# MEASURING PRICE ELASTICITY

If elasticity is zero, demand curve is perfectly inelastic. If elasticity is infinite, demand curve is perfectly elastic. And if elasticity is unitary, demand curve gently slopes downwards. If demand is elastic, consumers react more proportionately to a change in price. If demand is inelastic, consumers react less proportionately to a change in price. If demand is unit elastic (unitary), consumers react proportionately to a change in price.

The following are synonymous concepts:

- Perfectly elastic.
- Completely elastic
- Infinitely elastic.
- Absolutely elastic.

**Low and high price elasticity**

A product has low price elasticity if it is price inelastic. And it has high (strong) price elasticity if it is price elastic.

The demand of a rich man (a millionaire) tends to be inelastic as he buys virtually (almost) the same quantity irrespective of changes in price. While the demand of a poor man tends to be elastic as a small change in price forces him to switch to a substitute or an inferior item.

Thus the classification in table 2 are not specific; they vary among low and high income groups.

**Brand**

A particular brand of a commodity has elastic demand except it is the best brand, like Mercedes Benz and Jeep among vehicles, bournvita and lipton among beverages, etc.

The numerical (absolute) value of elasticity is referred to as **Coefficient**. The formula for calculating the coefficient or price elasticity value **(Ep)** is as follows:-

‘**Percentage change in Quantity demanded divided by the percentage change in price”.**

Note the following abbreviations:

**Ep is**

- price elasticity of demand as well as
- Numerical value of price elasticity.

Q = Quantity.

P = Price.

% ∆ in price = percentage change in price.

**Example 1**

The price of a shirt is N100 and the quantity demanded is 100 units. When the price falls to N9.00, the quantity demanded rises to 150 units. Calculate the coefficient of price elasticity of demand.

**1) Determining the original quantity**

Original (old or former) quantity refers to the first quantity in the sentence; that is 100 units in the above example. While new quantity refers to the second or latter quantity in the sentence; that is, 150 units in the above example.

**2) Determining the original price**

Original (old or former) price refers to the first price in the sentence; that is, N10.00 in the above example. While new price refers to the second or latter price in the sentence which is N9.00.

However, this depends on how the sentence is constructed. Nevertheless, efforts must be made to identity both the old and new prices and quantities.

**3) Determining the difference between the two quantities:**

**Old or original quantity minus new quantity From the example:**

Old quantity is 100 units and new quantity is 150 units. Difference in quantity = 150 – 100 = 50 units.

Notice that we ignore the negative sign or value in elasticity. Thus 100 – 150 = 50 and NOT “- 50” That is, all values are termed absolute and NOT algebraic.

**4) Determining the difference between the two prices:**

Old or original price minus new price

From the above example,

Old price is N10 and New price is N9

Difference in price is N10 – N9 = N1.00

Calculation of percentage change in both quantity and price:-

**Calculation of coefficient**

**Example 2**

The price of a cup of salt is N1.00, and the quantity demanded is 100 cups. When the price rises to N2.00 per cup, the quantity demanded falls to 95 cups. Calculate the absolute numerical value of the price elasticity of demand.

**Firstly, you should remember the formula:**

**Secondly, find the difference between:**

- Old and new quantities.
- Old and new prices as follow:

Difference in quantities = 100 – 95 = 5 Difference in prices = N2 – N1 = 1

**Thirdly. calculate the % change in both quantity and price as follow:**

**Fourthly, calculate the coefficient using the formula given above:-**

Note:

Always convert fractions to decimals as illustrated above. The coefficient of elasticity is not expressed in fraction but always in decimal.

**Example 3**

The price of a textbook is N120 and the quantity bought weekly is 1000 units. And when the price rises to N150, the quantity demanded is 750 units. Calculate the coefficient of the price elasticity of demand. Let us adopt tabular approach in finding solution to the above example.

Determine the value of A, B and X; and insert (state) type of elasticity in place of Y.

Note: You should properly understand the first and second examples before attempting example 3.

Secondly, the type of elasticity is determined by the numerical value of the price elasticity.

**Determining the type of elasticity of demand**

The coefficient which is the numerical value of elasticity is the major determinant of the “type of elasticity”. Thus students should ‘familiarize themselves even endeavour to sing with the following sentences:-

- If elasticity is greater than unity – one . (E> 1), demand is elastic.
- If elasticity is less than unity (E < I), demand is inelastic.
- If elasticity is unity; i.e ., it is equal to one (E= 1), demand is Unitary.
- If elasticity is infinite (E = 00), demand is perfectly elastic.
- If elasticity is zero (E = 0), demand is perfectly inelastic.

**Note**

- A demand curve of zero elasticity is called perfectly inelastic demand”
- A demand curve of constant elastic is called “Unit elasticity of demand”
- A demand curve of infinite elasticity is called “perfectly elastic demand”.

** Remember:**

After the calculation, if the coefficient (elasticity value) is greater than one, like 1.2,3,4, etc. (E> 1) as occurs in the example 1 above, **‘Demand is elastic’.**

That is, demand is elastic if the elasticity is greater than one (E > 1).

After the calculation, if the coefficient (elasticity value) is less than one (E < 1) like 0.1, 0.5, 0.8, etc, as occurs in example 2 above, ‘**Demand is inelastic’.**

That is, demand is inelastic if elasticity is less than one (E < 1).

After the calculation if the coefficient (elasticity value) equals one (E = 1) i.e. its value is exactly one, as occurs in example 3 above, ‘**Demand is unitary’.** That is, demand has unit elasticity, if elasticity is exactly one. Unit elasticity is also referred to as “Unitary elasticity of demand’.

There are three factors (things) involved in price elasticity:

- % ∆P.
- % ∆Q.
- the Quotient (coefficient).

If two are given (known), the third one can be determined.

**Example 4**

If elasticity of demand for rice is 1.5, the percentage change in price is 5%, find the percentage change in quantity demanded.

Note: If a commodity has elastic demand (1.5), its complement also has elastic demand (1.5), especially if they are perfect complement.