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## ELASTICITIES Microeconomics

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Introduction to Elasticities

- Elasticity is a measures of responsiveness.
- It measures how much something changes when there is a change in one of the factors that determines it.
- Elasticity will be examined in regard to demand and supply.

Elasticity of Demand

- Elasticity of demand is a measure of how much the demand for a product changes when there is a change in one of the factors that determines demand. There are three elasticities of demand to be examined:
- Price Elasticity of Demand (PED)
- Cross Elasticity of Demand (XED)
- Income Elasticity of Demand (YED)

Price Elasticity of Demand (PED)

Formula and Definition

- Price Elasticity of demand is a measure of how

much the quantity demanded of product

changes when there is a change in the price

of the product.

- It is usually calculated as follows:

PED = Percentage change in quantity demanded of the product

Percentage change in the price of the product

Price Elasticity of Demand (PED)

Example of PED Question

- A publishing firm discovers that when they lower the price of one of their monthly magazine from $5 to $4.50, the number of magazines that are bought by customers each month rises from 200,000 to 230,000

Task calculate the PED for the magazine

Price Elasticity of Demand (PED)

Example of PED Question & Solution

- Calculate the percentage change $5.00 to 4.50. Price has fallen by 50 cents.

Change in Price 50 cents (.5)

Original Price 5.00 (5) = .1 x 100 = 10%

.

Price Elasticity of Demand (PED)

Example of PED Question and Solution

- Calculate the percentage change in demand

Demand increased by 30,000

Change in Demand 30,000 = .15 x100 = 15%

Original Demand 200,000

Price Elasticity of Demand (PED)

Insert values in the equation for PED

PED = Percentage change in quantity demanded of the product .15

Percentage change in the price of the product. .10

= .15 / .10 = 1.5

- The PED for the monthly

magazine is 1.5.

- But what does this mean?

The Range of Values for Elasticity

- The possible range of values for price elasticity of demand usually goes from zero to infinity.
- The two extremes values are theoretical and the real value lies in between.
- If the PED is equal to zero, then a change in the price of the product will have no effect on the quantity demanded at all.
- The percentage change in quantity demanded would be zero.

A demand curve with a PED value of zero is shown in this graph.

Demand is said to be perfectly inelastic – it is completely unresponsive to price changes. Whether price is P1 or P2. or any other price, the quantity demanded will be Q.

A PEV value of infinity is best explained by using a diagram. A the Price P1 the demand curve goes on for ever and so the quantity demanded is infinite.

However, if the price is raised above P1 even by the smallest amount, demand will fall to zero, an infinite change. The value on the top of the PED equation would be infinity. Infinity divided by anything is infinity, no mater what the percentage change in price.

The Range of Values for Elasticity

- It must be remembered that the extreme values of PED are simply theoretical and there are no single products that would possess at PED value of zero or infinity.
- The range of values of PED is normally split into three categories:
- Inelastic Demand
- Elastic Demand
- Unit Elastic Demand

Inelastic Demand

- The value of PED is less than one and greater than zero. 0 to 1 = Inelastic Demand
- If a product has inelastic demand, then a change in the price of the product leads to a proportionally smaller change in the quantity demanded.
- If the price is raised, the quantity demanded will not fall by much in comparison and so the total revenue gained by the firm (the number of units sold x the price of the product) will increse

Inelastic Demand - Example

- When a price of a carton of yoghurt is raised from $1 to 1.20, the firms finds that the quantity demanded per week falls from 12000 cartoons to 10,800 cartoons. A 20% increase in price is a causing a 10% fall in the quantity demanded.

PED = % change in Quantity demanded10% = .5

% change in price 20%

Inelastic Demand - Example

- With PED of .5, this less than 1, so demand for yoghurt is inelastic.
- Before price increase revenue was $12,000 x$1 each = $12,000.
- After the price increase revenue was $10,800 x $1.20 = $12,960.

The “revenue boxes” in the diagram clearly show why a price increase causes an increase in total revenue. Before the price rise the firm was getting revenue equal to revenue box b + revenue box c. After the price increase the firm loses revenue box c, because quantity demanded falls from 10,800 but gains revenue box a because the remaining cartoons are now sold at $1.20 each. Since revenue box a is larger than revenue box c, the firms total revenue rises by $960.

