, the more substitutes that are available, the more elastic the demand tends to be. For example, if the price of Volvic mineral water went up by €0.25, consumers may switch to Ballygowan water. The closer the substitutability between goods, the more consumers will tend to switch from one substitute brand to another and thus the greater the PED will be.

• COMPLEMENTARY GOODS

If the good in question is the cheaper of two goods which are in joint demand, then the demand for it is likely to be relatively inelastic in response to changes in its own price. For example, if shoelaces are cheaper than shoes, then any change in the price of shoelaces will have very little effect on the demand for shoes.

• IS THE COMMODITY A LUXURY OR NECESSITY?

As consumers, it is not essential that we should possess luxuries. These are wants and are a discretionary expenditure. Therefore, PED for luxury goods will be relatively elastic. Necessities, however, are essential in our everyday lives – people have no choice but to buy them even when their price is increased. Therefore, PED for necessities will be relatively inelastic.

• THE PROPORTION OF INCOME THAT IS SPENT ON THE COMMODITY

This factor affecting elasticity of demand refers to the total income a person can spend on a particular good or service. In general, as income increases, so does the quantity demanded of goods. In general, the greater the proportion of income that is spent on a good, the more elastic the demand for it is likely to be in response to a change in its own price. A rise of 50% in the price of a bag of sugar is unlikely to have a significant effect on demand.

• THE DURABILITY OF THE COMMODITY

The more durable the commodity, the more elastic the demand for it is likely to be in response to a change in its own price. If products such as motor vehicles increase in price, it is likely that the public will extend the life of their existing model and postpone the purchase of a replacement.

• EXPECTATIONS AS TO FUTURE CHANGES IN PRICE

If, in the face of a price reduction, the public considers that prices are likely to fall even further, they may wait for the further reduction in price, in which case demand may not be very elastic on the initial price reduction.

• THE LENGTH OF TIME ALLOWED FOR ADJUSTMENT TO PRICE CHANGES

In the long run, demand is more elastic as consumers have time to adjust to a change in price. If the price of electricity rose by 80%, a consumer may economise on the use of various appliances in the short term. In the long term the consumer will have to consider substituting other forms of energy. The demand will be highly inelastic at first, but as time goes on will become more elastic. If the price of cigarettes goes up by €2 per pack, a smoker with very few available substitutes will most likely continue buying their daily cigarettes. This means that tobacco is inelastic because the change in price will not have a significant influence on the quantity demanded. However, if that smoker finds that they cannot afford to spend the extra €2 per day and begins to quit smoking over a period of time, the price elasticity of cigarettes for that consumer becomes elastic in the long run.

• CONSUMER PURCHASE HABITS/BRAND LOYALTY/ADVERTISING EFFECTIVENESS

A consumer may become strongly attached to a particular product through habit or loyalty to that brand. An increase in price for that good will not cause them to consume less of the product or switch to cheaper substitutes. The demand for such goods will therefore be price inelastic.

• NUMBER OF ALTERNATIVE USES THE GOOD HAS

A commodity that has a large number of uses will usually have a relatively inelastic demand. For example, sugar is used in direct consumption, sweetening purposes, baking, food processing, etc. Any increase in the price of sugar may only result in a small fall in its demand in each of these markets, but the total drop overall may be significant.

CROSS ELASTICTY OF DEMAND (CED)

+    = Substitute Good
= Complimentary Good

Note
Give definition of said good:

Substitute goods – goods that satisfy the same needs and thus can be considered as an alternative e.g. coke and pepsi.  An increase in the price of good A will result in an increase in the quantity demanded of its substitute as rational consumers will switch to the cheaper alternative.

Complementary good – a good that is used jointly with another good. The use of one involves the use of another e.g. cars and petrol.

Explain the size of the number

The bigger the number the closer the substitute / compliment
CED > 1 = Elastic
CED < 1 = Inelastic

Effect on Revenue & Sales

• An increase in price of a Good A will result in a decrease in quantity demanded of its complement.
• A decrease in price of a Good A will result in an increase in quantity demanded of its complement.
• An increase in price of a Good A will result in an increase in quantity demanded of its substitute.
• A decrease in price of a Good A will result in a decrease in quantity demanded of its substitute

INCOME ELASTICITY OF DEMAND (YED)

+    = Normal Good
–    = Inferior Good

Note

• Give definition of said good:
• If it is a normal good state whether it is a normal necessity or a normal luxury

Normal good – goods which obey the law of demand. As price rises, quantity demanded falls and vice versa. Normal goods have a positive income effect. As income rises, quantity demanded for normal goods rises and vice versa.

