Elasticity formulae and practice
Price elasticity of demand (PED)
Measures responsive of quantity demanded to change in the price of the product.
PED = % change in quantity demanded / % change in price
If the price of chocolate bars increases from $2 to $2.50 (increase in price of 25%) and quantity demanded decreases from 5000 sold per
day to 3000 per day (decrease in quantity demanded of 40%), then PED = -40/25 = -1.6
As economists we ignore the negative sign, as we know the relationship between price and quantity demanded is an inverse one.... the
downward sloping demand curve shows us this.
So what does a value of 1.6 tell us? If PED > 1, then we say that demand is price elastic, i.e. a change in price has lead to a more than
proportionate change in quantity demanded. If PED < 1, then demand is inelastic, i.e. a change in price has lead to a less than
proportionate change in quantity demanded. If PED = 1, then the product has unit elastic demand, i.e. a change in price has lead to an
exactly proportionate change in quantity demanded.
There are also two extreme values:
- if PED = 0 then demand is perfectly price inelastic, i.e. a change in price has lead to no change in quantity demanded
- if PED = ∞ then demand is perfectly price elastic, i.e. an increase in price means nothing will be demanded
Practice - calculate PED for the following products and comment on whether demand is elastic or inelastic.
1. The price of potatoes increased by 15% and quantity demanded fell by 5%
2. Sales of a particular T-shirt went from 50 per week to 80 per week when the price was discounted by 20%
3. When the price of admission to a theme park increased from $30 to $36, the numbered of tickets sold per day decreased from 900 to 630
4. The price of coffee went from $4 per packet to $4.50, and quantity demanded went from 800 packets to 700 packets.
PED = % change in quantity demanded / % change in price
If the price of chocolate bars increases from $2 to $2.50 (increase in price of 25%) and quantity demanded decreases from 5000 sold per
day to 3000 per day (decrease in quantity demanded of 40%), then PED = -40/25 = -1.6
As economists we ignore the negative sign, as we know the relationship between price and quantity demanded is an inverse one.... the
downward sloping demand curve shows us this.
So what does a value of 1.6 tell us? If PED > 1, then we say that demand is price elastic, i.e. a change in price has lead to a more than
proportionate change in quantity demanded. If PED < 1, then demand is inelastic, i.e. a change in price has lead to a less than
proportionate change in quantity demanded. If PED = 1, then the product has unit elastic demand, i.e. a change in price has lead to an
exactly proportionate change in quantity demanded.
There are also two extreme values:
- if PED = 0 then demand is perfectly price inelastic, i.e. a change in price has lead to no change in quantity demanded
- if PED = ∞ then demand is perfectly price elastic, i.e. an increase in price means nothing will be demanded
Practice - calculate PED for the following products and comment on whether demand is elastic or inelastic.
1. The price of potatoes increased by 15% and quantity demanded fell by 5%
2. Sales of a particular T-shirt went from 50 per week to 80 per week when the price was discounted by 20%
3. When the price of admission to a theme park increased from $30 to $36, the numbered of tickets sold per day decreased from 900 to 630
4. The price of coffee went from $4 per packet to $4.50, and quantity demanded went from 800 packets to 700 packets.
Price elasticity of supply (PES)
Measures responsiveness of quantity supplied to a change in the price of the product.
PES = % change in quantity supplied / % change in price
If the price of chocolate bars increases from $2 to $2.50 (increase in price of 25%) and quantity supplied increases from 5000 per day to
7500 per day (increase in quantity supplied of 50%), then PES = 50/25 = 2
So what does a value of 2 tell us? If PES > 1, then we say that supply is price elastic, i.e. a change in price has lead to a more than
proportionate change in quantity supplied. If PES < 1, then supply is inelastic, i.e. a change in price has lead to a less than proportionate
change in quantity supplied. If PES = 1, then the product has unit elastic supply, i.e. a change in price has lead to an exactly proportionate
change in quantity supplied.
There are also two extreme values:
- if PES = 0 then supply is perfectly price inelastic, i.e. a change in price has lead to no change in quantity supplied
- if PED = ∞ then supply is perfectly price elastic, i.e. a decrease in price means nothing will be supplied
Practice - calculate PES for the following products and comment on whether supply is elastic or inelastic.
1. The price of potatoes increased by 15% and quantity supplied increased by 3%
2. The price of T-shirts increases from $25 to $30 and quantity supplied increases from 600 to 780.
PES = % change in quantity supplied / % change in price
If the price of chocolate bars increases from $2 to $2.50 (increase in price of 25%) and quantity supplied increases from 5000 per day to
7500 per day (increase in quantity supplied of 50%), then PES = 50/25 = 2
So what does a value of 2 tell us? If PES > 1, then we say that supply is price elastic, i.e. a change in price has lead to a more than
proportionate change in quantity supplied. If PES < 1, then supply is inelastic, i.e. a change in price has lead to a less than proportionate
change in quantity supplied. If PES = 1, then the product has unit elastic supply, i.e. a change in price has lead to an exactly proportionate
change in quantity supplied.