Elastic Demand

- When the value of the PED is greater than one and less than infinity. > 1 = elastic demand.
- If a product has elastic demand, then a change in the price of a product leads to a greater than proportionate change in the quantity demanded of it.
- If the price is raised, the quantity demanded will fall by more in comparison, and so the total revenue gained by the firm will fall.

Elastic Demand Example

- When the price of a hot dog is raised from $2 to $2.10 a hot dog seller finds that quantity demanded per weeks falls from a 200 hot dogs to 180 hot dogs.
- A 5% increase in price is causing a 10% fall in the quantity demanded.

PED = % change in Quantity demanded10% = 2

% change in price 5%

Elastic Demand Example

- In this example the PED is 2, greater than 1, so the demand for hot dog is elastic.
- Before the price rise, the total revenue gained by the hot dog seller was 200 x $2 = $400.
- After the increase, the total revenue becomes 180 x $2.10 = $378.
- The seller has caused a fall in revenue by increasing price.

The revenue boxes in the diagram clearly show why a price increase causes a decrease in total revenue, when the demand for a product is elastic. Before the price rise the hot dog seller was earning revenue equal to revenue box b + revenue box c. After the price increase the hot dog seller lost revenue box c but gains revenue box a. Since revenue box a (180 x 10 cents = $18) is clearly smaller than revenue box c (20 x $2 = $40) , the hot dog seller’s total revenue falls by $22. If a firm has elastic demand for its product is should not raise the price of the product.

Unit Elastic Demand

- The value of PED is equal to one
- If a product has unit elastic demand, then a change in the price of the product leads to a proportionate, opposite, change in the quantity demanded of it.
- This means that if the price is raised by a certain percentage, then the quantity demanded will fall by the same percentage.
- PED is equal to 1 and the total revenue gained by the firm will not change.

A curve that has unit elasticity at every point is shown in this graph. It is know as Rectangular Hyperbola. The rectangular hyperbola is drawn in such a way that the price times quantity at any point is constant. This means that the revenue boxes always have the same area and if the revenue does not change, when price changes, then PED must be unity.

The two rectangles a & b have the same area.

a + b is equal to b + c.

Mathematical Note about Elasticity

- It is a common mistake for students to assumed that elasticity is a measure of the slope of the demand curve and the value is always the same any point on the curve.
- For a straight line, downward sloping demand curve, the value of PED falls as price falls.

ELASTICITY

For a straight-line, downward sloping demand curve, the value of PED falls as price falls. When the price falls from $20 to $18, the quantity demanded increases from 60 to 80 units. The PED equals 3.3, which is elastic. This is evident as we move from a to b.

But..

When the price falls from $10 to $8, the quantity demanded increases from 160 to 180 units. The PED equals 0.625, which is inelastic. This is evident as we move from point c to point d.

Why does elasticity vary on a demand curve?

- The value of PED falls as we move down a demand curve.
- Low priced products have a more inelastic demand than high priced products, because consumers are less concerned when the price of inexpensive product rises, than they are when the price of an expensive product falls.

Determinants of Price Elasticity of Demand

- Different products will have different values for PED.

For example:

- The demand for restaurant meal may have a PED value of 3 (clearly elastic)
- The demand for petrol may have a PED value of 0.4 which is inelastic.

What actually determines the value of PED for a product?

1. The number and closeness of substitutes

- The number and closeness of substitutes that are available is certainly the most important determinant of PED.
- It is fair to say that the more substitutes there are for a product, the more elastic will be the demand for it.
- Also the closer the substitutes available the more elastic will be the demand.

What actually determines the value of PED for a product?

- The number and closeness of substitutes

Example

- There are many brands of butter available, so an increase in price of one brand will lead a large number of customers changing their demands to another brand.
- Demand for products with lots of substitutes such as brand of household products, types of meat, and types of fruit, will tend to have elastic demand.

What actually determines the value of PED for a product?

1. The number and closeness of substitutes

- Products with few substitutes such as oil, will tend to have relatively inelastic demand, with the demand falling relatively little as the price goes up.

What actually determines the value of PED for a product?

- The necessity of the product and how widely the product is defined
- Food is an inelastic product, thus we would expect food to be very inelastic which is true.

BUT...

- If we define food more narrowly and consider meat we would expect demand to be less inelastic, since there are alternatives like vegetables.
- If we define meat more narrowly to chicken, beef and lamb and pork, the demand for each would be relatively elastic since the consumer can change easily.
- If we talk about a particular type of chicken elasticity increases further and so.