Inferior good – goods which do not obey the law of demand. Inferior goods have a negative income effect. As income rises, quantity demanded for inferior goods falls and vice versa. Explain the size of the number:

• YED > 1 = Elastic
• YED < 1 = Inelastic

Revenue & Sales

• An increase in income will lead to an increase in quantity demanded of normal goods and a decrease in the quantity demanded of inferior goods.
• A decrease in income will lead to a decrease in quantity demanded of normal goods and an increase in the quantity demanded of inferior goods.

Note:

• Always define the type of good – normal/inferior/giffen/substitute/complimentary
• Always define the type of elasticity – elastic / inelastic

### Question 1

 (1a) Which figure stated below is most likely to represent each of the following? Income elasticity of demand for low-price cuts of meat. Income elasticity of demand for the latest smartphone Price elasticity of demand for petrol. –1.6            –0.1          +4.3 Give reasons for your choice in each case.

YED for low-price cuts of meat = –1.6.

• Low-price cuts of meat are inferior goods and so have a negative YED.
• Low-price cuts of meat are not a necessity so it is income elastic (YED > 1).

YED for the latest smartphone = +4.3.

• The latest smartphone is a normal good so they have a positive YED.
• The latest smartphone is a luxury so they are income elastic (YED >1).

PED for petrol = –0.1.

• Petrol is a normal good so it has a negative PED.
• Petrol is a necessity so it is price inelastic (PED < 1).
 1b Assume income elasticity of demand for expensive digital cameras is +2.5 and total sales for a large multinational company in 2008 were 100,000 units. Calculate the expected total sales for the year if consumers’ incomes are expected to fall by 8% in 2009. Show your workings.

• If income decreases by 8% then sales will decrease by (8% × 2.5) = 20%.
• Sales will fall by 20% of 100,000 units = 20,000 units.
• Sales in 2009 will equal 100,000 – 20,000 = 80,000 units.

### Question 2

 A consumer buys 10 units of Good A when the price of Good B is €5. When the price of Good B rises to €6 (the price of Good A remaining unchanged), the consumer buys 14 units of Good A.
 2 (i) Define cross elasticity of demand.

Cross elasticity measures the proportionate/percentage change in the quantity demanded for one good caused by the proportionate/percentage change in the price of other goods.

 2 (ii) Using an appropriate formula, calculate this consumer’s cross elasticity of demand for Good A. Show your workings.

QA1 = 10 (original quantity)

QA2 = 14 (new quantity)

ΔQA = +4 (positive because there is an increase of 4 units)

PB1 = 5 (original price)

PB2 = 6 (new price)

ΔPB = +1 (positive as there is an increase of €1) 2 (iii) Is Good A a substitute good for, or a complement to, Good B? Explain your reasoning.

Good A is a substitute good because it has a + sign. This means that as the price of Good B increased, the consumer switched from consuming Good B to the cheaper alternative, Good A.

### Question 3

 Cross Elasticity of Demand between Good A and Good B = +2.5 Cross Elasticity of Demand between Good A and Good C = –0.3 Cross Elasticity of Demand between Good A and Good D = +0.3 Cross Elasticity of Demand between Good A and Good E = –1.4 Which of these goods are complements to Good A? Explain your answer. Which of these goods is the closest substitute for Good A? Explain your answer.

Good C and Good E are complements to Good A as they have negative signs, which indicates a negative relationship between the quantity demanded of Good A and the prices of Good C and Good E, i.e. if the price of Good C and Good E increases (+), the quantity demanded of Good A decreases (–).

Good E is the closest complement to Good A. The closest substitute is Good B. A positive sign indicates that Good B is a substitute good for Good A. This means there is a positive relationship between Good A and Good B. If the price of Good A increases (+), the quantity demanded of Good B also increases (+), as the consumer will switch to the cheaper alternative, Good B. The bigger the number, the closer the substitute.

### Question 4

 A consumer buys 80 units of Good A when the price of Good B is €100. When the price of Good B falls to €90 (the price of Good A remaining unchanged), the consumer buys 12 units of Good A

 Q4 (i) Using an appropriate formula, calculate this consumers cross elasticity of demand for Good A (show your workings). 