Elasticity - is measure of sensitivity of one variable to another.

Price elasticity of demand - measures the sensitivity of quantity demanded to price changes. It tells us what percentage change in the quantity demanded for a good will be following a one percent increase in the price of that good.

Let's denote quantity and price by Q and P, to give us the expression for price elasticity of demand.

Ed = (∆Q / Q) ๗ (∆P / P)

Example:

Suppose that at a price of $100 monthly sales of bicycles in a city are 1000. Next month the price of a bicycles goes up to $101. As a result of a price increase the quantity of bicycles demanded per month falls to 1990. The percentage change in the price of bicycles is the $1 increase in price (∆P) divided by the initial price (P) of $100 multiplied by 100 % to convert the resulting decimal into percentage.

The percentage change in price is therefore ∆P / P * 100 % = (101 - 100) / 100 * 100 %  = 1%

The percentage change in quantity demanded is ∆Q / Q * 100 % = (1990 - 2000) / 2000 * 100 %  =  - 0,5 %

The price elasticity of demand is usually a negative number. When the price of a good increases the quantity demanded is usually falls.

Determination of Price Elasticity of Demand.

The availability of substitutions

The more substitute goods there are for a good, whose price rises, the more elastic is the demand for good.

The period of adjustment to price changes.

The demand for a good is generally more elastic in the long run than in a shirt run because people generally find more substitutes for a good as time goes by.

The portion of consumer budget allocated to the product.

Large percentage increases in the price if goods that constitute small portions of your total budget might have little effect on your purchases of these goods if you regard them as necessities.   

Income elasticity of demand.

It measures a percentage change in quantity purchased in response to each 1% in income.

Ei = (∆Q / Q ) ธ (∆ I / I )

If Ei > 0 => normal good
If Ei < 0 => inferior good
If E=0  => income elasticity for goods whose consumption is completely unresponsive to changes in income => e.g. necessity.

If Ei >1 => luxury goods, because as income increases the share of that goods also increases. (E.g. foreign travel)            

Example.

Suppose the consumer is consuming apples and oranges. Price of an apple is $5 and the price of an orange is $40. The demand for apples is 56 units while the demand for oranges is 87 units. The consumer has an income of $200. Suppose the consumer's income increased to $300 while the demand for oranges has decreases to 70 units and the price of apple has decreased to $2.

a) calculate the income elasticity of demand for oranges.

Ei = (( Q current - Q previous) / Q previous) ๗  (∆P/P) = ((70 - 87) / 87) ๗ ((300-200) / 200) = - 0.2 / 0.5 = - 0.4

Cross elasticity of demand.

It measures the sensitivity of the demand for one good to a one percent change in the price of another good.

When it is positive the two goods are substitutes (Coca -cola and Pepsi)

When it is negative the two goods are complements (Coffee & milk, bread & butter).

Example:

Suppose the consumer is consuming apples and oranges. Price of an apple is $5, price of an orange is $10. The demand for apples is 56 units, while the demand for oranges is 87 units. The consumer has an income of $200. Suppose that the consumer income has increased to $300, while the demand for oranges has decreased to 70 units and the price of an apple has decreased to $2.

In general gross elasticity of demand defined as:

Ei = (∆Qx / Qx ) ๗  (∆ Py / Py )

E cross for oranges  = ((70 -87) / 87) ๗ ((2 - 5) / 5) = 0.33