Elasticity among different consumers and cultures

- Necessity will change from consumer to consumer, since different people have different tastes and necessity is often a subjective view.
- For example: In Malaysia chicken is very popular and so demand is less elastic than it would be in Italy, where it is not valued as highly.

Elasticity and Addictive Substances

- Necessity may go to extremes when individuals consider products to be very “necessary such as habit forming goods like cigarettes, alcohol or hard drugs.
- These products may have relatively inelastic demand.

What actually determines the value of PED for a product?

- The time period considered
- As the price of a product changes, it often takes times for consumers to change their buying and consumption habits.
- PED thus tends to be inelastic in the short term and then becomes more elastic, the longer the time period is measured over.

Price Elasticity of Demand & Taxation

- Governments needs to be aware of the possible consequences when they impose indirect taxes, such as sales tax, on products.
- Higher taxes mean that the quantity demanded of the product in question is likely to fall if the product is characterized by elastic demand.
- Governments normally place additional taxes on products, where demand is relatively inelastic.

CROSS ELASTICITY OF DEMAND (XED) (p56)

Formula & Definition

- Cross elasticity of demand is a measure of how much the demand for a product changes when there is a change in the price of another product. It is usually calculated as follows:

XED = Percentage of change in quantity demanded of the product X

Percentage change in the price of product Y.

Cross Elasticity of Demand Example (p56)

- The owners of a pizza stand find that when their competitor, a hamburger stand, lowers the price of burger from $2 to $1.80, the number of pizza slices that they sell each week falls from 400 to 380, because of the lower priced burgers.
- Calculate the cross elasticity for the pizza slices.

Cross Elasticity of Demand Example (p56)

Step 1

- The price of the competitors burgers has fallen from 20 cents from an original price, which is a change of -10%.

-20 x 100 = -10%

200

Cross Elasticity of Demand Example (p56)

Step 2

- The quantity demanded of the pizza slices has fallen by 20 from an original demand of 400, which is a change of -5%.

-20 x 100 = -5%

400

Cross Elasticity of Demand Example (p56)

- If we put the values into the equation for XED:

-5% (-.05)

-10% (-.1) which gives a value of +0.5

The Range of values for Cross Elasticity of Demand

- XED explains the relationship between products.
- Unlike PED, where the vast majority of products have a positive value for PED, the value of XED may be positive or negative, and the sign is important, since it tells us what the relationshipbetween the two goods in question is.

Positive (+) Cross Elasticity of Demand

- If the value of a XED is positive, then the two goods in questions may be said to be substitutes for each other.
- Products that are very close substitutes will have a higher positive value than products that are not so close.

Negative (-) Cross Elasticity of Demand

- If the value of XED is negative, then the two goods in question may be said to be compliments for each other.
- Products that are very close substitutes will have a lower negative value than products that are not so close.
- Eg: A large rise in the price of an Xbox gaming machine, may lead to fall in demand for machines, but also a fall in demand for the associated games.

Zero Value: Cross Elasticity of Demand

- Some products such as matchsticks and houses are not connected.
- An increase in the price of one the products will have no impact on the other.
- The XED value would be zero, because the goods are unrelated.

The Importance of XED for business

- It is essential that firms are aware of the possible impact on the demand for their products that may arise, if there is a change in the price of close rival’s product.
- Firms that produce complementary products, such as power tools and accessories need to understand the relationship between price changes for one product and impact on demand for other related products.

Exercise – Cross Elasticity of Demand

- Amtrak reduces its fares for business class on its high speed rail network between Washington and New York, from $150 to $99. As a result demand for travel on American Eagle flights falls from 5000 seats per week to 4000 seats per week.
- Calculate the cross elasticity for air travel.

Answer to Amtrak Exercise

- 150-99 = 51
- 51 / 150 = 0.34
- 0.34 x 100 = 34%
- 5000-4000 = 1000
- 1000 / 5000 = 0.20 x 100 = 20%
- 34%/20% = 1.7

INCOME ELASTICITY OF DEMAND (YED) (p58)

Formula and Definition

- Income elasticity of demand is a measure of how much the demand for a product changes when there is a change in the consumers income. It is calculated as follows:

YED = Percentage change in quantity demanded of the product

Percentage change in the income of the consumer

Income Elasticity of DemandExample

- A person has an increase in annual income from $60,000 per year to $66,000 per year.
- Their spending on holidays increases from $2500 to $3000.
- Calculate the income elasticity of demand for holidays.

