There are many forms of Elasticity of Demand, and the basic mathematical formula is:

Coefficient of Elasticity = % change in quantity demanded / % change in relevant variable

*The Price Elasticity of Demand*

The price elasticity of demand is the amount at which consumer demand for a product or service will vary with price, ie the responsiveness of demand to changes in Po.

Based on general formula, the own price (Po) elasticity of demand for a product, denoted as Ed, may be calculated as such:

Ed = % change in quantity demanded / % change in Po

*Cross Price Elasticity of Demand*

The Cross Price Elasticity of Demand (aka cross elasticity) is also seen as the measure of responsiveness of product demand when there is a change in price of either complimentary or substitution products. An example here, might well be the change in demand for butter if there is a decrease in the price for margarine (ie the responsiveness of demand to changes in Ps and Pc.

This can be calculated as follows:

A = product of interest

B = complimentary/substitue product

cross price elasticity = % change in demand for A / % change in the price of B

It should be obvious that in substitute products the cross price elasticity will be a positive number, ie a rise in price of a substitute good will likely raise the demand seen for interested product. And vice versa, in complimentary products the cross price elasticity will be a negative value. If the goods are unrelated then the value will be negligible or zero. Thus a CPE of:

‘1’ would mean a unitary CPE.

<1 would mean an inelastic CPE.

>1 would mean an elastic CPE.

*Income Elasticity of Demand*

It should be understood that the price elasticity of demand is variable due to factors other than Po. One very important factor is ‘real income’ (nominal income adjusted for inflation). Therefore Income Elasticity of Demand is important. This measures the responsiveness of demand due to a change in the income of consumers. A simple example here would what would happen to the demand for housing if average salaries were increased by £500 per month.

We can calculate this mathematically:

Income Ed = % change in demand / % change in income

For **normal goods** the Income Ed is seen as a positive value, ie the more earned the more bought. But there are casses when the value is negative and so can be used to classify products. Normal goods can be split into two more further categories; Necessities and Luxuries.

- Necessities are goods such as bread, milk and flour and the Income Ed will be <1, which means that the demand will increase at a slower proportion than increases in salary.
- Luxuries will see a varied Income Ed, with little or no demand below a certain income level, but thereafter there will be a disproportionate rise in demand for these goods. These goods will be Veblen Goods such as luxury cars, luxury houses and luxury holidays.

**Inferior goods** have a negative Income Ed. This means less is bought as income increases, which could be goods such as junk foods, or non branded clothing.

In times of boom, luxury products will see a disproportionate rise in demand, and offer great returns to savvy investors. However, necessities offer a more stable market, as there is demand through recessions etc as the Income Ed is <1 and are there said to have an inelastic Income Ed.

*Arc Elasticity of Demand*

This measures the responsiveness of demand between two points on a demand curve. It must be noted that the Arc Of Elasticity is measured at the midpoint between these two points, say X and Y. Arc Elasticity is therefore always expressed as an average of quantity and price.

*Point Elasticity of Demand*

This is not commonly used by businesses, as no one is particularly interested in what an infinitesimally small change in price would have on demand, but it does have a role in mathematical demand forecasting.

It should be noted, that products with:

- a price elasticity of <1 are said to be fairly ‘inelastic’ (thus as the price changes there will be little affect to the demand for that product. An example would be bread, because if the price of bread went up people would still need to eat and would thus purchase the bread but if the price went down people would not really look to buy more bread as they would be unable to consume before it went stale).
- a price elasticity of >1 are said to be fairly ‘elastic’ (thus there would be considerable change in the demand for the product as the price of that product changes)
- a price elasticity equal to 1 are said to have a ‘unitary’ elasticity of demand. This means that the change in demand is perfectly correlated to the change in price.
- It should be noted that the correlation is ‘usually’ a negative number (-) but this is ignored and always referred to as positive.

Price Elasticity should also be calculated for each change in price. This theory, although impossible to calculate in reality, should be understood because understanding price changes has a very real affect on sales revenue.

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