There are also two extreme values:
- if PES = 0 then supply is perfectly price inelastic, i.e. a change in price has lead to no change in quantity supplied
- if PED = ∞ then supply is perfectly price elastic, i.e. a decrease in price means nothing will be supplied
Practice - calculate PES for the following products and comment on whether supply is elastic or inelastic.
1. The price of potatoes increased by 15% and quantity supplied increased by 3%
2. The price of T-shirts increases from $25 to $30 and quantity supplied increases from 600 to 780.
Cross elasticity of demand (XED)
Measures responsiveness of the quantity demanded of one good to a change in the price of another good.
XED = % change in quantity demanded of Good X / % change in price of Good Y
If XED > 0, i.e. a positive value, the goods in question are substitutes for each other, e.g. an increase in the price of Pepsi has led to an
increase in the quantity of Coke demanded.
If XED < 0, i.e. a negative value, the goods are complements, e.g. an increase in the price of cars led to a decrease in the quantity of
petrol demanded.
If XED = 0, there is no relationship at all between the goods. The higher the number, the closer the relationship.
Practice - calculate XED for the following products and comment on the relationship
1. When the price of coffee went from $4 per packet to $4.50, the quantity of sugar demanded fell from 500 to 450.
2. As a result of the increase in the price of coffee, the quantity of tea demanded increased by 5%.
3. As a result of the increase in the price of coffee, the demand for cheese remained the same.
XED = % change in quantity demanded of Good X / % change in price of Good Y
If XED > 0, i.e. a positive value, the goods in question are substitutes for each other, e.g. an increase in the price of Pepsi has led to an
increase in the quantity of Coke demanded.
If XED < 0, i.e. a negative value, the goods are complements, e.g. an increase in the price of cars led to a decrease in the quantity of
petrol demanded.
If XED = 0, there is no relationship at all between the goods. The higher the number, the closer the relationship.
Practice - calculate XED for the following products and comment on the relationship
1. When the price of coffee went from $4 per packet to $4.50, the quantity of sugar demanded fell from 500 to 450.
2. As a result of the increase in the price of coffee, the quantity of tea demanded increased by 5%.
3. As a result of the increase in the price of coffee, the demand for cheese remained the same.
Income elasticity of demand (YED)
Meaures responsiveness of the demand for a product to a change in consumer incomes.
YED = % change in quantity demanded / % change in income
If YED > 0, i.e. a positive value, the goods in question are normal goods, i.e. we demand more of these goods as our income increases.
Necessities tend to be income inelastic, i.e. 0 < YED < 1, as demand changes only a little when income changes. An example would
be some sort of staple food, e.g. if incomes in Asia increase, the demand for rice increases less than proportionately.
Superior good/luxury goods tend to be income elastic, i.e. YED > 1, as demand will change more than proportionately.
If YED < 0, i.e. a negative value, the goods in question are inferior goods, i.e. we demand less of them as our income increases - we switch
our income away from these goods. As our income increases we may buy less stewing steak (inferior good) and more fillet steak (normal
good).
Practice - calculate YED for the following products and comment on the type of good this indicates
Monica's income increased from $20000 per year to $22000 per year.
1. Her spending on clothes went from $3000 per year to $4500 per year.
2. The number of loaves of bread she bought went from 50 per year to 60 per year.
3. She bought 20 tins of beans instead of 30.
YED = % change in quantity demanded / % change in income
If YED > 0, i.e. a positive value, the goods in question are normal goods, i.e. we demand more of these goods as our income increases.
Necessities tend to be income inelastic, i.e. 0 < YED < 1, as demand changes only a little when income changes. An example would
be some sort of staple food, e.g. if incomes in Asia increase, the demand for rice increases less than proportionately.
Superior good/luxury goods tend to be income elastic, i.e. YED > 1, as demand will change more than proportionately.
If YED < 0, i.e. a negative value, the goods in question are inferior goods, i.e. we demand less of them as our income increases - we switch
our income away from these goods. As our income increases we may buy less stewing steak (inferior good) and more fillet steak (normal
good).
Practice - calculate YED for the following products and comment on the type of good this indicates
Monica's income increased from $20000 per year to $22000 per year.
1. Her spending on clothes went from $3000 per year to $4500 per year.
2. The number of loaves of bread she bought went from 50 per year to 60 per year.
3. She bought 20 tins of beans instead of 30.