Elasticity is part of the IB Syllabus for microeconomics.

## Price Elasticity of Demand

• Formula • Definition

The price elasticity of demand measures the change in quantity demand and the price change of a good.It reveals the percent change in quantity demanded in response to a one percent change in price.

• Possible range of values:

• If Ped = 0 then demand is perfectly inelastic. This means that demand does not change at all when the price changes – the demand curve will be vertical.
• If Ped is between 0 and 1 then demand is inelastic. Producers know then the change in demand will be proportionately smaller than the percentage change in price.
• If Ped = 1 , then demand is said to be unit elastic, or perfectly elastic. A 25% rise in price would lead to a 25% contraction, or decrease, in demand. A point that is unit elastic in all directions also represents the quantity and price that will provide maximum revenue.
• If Ped > 1, then demand responds more than proportionately to a change in price i.e. demand is elastic. For example a 10% increase in the price of a good might lead to a 20% drop in demand. The price elasticity of demand for this price change is –1.5.
• The sign of the number does not matter. Use the absolute value.

• Below are diagrams illustrating the range of values of elasticity Values for price elasticity of demand can range from 0 (Figure 1) to infinity (Figure 2).

If PED is 0, the quantity of demand will not change no matter how much price shifts (Figure 1). If PED is infinity, price remains constant no matter how the quantity changes (Figure 2).

• Varying elasticity along a straight-line D curve 

which can be found on the link above.

• Determinants of price elasticity of demand...

1. Number of close substitutes for a good and the quality/rarity of the product.

2. Cost of switching between different products.

3. Time period allotted for following a change in price.

4. Rarity of the good or the degreee of necessity.

5. Percentage of a consumer's income allocated to spend on the good.

6. Relative availability of the good.

Elasticity can be thought of as a rubber band. A rubber band can be elastic- stretching a lot with some force- inelastic, stretching little with the same force, unit elastic- stretching proportionally to the force used, or perfectly inelastic- not stretching at all no matter how much force is put on it. For elasticity of demand, force would be the change in price, and how much it stretches would be the change in quantity demanded. If the price of a good changes, it can either have a small, large, or even no effect on the quantity demanded. This is due to the above determinants. For example the number of close substitutes for the good.

## Cross Elasticity of Demand

• Definition: The cross elasticity of demand measures the reactiveness or responsiveness of demand for one good, compared to the change in the price of another good, due to compatibly between the two goods or services.

• Formula: PEDx,y =Percentage change in quantity demanded / percentage change in price

• To Calculate % change in Quantity of X, use the following formula:

[QDemand(NEW) - QDemand (OLD)]
[QDemand(OLD)]

To calculate % change in Price of Y, use the following formula:
[Price(NEW) -Price(OLD)]
[Price(OLD)]

Example: 700,000= Q(new) of X, and 500,000= Q(old) of X. P(new) of Good Y = $10 , P(old) of Good Y =$9

(700,000-500,000) = 2
(500,000) 5

(10-9) / (9) = 1/9.

Then replace the values into the PEDx,y formula: (2/5) / (1/9) = 3.6

PEDx,y = 3.6 for Goods X and Y

• Significance of sign with respect to complements and substitutes: If the cross elasticity of demand is positive then the two goods being compared are substitutes. If the two goods are substitutes, then theoretically if the demand of one good decreases, then the other increases.

If it is negative the goods are compliments. If two goods are compliments, when the demand for one good rises, the other will too. ex: Peanut Butter & Jelly

If the absolute value of the cross elasticity of demand is more than one, then the relationship between the goods is strong. If the absolute value is less than one, the goods have a weak relationship, this means a change in price in one good will have a small effect on quantity demanded of another.

• Example: Apple Ipod and MP3 Players are substitute goods; they provide the same type of service, so either one can be used for the same task and they compete with eachother in the same catagory.
• Example: Apple Ipods and Apple Headphones are complementary goods because the head phones help you enjoy the service (music/sound) provided by the ipod.

## Income Elasticity of Demand

Definition: the Income Elasticity of Demand measures the change in the quantity demanded of a good, for a change in income. Income Elasticity of Demand is quantifed with the formula % change in quantity demanded divided by the % change in real income. Income Elasticity of Demand referrers to inferior and normal goods that shows the diffrence between necessary goods and a luxury or superior goods.

• Income Elasticity of Demand=

% change in Quantity demanded

% change in real income

(Income elasticity of Demand can be abbreviated as yED)

Example: In the year 2000, the quantity demanded of computers was 15000 when income was 40000 dollars a year. The year 2005, quantity demanded of computers rose to 20000 and income rose to 50000 a year. What is yED

20000-15000/15000----------> 5000/15000= 33% rise

50000-40000/40000---------> 10000/40000= 25% rise

0.33/ 0.25= 1.32 yED= 1.32

Normal Goods

• Normal goods are goods for which demand increases when income increases, and then falls when income decreases, but the price is always the same. A normal good also has an income elasticity of demand that is positive, but is less than one. Note that goods with an income elasticity of demand that is greater than one are luxury goods.
• Normal goods are in direct relation to income. "Cars" are a great example of this. As your real income increases, the demand of cars will increase because you have more money. As your real income decreases, the demand of cars will decrease because you do not have the money for a car. Therefore, cars are normal goods.
• Ex: A worker's income doubles from $20,000 to$45,000. When their income rises they will but more normal goods, and less inferior goods. It is also true that they will increase overall consumption of goods, regardless of which type they are.

