So in last class
we talked about elasticity of demand
In this class
we're gonna be focusing on elasticity of supply
when they demand for a good increases
its equilibrium price rises
and equilibrium quantity of the good increases
This is what we have seen from chapter two
But does the price rise by a large amount
And the quantity increase by a little
Or does the price barely rise
And the quantity increased by a large amount
That is
the answer depends on the elasticity of supply of the good
The elasticity of supply
measures the responsiveness of the quantity supplied
to a change in the price of a good
When all other influences on selling plans remain the same
So formally
elasticity of supply
equals to change of quantity supplied
divided by change of price
which equals to change of q over q
divided by change of p over p
and that is change of q
over change of p times p over q
where q here indicates quantity supplied
for example
if it one percent increase in price
results in a two percent increase in quantity supplied
the elasticity of supply
this is two percent divided by one percent That is two
So we have talked about what is the elasticity of supply
Now let's take a look at the algebraic
So along a linear supply curve with a function
of q equals to g plus h times p
p here is price
where h is the slope
or h equals to change of q over change of p
this is the elasticity of supply equals to
change of q over change of p
times p over q is just h times p over q
again let's use an example to illustrate this
Assume that the estimated linear supply function for corn
is q equals to ten point two plus zero point twenty five p
where q here is quantity of corn supplied
in million bushels per year
And p here is the price of it
If p equals to seven dollars and twenty cents
and q equals to twelve units
the elasticity of supply is change of q over change of p times p
over q were change of q over change of p
is just zero point two five from the supply function
p over q which is seven point two divided by twelve
We get that the elasticity of supply is zero point one five
Now we know how to calculate elasticity of supply
Now let's take a look at figure three point six
The elasticity of supply varies along the supply curve
The higher the price
the larger is the supply elasticity
For example
at point eight
when the price is five dollars and sixty cents
quantity is eleven point six units
the elasticity of supply at this point
is zero point one two five
as the price increases from five sixty to seven twenty
quantity supplied also increases from eleven point six to twelve
The elasticity of supply
increases from zero point one two five
to zero point one five
So we've looked at the elasticity along the supply curve
And we know that if the supply curve is linear
the elasticity of supply varies along the curve
Now let's take a look at a few extreme cases
of elasticity of supply
firstly
let's take a look at this perfectly inelastic supply
When supply is perfectly inelastic
the supply curve is vertical
and the elasticity of supply is zero
Very similar to our elasticity of demand
So the second extreme we're going to be looking at
is the perfectly elastic supply
This is very similar to our perfectly elastic demand
When supply is perfectly elastic
the supply curve is horizontal
and the elasticity of supply is infinity
The third extreme case is when we have a unit elastic supply
supply is unit elastic
If the supply curve is linear and passes through the origin
Now let's take a look at the factors
that can influence the elasticity of supply
So we're gonna be focusing on two factors
resources substitution possibility
time frame for supply decision
Firstly
resource substitution possibilities
the easier it is to substitute among the resources
used to produce a good or service
The greater is its elasticity of supply
On the other hand time frame for supply decision
the more time that passes after a price change
the greater is the elasticity of supply
the reason why the longer the period
the greater the elasticity supply
is that if suppose we're in an immediate time
we cannot do anything relatively inelastic supply
But if it's a short run
we can adjust variable like labor
Now the elasticity increases
in the long run
because mostly all variables are just a bowl
Now we can adjust all costs
The supply become more elastic
So so far we've introduced elasticity of demand
elasticity of supply
Now let's talk about more elasticity of demand
Another one we're going to introduce is called
income elasticity of demand
The income elasticity of demand measures
how the quantity demanded of a good
response to a change in income
other things remaining the same
So formally
income elasticity equals to percentage change in quantity demanded
divided by percentage change in income
which is change of q over q divided by
change of income over income
which is change of q over change of y
times y over q where y stands for income
for example
if there's a one percent increase in income
results in a three percent increase in quantity demanded
this the income elasticity of demand
is three percent over one percent
That is three
Again
let's take a look at the example to illustrate this idea
Suppose the estimated demand function for avocado
is that q equals two hundred and four
minus forty p plus twenty pt
plus zero point zero one y
Where p here is price of avocados
pt here is price of tomatoes
Why is our monthly income
So the question is
what would be the income elasticity of demand
for avocados if q equals to fifty and income equals to four thousand
based on the formula we introduced before
the elasticity of income equals to
change of q over change of y
times y over q
and how do we derive this change of q over change of y
we can get it from the estimated demand function for avocados
The function decayed that when income increased by one unit
the total quantity demanded for avocado increases by
zero point zero one unit
So change of q over change of y is just zero point zero one
So zero point zero one times
the income over quantity demanded ratio
which is four thousand divided by fifty
We get that the income elasticity at this point
is zero point eight
So how do we interpret this income elasticity
If the income elasticity of demand is greater than one
Demand is income elastic
And the good is a normal good
If the income elasticity of demand is greater than zero
but less than one
demand is income in elastic
and the good is a normal good
among the normal goods
the necessities are less income elastic
where the luxury goods are more income elastic
If the income elasticity of demand is less than zero
means that when income increases
quantity demanded decreases
Now this good is an inferior good
Another elasticity we're gonna introduce here is called
cross price elasticity
The cross elasticity of demand is a measure
of the responsiveness of demand for good
to a change in the price of a substitute
or a complement
Other things remaining the same
so formally cross price elasticity
equals to the percentage change in quantity demanded
divided by the percentage change
for the price of another good
And this good can be substitute or complement
And that equals to change of q over q
divided by change of p over p
and that equals to change of q over change of p
times p over q
for example
if there's a one percent increase in the price of a related good
results in a three percent decrease in the quantity demanded
the cross price elasticity of demand
is this negative three percent
divided by one percentand that's negative three
So how do we interpret this cross price elasticity
If the cross price elasticity is positive
means that when the price of related goods increases
the quantity demanded for this good also increases
then these two goods are substitutes
On the other hand
if the cross price elasticity is negative
means that when the price of related good increases
quantity demand for this good decreases
then these two products are complements
The closer is the substitute or complement to this good
the more cross price elastic is the demand
Now let's use an example to show this cross price elasticity
Again
the estimated demand function for avocados
is q equals to hundred and four minus forty p
plus twenty pt plus zero point zero one y
And again
p here is price of avocados
pt here as price of tomatoes
y here is our monthly income
So the question is
what would be the cross price elasticity
between the price of tomatoes and the quantity of avocados
if q is fifty units and price of tomatoes is zero point eight dollars
So we have already shown that cross price elasticity
equals to change of q over change of the price
of related good times price over q
in this case
change of q over change of price of tomatoes
is just the coefficient on the demand function
which is twenty
So the cross price elasticity
is just twenty times price over quantity ratio
which is zero point eight divided by fifty
So the cross price elasticity is zero point three two
So in this case
cross price elasticity is a positive number
which tells us when price of tomatoes increases
quantity demanded for avocados increases
This
Those two products are substitutes
That's everything for this class
I'll see you guys in the next class