## Price Elasticity of Supply – Background

As a Supplier of Commodity, one would like to supply a particular quantity when the price are high. However, if there is a fall in the price, the supplier would like to sell a different quantity. In other words, there is a **change in the quantity supplied of a commodity (increase or decrease), due to a change in its price (increase or decrease in price)**. The extent of change in the quantity supplied of a commodity , due a given change in the price of the commodity , is determined by the Price elasticity of supply of that commodity.

### Price Elasticity of Supply

The concept of price elasticity of supply points out the reaction of the Sellers , to a particular change in the price of the commodity. It explains the **quantitative changes in the supply of a commodity,** due to a given change in the price of the commodity.

**Price elasticity of supply refers to the degree of responsiveness of the supply of a commodity , with reference to change in the price of the commodity.**

### Methods for Measuring Price Elasticity of Supply

Price elasticity of supply can be measured through the following methods : –

- Percentage Method
- Geometric Method

#### Percentage Method of Measuring Price Elasticity of Supply

The most common method for measuring the price elasticity of supply (we would refer to it as “**E**_{S“}) is the Percentage Method, which is also known as the proportionate method. According to the Percentage method, Price elasticity of Supply is measured as the ratio of (a) Percentage change in the quantity supplied **to** (b) the percentage change in price.

**Price Elasticity of Supply Formula – Percentage Method**

E_{S} = %ΔQ/%ΔP

Where,

E_{S} – Price Elasticity of Supply

ΔQ – Change in quantity supplied = ( New Quantity after change (Q_{1}) – Initial Quantity before change (Q) )

%ΔQ – Percentage Change in Quantity Supplied = (ΔQ/Q ) ×100

ΔP – Change in Price = New Price after change (P_{1}) – Initial Price before change (P)

%ΔP – Percentage Change in Price = ΔP/P ×100

**Example – **

Suppose, at the price of Rs. 10 per unit, a firm supplies 50 units of a commodity. When the price rises to Rs. 12 per unit, the firm increases the supply to 70 units. The price elasticity will be calculated as,

E_{S} = %ΔQ/%ΔP

%ΔQ = Change in quantity supplied/Initial Quantity ×100

%ΔQ = ΔQ/Q ×100

%ΔQ = (70-50)/50 ×100 = 40%

Similarly,

%ΔP = ΔP/P ×100

%ΔP = 12-10/10 ×100 = 20%

E_{S} = 40%/20% = 2

E_{S} = 2

The percentage method can be converted into proportionate method

E_{S} = (ΔQ/Q ×~~100~~)/(ΔP/P ×~~100~~)

E_{S} = ΔQ/P × ΔP/Q

#### Price elasticity of Supply is always positive

So far we have seen that the concept of elasticity of supply is similar to that of elasticity of demand. However, unlike elasticity of demand, elasticity of supply will always have a positive sign. This occurrence is due to the direct relationship between price and quantity supplied.

#### Geometric Method of Measuring Price Elasticity of Supply

According to the Geometric method, **elasticity is measured at a given point on the supply curve**. This method is also known as the **arc method or the point method**. The measurement of elasticity of supply for the supply curve SS can be measured as explained below.

At point A, the price is OP and the quantity supplied is OQ. When the price rises to , quantity supplied also rises to . The supply curve is extended beyond the Y-axis, so that it meets the X-axis at point L. At point A, elasticity of supply is equal to,

**Price Elasticity of Supply Formula – Geometric Method**

E_{S} = ΔQ/ΔP × P/Q

From the diagram,

ΔQ = QQ_{1 }ΔP = PP_{1 }P= OP

Q = OQ

Therefore,

E_{S} = QQ_{1}/PP_{1 }× OP/OQ

But,

QQ_{1} = AC, PP_{1} = BC, and OP = AQ

E_{S} = AC/BC× AQ/OQ ………1

Now, ΔBAC and ΔALQ are similar triangle on account of AAA property of similar triangles, therefore the ratio of their sides will be equal.

AC/BC = LQ/AQ……………2

Substituting this value in equation 1, we get,

E_{S} = LQ/AQ× AQ/OQ

E_{S} = LQ/OQ = Intercept on X-axis/Quantity supplied at that price