Elasticity of supply shows how much the quantity supplied changes when price changes.
Meaning:
Elasticity of supply (Es) by the percentage method is the ratio of the percentage change in quantity supplied to the percentage change in price.
Formula:
\[E_s=\frac{\frac{\Delta q_s}{q_s}}{\frac{\Delta P}{P}}=\frac{\Delta q_s}{\Delta P}\times\frac{P}{q_s}\]
If an increase in the price of a ballpoint pen from ₹40 to ₹50 results in an increase in quantity supplied from 1,000 to 1,500, what is the elasticity of supply?
Solution:
Q = 1,000
ΔQ = 1,500 - 1,000 = 500
P = 40
ΔP = 50 - 40 = 10
es = `(ΔQ)/(ΔP) xx P/Q`
= `(ΔQ)/(ΔP) xx P/Q`
= `500/10 xx 40/1000` = 2
The price of a commodity is ₹10 per unit and quantity supplied is 500 units. If price falls by 10% and quantity supplied falls to 400 units, calculate its price elasticity of supply.
Solution:
% change in quantity supplied = `500 - 400/500 xx 100` = `100/500 xx 100`
es = `"% Change in quantity supplied"/"% Change in price"` = `20/10` = 2
A producer supplies 200 units of a good at ₹10 per unit. Price elasticity of supply is 2. How many units will the producer supply at ₹11 per unit.
Solution:
es = `(ΔQ)/(ΔP) xx P/Q`
2 = `(ΔQ)/11-10 xx 10/200` =`(ΔQ)/1 xx 10/200`
2 = `Q/20`
ΔQ = 2 × 20 = 40
Therefore, the producer will supply 200 + 40 = 240 units at ₹11 per unit.
The quantity supplied of a commodity at a price ₹8 per unit is 400 units. Its price elasticity is 2. Calculate the price at which its quantity supplied will be 600 units.
Solution:
es = `(ΔQ)/(ΔP) xx P/Q`
2 = `(600-400)/(ΔP) xx 8/400` = `200/(ΔP) xx 1/50` = `4/(ΔP)`
ΔP = `4/2` = 2
∴ New price = 8 + 2 = ₹10.
A producer supplies 400 units of a commodity at no per unit. Price elasticity of supply is 1.25. How many units will the producer supply at ₹20 per unit?
Solution:
es = `(ΔQ)/(ΔP) xx P/Q`
1.25 = `(ΔQ)/20-10 xx 10/400` = `(ΔQ)/10 xx 10/400` = `(ΔQ)/400`
ΔQ = 400 x 1.25 = 500
∴ The producer will supply = Q + ΔQ = 400 + 500 = 900 units
With a fall in the price of a commodity from ₹10 per unit to ₹8 per unit, the quantity supplied of the commodity falls by 500 units. The price elasticity of supply is 2. Calculate the quantity supplied of this commodity at the price of ₹8 per unit.
Solution:
Here P = 10, P1 = 8, ΔP = 10 - 8 = 2, ΔQ = 500, es = 2
es = `(ΔQ)/(ΔP) xx P/Q`
2 = `500/2 xx 10/Q` = `2500/Q`
Q = `2500/2` = 2500
∴ Quantity supplied at the price of ₹8 per unit = 1250 - 500 = 750 units
500 units of a commodity are supplied at a price of ₹5 per unit. At what price 600 units of the commodity will be supplied? The price elasticity of supply is 1.
Solution:
Here, P = 5, Q = 500, Q1 = 600, ΔQ = 600 - 500 = 100 units, es = 1
es = `(ΔQ)/(ΔP) xx P/Q`
1 = `100/(ΔP) xx 5/500` = `1/(ΔP)`
(ΔP) = 1
∴ New price = P + ΔP = 5 + 1 = 6
∴ 600 units of the commodity will be supplied at ₹6 per unit.
Given es = 3, P = 40, P1 = 42, ΔQ = 150. How many units of the commodity will be supplied at P1 price.
Solution:
es = `(ΔQ)/(ΔP) xx P/Q`
3 = `150/(42-40) xx 40/Q` = `3000/Q`
Q = `3000/3` = 1000
Quantity supplied at the price of ₹42 per unit = Q + ΔQ = 1000 + 150 = 1150 units
Diagram:
Elasticity of supply depends on time:
