Hello everyone
In last class
we talked about supply and demand
So today we're gonna focus on
how shapes of supply and demand curves matter
In other words
we're gonna talk about the sensitivity
of the quantity demanded for price
and sensitivity of the quantity supplied to price
So you know that one supply decreases
the equilibrium price rises
and the equilibrium quantity decreases from last class
But does the price rise by a large amount
and the quantity decrease by a little
Or does the price barely rights
and the quantity decrease a large amount
The answer depends on the responsiveness
of the quantity demanded of a good
to a change in its price
So the shapes of the supply and demand curves
determined by how much a shock of facts
the equilibrium priceand quantity
So for example
our avocado example from last chapter
we've seen that the supply of avocados depends on the price
of avocados and the price of fertilizer
So see figure three point one
a fifty five cents increase in the price of fertilizer
shifts the avocado supply curve to the left from s one to s two
How the effect of a supply shock
depends on the shape of the demand curve
Panel A here is our typical downward sloping linear demand curve
the equilibrium price increases from two dollars
to two dollars twenty cents
while the quantity decreases from eighty units to seventy two units
Panel B here
if the demand curve was vertical
Now with a decrease in the supply
supply curve shifts from s one to s two
price increases relatively more compared to panel A
where the price increases from two dollars to two dollars seventy three cents
And if you look at the quantity
because the demand curve was vertical
so the quantity stays constant
Panel C here
is if the demand curve was horizontal
with the horizontal demand curve
when there's a decrease in supply price stays constant
but the quantity decrease by a lot more
This how much the equilibrium quantity and price change
depends on the shape of demand curve
So in order to show that we're gonna introduce elasticity
which is a commonly used a measurement
of the sensitivity of one variable
Elasticity formerly is the percentage change in one variable
in response to a given percentage change in another variable
So here we're gonna focus on price elasticity of demand
Price elasticity of demand
is the percentage change in the quantity demanded
in response to a given percentage change in the price
At a particular point on the demand curve
So mathematically speaking
it is just percentage change in the quantity demanded
divided by percentage change in the price
Formally
price elasticity of demand
where we use ed to indicate it
equals to the percentage change in quantity demanded
divided by percentage change in price
which equals to change of q over q
divided by change of p over p
where delta here indicates a change
for example
if a one percent in price
results in a three percent decrease
in the quantity demanded
This the elasticity of demand is negative three percent
divided by one percent which is negative three
So when a one percent change in price
cause sports more than one percent changing in quantity demanded
the good has price elastic demand
When a one percent change in price produces
less than one percent change in quantity demanded
The good has price inelastic demand
When a one percent change in price
leads to a one percent change in quantity demanded
we call this good has a unit elastic demand
So we've talked about what is the price elasticity of demand
Now let's take a look at the algebra
Along a linear demand curve with a function of q
which is quantity demanded equals to a minus b times price
where b is the ratio of the fault in quantity to the rise in price
where b here equals to change of q over change of p
so the elasticity of demand can be written as
change of q over q divided by change of p over p
that is b times p over q
let's use the example to show this algebra of it
The estimated linear demand function for corn
Suppose
is q equals to fifteen point six minus zero point five times p
where q here is the quantity demanded
a million bushes per year and p is the price of it
What is the elasticity of demand at the point
on the demand curve
when the price is seven dollars Twenty cents
to solve this problem
we know that the slope coefficient
for this demand function is b
which equals to zero point five
We can substitute b p and q into this function
We find that the elasticity of demand at this point on the demand curves
thus elasticity of demand equals to
negative b times p over q
so which equals to negative zero point five times
seven dollars twenty cents divided by the quantity which is twelve
It gives us that the elasticity of demand at this point
is negative zero point three
at this point on the demand curvea
one percent increase in the price of corn
leads to a zero point three percent fall in the quantity of corn demanded
So a price increase causes a less
than proportionate fell in the quantity of corn demanded
at this point on the demand curve
So at this point
on the demand curve
the demand for corn is relatively inelastic
Here is figure three point two
It shows the elasticity along a linear demand curve
Let's first take a look at the midpoint point a
At this point,
the elasticity of demand equals to the inverse of the slope of the curve
which is negative half times price over quantity
which is fifteen point six divided by seven point eight
That gives us negative half times two
which is negative one
Now let's take a look at another point point b
At this point
the elasticity of demand equals two inverse of the slope of the curve
which is again negative half
times the price over quantity ratio at this point
which is twenty three point four divided by three point nine
and that is negative three
And the third point that we're going to focus on here is point c
at this point again
the elasticity of demand equals to the inverse of the slope of the curve
again