Income Elasticity of DemandExample

Step 1

- The person’s income has increased by $6000 from an original income of $60,000, which is a change of 10%+.

+ $6000 x 100 = +10%

60,000

Income Elasticity of DemandExample

Step 2

- The quantity demanded of holidays has increased by $500 from an original demand of $2500, which is a change of +20%.

500 x 100 = +20%

2,500

Income Elasticity of DemandExample

Step 3

Insert values into the equation for PED.

+20% (.2)

+10% (.1) which is gives a value of +2.

What does this mean??

The range of values for income elasticity of demand

- Like XED, the sign obtained from the equation is important.
- The sign of YED tells whether the product we are looking at is a normal good or an inferior good.
- Demand for a normal good rises as income rises.
- Demand for an inferior good falls as income rises.

The range of values for income elasticity of demand

Normal Goods

- For normal goods the value of YED is positive.
- The demand increases as income increases.
- If the percentage increase in quantity demanded is less than the percentage increase in income, then a YED value between 0 and 1 is obtained = income-inelastic.
- If the percentage increase in quantity demanded is greater than the percentage increase in income, then a YED value greater than 1 is obtained = income-elastic.

The range of values for income elasticity of demand

Necessity Goods

- Necessity goods are products that have low income elasticity.
- The demand for them will change very little income rises.
- Eg: Demand for bread does not usually increase as income rises.

The range of values for income elasticity of demand

Superior Goods

- Superior goods are products that high income elasticity.
- The demand for them changes significantly if income rises.
- As people have more income, they spend more money on wants (non essential items)
- The demand for holidays in foreign countries is likely to be income elastic.

The range of values for income elasticity of demand

Inferior Goods

- The value of YED is negative, because the demand decreases as income increases.
- People start to switch their expenditure from inferior goods that they have been buying to superior goods, which they can now afford to buy.
- Eg: The demand for no frills/home brand products falls as income rises because people switch to buying branded labels.

THE ENGEL CURVE AND INCOME ELASTICITY

An Engel Curve shows the relationship between income and the demand for a product over time.

It is named after Ernst Engel, a 19th century German economist. In the graph opposite as income in a country increases over time, the demand for potatoes may increase, then become constant, and then begin to fall as people begin to buy superior products, instead such as pasta.

Income Elasticity of Demand

- A person’s income increases from $60,000 per year to $80,000 per year. Their spending in fine dining restaurants increases from $180 per month to $300 per month.
- Calculate the income elasticity of demand for fine dining restaurants.

Answer

- 60,000 – 80,000 = 33.3% increase
- 180-300 = 66.6% increase
- 66.6%/33.3%= 2

Answer to Exercise

20000

60000 = .33333

120 = .6666

180

.6666

.3333 = 2

With answer of 2, our product is clearly income inelastic.

PRICE ELASTICITY OF SUPPLY (PES)

Formula and Definition

- Price elasticity of supply is a measure of how much the supply of a product changes when there is a change in the price of the product.
- It is calculated as follows:

PES = Percentage change in quantity supplied of the product

Percentage change in the price of the product

Price Elasticity of Supply Example

- A publishing firm realises that they can now sell their monthly magazine for $5.50 instead of $5.00.
- They increase their supply from 200,000 to 230,000 magazines per month.
- Calculate the Price Elasticity of Supply

Price Elasticity of Supply Example

Step 1

- The price has risen by 50 cents from an original price of $5, which is a change of +10%.

50 x 100 = 10%

500

Price Elasticity of Supply Example

Step 2

- The quantity supplied has increased by 30,000 from an original supply of 200,000, which is a change of 15%.

30,000 x 100 = 15%

200,000

Price Elasticity of Supply Example

Step 3

Insert figures into the equation:

15% (.15)

10% (.10) = 1.5

Note:

The value of PES , will almost always be

positive.

The Range of Values Price Elasticity of Supply (PES)

- The positive range of values for PES usually goes from zero to infinity.
- Unlike PED, you will encounter examples of both extreme values.

The Range of Values Price Elasticity of Supply (PES)

PES Equals 0

- If PES is equal to zero, then a change in the price of the product will have no effect on the quantity supplied at all.
- The percentage change in quantity supplied would be zero and so would the value on top of the PES equation.

