3.4 Point and Arc Elasticity of Demand

In the realm of economics, understanding how consumers respond to price fluctuations is paramount. This is where the concept of elasticity of demand comes into play. Point and Arc Elasticity of Demand provide valuable insights into the behavior of consumers and help businesses make informed decisions about pricing strategies, production levels, and marketing campaigns. In this blog post, we are going to explore these two concepts of elasticity. This topic is equally important for the students of economics across all the major Boards and Universities such as FBISE, BISERWP, BISELHR, MU, DU, PU, NCERT, CBSE & others & across all the business & finance disciplines.

Point and Arc Elasticity of Demand

Point Elasticity of Demand

It is the second method to measure price elasticity of demand. Point elasticity of demand measures the elasticity of demand at some specific point on demand line. Concept of point elasticity express the small change in quantity demand. For better understanding, follow the table and diagram below:

Table Point Elasticity of Demand

Q.D (x)	Price (x)
17	10
18	8
19	6
20	4

Figure Point Elasticity of Demand

Explanation

In above table, at the price of x is 8, the quantity demand is 18 which is shown in the figure at E. When price reduces to 6, at this point there is a slight change in quantity demand and it increases to 19 which is shown in the above figure at E1. These two points are so closed to each other which shows the point elasticity of demand.

There are two methods to calculate point elasticity of demand:

Mathematical Method to calculate point elasticity of demand
Geometric Method to calculate point elasticity of demand.

Mathematical method to calculate Point Elasticity of Demand

$\mathbf{P.E.D =}\frac{\mathbf{\mathrm{\Delta}Q}}{\mathbf{\mathrm{\Delta}P}}\mathbf{\times}\frac{\mathbf{P}}{\mathbf{Q}}\$

$\textbf{Where 𝛥Q = 19-18 = 1, 𝛥P = 6-8 = -2, P = 8 and Q = 18}$

$\mathbf{P.E.D =}\frac{\mathbf{\mathrm{\Delta}Q}}{\mathbf{\mathrm{\Delta}P}}\mathbf{\times}\frac{\mathbf{P}}{\mathbf{Q}}\$

$\mathbf{P.E.D =}\frac{\mathbf{1}}{\mathbf{- 2}}\mathbf{\times}\frac{\mathbf{8}}{\mathbf{18}}\mathbf{=}\frac{\mathbf{8}}{\mathbf{- 36}}\mathbf{- 0.22 = 0.22}\$

Geometric Method to calculate Point Elasticity of Demand

Under this method, we take the ratio of length on x-axis and y-axis on the demand line. For example, we want to calculate the elasticity at point E on the demand line then we have to divide the distance of AE with BE. We assume that here the distance between AE is 5 cm and distance between BE is 2 cm, then the formula and calculation will be:

$\mathbf{PED =}\frac{\mathbf{Length\ of\ lower\ Part}}{\mathbf{Length\ of\ upper\ Part}}\mathbf{=}\frac{\mathbf{AE}}{\mathbf{BE}}\mathbf{=}\frac{\mathbf{5}}{\mathbf{2}}\mathbf{= 2.5}\$

At the mid-point, the elasticity will always be equal to unitary or 1, below this point, it will be less than unitary and above this point it will be more than unitary.

Arc Elasticity of Demand

Huge change in quantity demand with respect to price can be calculated through Arc elasticity of demand. It calculates the elasticity of demand between two point of quantity demand on demand line. We can understand it through following example and figure given below:

Table Arc Elasticity of Demand

Q.D (x)	Price (x)
100	2
70	4

Figure Arc Elasticity of Demand

The distance between point a and b on the demand line indicates that there is a drastic change in quantity demand from Q1 to Q2 from point a to point b.

Mathematical method to calculate Arc elasticity of demand

$\mathbf{AED =}\frac{\frac{\mathbf{Q}\mathbf{2 - Q}\mathbf{1}}{\mathbf{Q}\mathbf{2 + Q}\mathbf{1}}}{\frac{\mathbf{P}\mathbf{2 - P}\mathbf{1}}{\mathbf{P}\mathbf{2 + P}\mathbf{1}}}\$

$\mathbf{AED =}\frac{\frac{\mathbf{70 - 100}}{\mathbf{70 + 100}}}{\frac{\mathbf{4 - 2}}{\mathbf{4 + 2}}}\$

$\mathbf{AED =}\frac{\frac{\mathbf{- 30}}{\mathbf{170}}}{\frac{\mathbf{2}}{\mathbf{6}}}\$

$\mathbf{AED =}\frac{\mathbf{- 30}}{\mathbf{170}}\mathbf{\times}\frac{\mathbf{6}}{\mathbf{2}}\$

$\mathbf{AED =}\frac{\mathbf{- 180}}{\mathbf{340}}\mathbf{= - 0.53}\$

Factors or Determinants of Elasticity of Demand

Elasticity of demand depends on different factors given below:

1. Nature of Good

Goods are different in their nature that is why their elasticity of demand differentiate with each other. Further detail is given below:

Necessities

Daily consumable food items are compulsory for living so their demand is less elastic because of their importance such as wheat, rice, sugar, tea, milk etc.

Durable Goods

Durable goods are more elastic because when their price rises, people prefer to use old ones such as car, motorcycle, furniture etc.

Luxuries and Comforts

Luxuries and comfort oriented goods are more elastic because when their price rises, people prefer to buy less. Such as cars, imported items etc.

Perishable Goods

Perishable goods are less elastic because people tends to buy even on higher prices such as vegetables, fruits etc.

2. Consumers Choices Fashion

Goods those are bought by the people as a fashion are less elastic because normally fashionable consumer never compromise on fashion so they buy even at higher prices such as garments, cosmetics etc.

3. Consumer’s Income

Consumer’s demand belongs to high income slab remains less elastic because they continue buying even at higher prices due to their high income. Consumer’s demand belongs to low income slab is more elastic because their quantity demand declines as price rises because of low income.

4. Specific and Alternatives

Goods which are used for specific purpose have less elastic demand for example, pen is a specific product for writing so its demand is less elastic. In contrast electricity will be more elastic because when prices hikes, people reduce its consumption.

5. Substitutes

Goods those have close substitutes, has more elastic demand because when price hikes, people shift their demand to substitutes or alternatives those have less price. For example, if price coffee rises, people increase the demand of tea if its price is low as compare to coffee.

6. Custom, Habits, Hobbies

Products which are used as a custom or habits or hobbies have less elastic demand. People demand remains intact even at higher prices. For example, in Pakistani, Indian culture, Gold is used as custom, similarly use of cigarette as a habit etc.

7. Weather

Weather is another factor which determines the elasticity of demand. For example, in summer, the demand of cold drinks and ice cream is less elastic similarly, in winter, demand of warm clothing is less elastic.

2.1 Theory of Consumer Behaviour

2.2 Total Utility, Marginal Utility, Point of Satiety & Types of Utilities

2.3 The Law of Diminishing Marginal Utility DMU

2.4 The Law of Equal Marginal Utility EMU

3.1 Demand, Individual Demand, Aggregate Demand, Law of Demand

3.2 Change and Shift in Demand, Extension and Contraction in Demand, Rise and Fall in Demand

3.3 Elasticity of Demand