negative half times price over quantity ratio at this point
which is seven point two divided by twelve
So as we see that
At this point c
the elasticity of demand is negative zero point three
So as we can see that the elasticity of demand varies
along the demand curve
So the elasticity of demand is different at every point
along a downward sloping linear demand curve
In addition we have just seen at the midpoint
where we have the elasticity of demand equals to negative one
that's what we call unit elastic
At prices above the midpoint of the demand curve
Demand is elastic
At prices below the midpoint of the demand curve
demand is inelastic
Now
let's take a look at some extreme cases
This figure three point three here illustrates the case of a good
that has a perfectly inelastic demand
The demand curve is vertical
in which the price elasticity is zero
Along a vertical demand curve
Elasticity is zero
That's what we call perfectly inelastic demand
That means the quantity demanded is unchanged regardless of the price
A demand curve is vertical for essential goods
goods that people feel they must have and will pay anything to get
So what would cause demand to be perfectly inelastic
It's all about substitutes
When there is no substitutes
Demand will be perfectly inelastic
because you have to have q it doesn't matter what the prices
for example
insulin for diabetics
diabetics
without getting that insulin to manage their diabetes
will be in very serious health condition
And there's no substitutes for it
So diabetics demand for insulin is relatively very inelastic
So for a perfectly inelastic demand curve
when supply increases
the quantity demanded stays constant while price increases
Now let's consider the opposite
Figure three point four here
illustrate the case of perfectly elastic demand
a horizontal demand curve in which the price elasticity is infinity
So along a horizontal demand curve
elasticity is infinity
perfectly elastic demand
When a demand is perfectly elastic
people are willing to buy as much as sperm cell
at any price less than or equal to p star
If the price increases even slightly above p star
demand falls to zero
a small increase in price cause an infinite drop
in quantity demanded in this case
In this case
consumers do not care about the quantity
They just care about the price
That is
there are infinitely good substitutes
would be one
would be one where there are
essentially perfect substitutes
for example
coke versus pepsi
When you want to have a cola drink
and the price of a coke increases
you will just have a pepsi instead
Thus
If there's a supply shock to a provider
that's facing a perfectly elastic demand curve
they cannot raise their price
because people would just switch
So quantity will decrease
and price stays constant
So the price elasticity of demand will typically
be between zero and negative infinity
And the larger the absolute value of it
the more quantity will change when price changes
Now let's take a look at the factors
that can influence the elasticity of demand
So we're gonna focus on three factors
the closeness of substitutes
the proportion of income spent on the good
the time elapsed since a price change
So firstly
closeness of substitute
the closer the substitutes for a good or service
The more elastic is the demand for the good or service
Secondly
proportion of income spent on the good
the greater the proportion of income consumers spend on a good
the larger is the elasticity of demand for that Good
The last factor is time elapsed since price change
the more time consumers have to adjust to a price change
or the longer that a good can be stored without losing its value
The more elastic is the demand for that good
The next topic that we're gonna be focusing on
is the demand elasticity and revenue
Any shock that causes equilibrium price to change
will affect industry's revenue
So what is revenue
The total revenue from the sale of a good or service
equals the price of the good multiplied by the quantity soap
So total revenue equals to price times quantity
So as we can see when price changes
total revenue also changes
But a rise in price doesn't always increase total revenue
because when price increases
quantity demanded decreases
Total change on revenue This is ambiguous
Let's take a look at figure three point five
which shows a effect of a price change on revenue
Initially
the price was at p equals to p one
So when price was at p one
quantity is at q one
So total revenue price times quantity is the area a plus b
now suppose
the supplier wants to increase the price
Price increases from p one to p two
Now what happened to revenue
as price increases
Quantity demanded decreases from q one to q two
So even though now the supplier can charge a higher price
but the total quantity they can sell decreases
So now the revenue increases by area c
but decreases by area b resulting in revenue off a plus c
this given the increase of c and the decrease of area b
the change of total revenue This is ambiguous
Now let's take a look at couple extreme cases
The first extreme case is if a demand is perfectly inelastic
we know that the demand curve is a vertical line
which means no matter how price changes
quantity demanded remains the same
If the demand is perfectly inelastic then
when the price rises
the quantity demanded will not change
Thus
The more the price rises
the bigger is the total revenue
The second extreme case is if the demand is perfectly elastic
when the demand is perfectly elastic
that means firms can sell as much
as they produce at the market price
p one
So the more the firm produces
the more is the total revenue earned
Because when total quantity increases
price is fixed at the price of p one
The third extreme case is if we have a unit elastic demand
unit elastic demand means price and quantity change
in exactly the same proportion
In this case
any rise in price will be exactly offset by a fall in quantity
leaving total revenue unchanged