A supply curve with a value of zeros is shown in this graph. Supply is said to be perfectlyinelastic – it is completely unresponsive to price changes Whether price is P1 or P2, or any other price, the quantity supplied will be Q.

Supply is perfectly elastic. At the price P1, the supply curve goes on forever and the supply curve is infinite. However, if the price falls below P1, even by the smallest amount, supply will fall to zero, an infinite change.

International Trade & Perfectly Elastic Supply

- In international trade, it often assumed that the supply of commodities, such as wheat, available to a country for import is infinite.
- The consumers in the country have all they want as long as they are prepared to pay the current world market price.
- The market in the country will have “world supply” curve that is perfectly elastic as the current world market price.

Inelastic Supply

- The value of PES is less than one and greater than zero.
- If a product has inelastic supply, then a change in the price of the product leads to less than proportionate change in the quantity supplied of it.

Elastic Supply

- The value of PES is greater than one and less than infinity.
- If a product has elastic supply, then a change in the price of the product leads to greater than proportionate change in the quantity supplied of it.

Unit Elastic Supply

- The value of PES is equal to one.
- If a product has unit elastic supply, then a change in the price of the product leads to a proportionate change in the quantity supplied of it and so the value of PES is equal to one.

SUPPLY CURVES WITH DIFFERENT VALUES

Curves S1 and S2 have a PES value of one along their entire length. This is because the percentage change in price is always equal to the percentage change in quantity supplied. Any straight line supply curve passing through the origin has elasticity of supply of one. Curve S3 has PES value of less than one along its entire length. The percentage change in price is always greater than the percentage change in quantity supplied. Any straight line supply curve starting from the x-axis has PES value less than one. Curve S4has PES value greater than one along its entire length. The percentage change in quantity supplied is always greater than the percentage change in price. Any straight-line supply curve starting from y axis has PES value greater than one.

Determinants of Price Elasticity of Supply

- How much costs rise as output is increased
- If total costs rise significantly as a producer attempts to increase supply, then is likely that the producer will not raise the supply and so the elasticity of supply for the product will be relatively inelastic.
- It would take large price rises to make increasing the supply worthwhile.
- However, if total costs do not rise quickly, then the producer will raise the supply and take advantage of the slow increase in costs to benefit from the higher prices thus making more profits.
- Total costs will not rise quickly if the firm has a lot of spare capacity and if the costs of factor inputs do not rise quickly.

Determinants of Price Elasticity of Supply

- The time period considered
- The amount of time over which PES is measured will affect its value.
- In general terms, the longer the time period considered the more elastic will be supply.

Immediate Time Periods

- Firms are not able to increase their supply very much, if at all, if price increases, since they cannot immediately increase the number of factors of production they employ.
- The value of PES will be very inelastic.

Determinants of Price Elasticity of Supply

2. The time period considered

Short Run

- Firms may be able to increase the quantity of some of the factors that they employ, or
- BUT, they may not be able to increase all their factors, such as the number of machines they use or the size of their factory.
- The value of PES will be more elastic than the immediate time period.

Determinants of Price Elasticity of Supply

2. The time period considered

Long Run

- Firms may be able to increase the quantity of all the factors that they employ and so the value of PES will be much elastic.

ELASTICITY OF SUPPLY - EXERCISES

- A low cost airline abruptly goes out of business on a major international route. With less competition a legacy carrier now decides to increase economy fares from $200 to $350.
- At this price it decides to use a larger aircraft on the route which increases supply from 1000 seats per week to 1500 seats per week.
- Calculate the Elasticity of Supply.

Answer

- 350-200=150/200=75%
- 1500-1000=500/1000=50%
- 50%/75%=.67

Examinations Questions

SHORT RESPONSE QUESTIONS

With the help of examples, explain the determinants of the price elasticity of demand. (10 marks)

A businessperson wants to increase her revenues. Using appropriate diagrams, explain why knowledge of price elasticity of demand would be useful. (10 marks)

Examination Questions

SHORT RESPONSE QUESTIONS

3. With the help of examples, explain the concept of

cross elasticity of supply (10 marks)

4. With the help of examples, explain the determinants

of price elasticity of supply (10 marks)

5. Using income elasticity of demand, explain the

difference between normal, necessity and inferior

goods? (10 marks)

Examination Questions

Essay Question

1a. Explain the concept of elasticity of

demand (10 marks)

1b. Discuss why it may be important for a

firm to have knowledge of elasticity of

demand. (15 marks)

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