Inferior goods:

• An Inferior good is a good that decreases in demand when consumer income rises, unlike Normal Goods, for which the opposite is observed. Normal goods are those for which consumers' demand increases when their income increases. Inferiority, in this sense, is an observable fact relating to affordability rather than a statement about the quality of the good. As a rule, too much of a good thing is easily achieved with such goods, and as more costly substitutes that offer more pleasure or at least variety become available, the use of the inferior goods diminishes. Depending on consumer or market indifference Curves, the amount of a good bought can either increase, decrease, or stay the same when income increases. An inferior good has an income elasticity of demand less than zero (negative).
• Ex: A worker's income decreases, and so they buy more inferior goods, and less normal goods. Their overall consumption of both types of goods will decrease.

### Price Elasticity of Supply

Price Elasticity of supply- measures the quantity supplied to the change in price. The same basic idea as price elasticity of demand, just with supply. The formula is also basically the same. As a general rule, if prices rise, then so will supply (proportionate change in price to proportionate change in supply). The more elastic, the more sensitive price is and vise versa.

• Formula PES

PES = %change Q supplied / % change in price

Example: In response to a 20% rise in the price of a good, the quantity supplied increases by 40%, the price elasticity of supply would be 40%/20% = 2.

• Possible range of values: When PES is less than one, it is said to be inelastic because a change in the price of the good has little effect on the quantity supplied. When PES is equal to 0, it is said to be unit elastic. When PES is greater than 1 it is said to be elastic because the change in price has a bigger effect on quantity supplied.

• Diagrams illustrating the range of values of elasticity

PES, inelastic graph. S3 perfectly inelastic. PES elastic graph. S6 is perfectly elastic.  PES Unit elastic.
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• Determinants of price elasticity of supply:

1) Availiblility (usually of raw materials) .

2) Length and complexity of production.

3) Time to respond to changes in price .

4) Excess Capacity- sometimes a producer will have extra resources on hand and will be able to respond faster.

5) Inventory- a producer who already has the supply of goods that are demanded or readily availible storage capacity can react to increase supply quickly.

Necessities vs. Luxuries - Because necessities are goods that people need to consume, they tend to have an inelastic demand. This means that when the price of a necessity rises, quantity demanded for the necessity does not change much. Luxuries are not goods that people need (people just consume them if they are able). Because of this, an increase in the price of a luxury tends to be associated with a large decrease in the quantity demanded for the luxury. Economists usually find that luxuries have elastic demand.

Availability of Close Substitutes - Products that have readily available substitutes tend to have elastic demand. This is because consumers will switch to the available substitute when the price of the product rises, causing a large decrease in quantity demanded. Why would anyone buy a certain good when there is something else just as good, but cheaper? Quantity demanded of that good will fall almost to zero. When products do not already have available substitutes, consumers are not able to switcth to another good when the price of the product rises and so a decrease in quantity demanded will be smaller. Products without readily available substitutes tend to have more inelastic demand.

Time Horizon - Most products have more elastic demand over a longer period of time. Goods are more elastic in the long run, because in the short run, prices does not affect you as much as the long run. The reason is that more substitutes will become available in the future than are currently available. Also, people may change their consumption behavior in the future because if you need something sooner than later, it become's more inelastic due to the fact you are willing to pay a higher price to get it sooner.

Definition of the Market - The more broadly we define an item, the more possible substitutes and the more elastic the demand. A jet powered, six setting shower head is more inelastic than bathroom accessories.

## Application of Concepts of Elasticity

PED (Price Elasticity of Demand): a measure used to show the responsiveness, or elasticity of the quantity demanded of a good or service to a change in its price the effect of price changes on total revenue.

PED is an indicator of the total revenue for a business. The total revenue is the product of the quantity and price of a good (PxQ), and since PED relates the percent changes in these quantities, they are strongly related. On a demand curve, any point with a PED of exactly 1 (unit elastic) in every direction to any other other point is a point of maximum revenue. This means that at a point that is unit elastic in all directions, any direction you move will you give you a point with lesser (or equal) total revenue.

• PED and taxation: can predict where an imposed tax will fall.

• Cross-elasticity of demand: relevance for firms.

Consider a high cross-elasticity of demand between two goods produced by two different firms who are in competition. The two goods are almost perfect subsitutes for each other. If one of the firms drops their price of their good slightly, it will significantly affect the business of the other firm, because these two products are perfect subsitutes so people will want to buy the good that cost less. Therefore, the change in price of one good can affect the quantity of another good.

• Significance of income elasticity for sectoral change (primary to secondary to tertiary) as economic growth occurs.

Developing countries usually produce mostly primary goods, which are relatively income inelastic when compared to tertiary goods. When global income rises, more money tends to be spent on secondary and tertiary goods, which are produced in more developed countries. In comparison, the consumption of primary goods rises only marginally and the developing country is faced with a barrier to development.

• Flat rate and ad valorem taxes.

If it is elastic, then there isn't any substitutions but if it is inelastic, then there is substitution, such as water is a substitution for coke.