[all] [right] this video is going to go over how to find equilibrium price and quantity
Mathematically for your introductory microeconomics course so there are four steps
Here that you'll need to go through [and] you should be able [to] solve any of these problems, [so] [the] first step
is to solve
the demand and
supply functions
in terms of quantity
So by this, I [mean] you have q
equals blah blah blah blah blah
Instead of p equals blah blah blah blah blah, and we'll go through an example in a second, the second step
is to set
Quantity of supply equal to quantity demanded or you set the quantities
equal to each other
The third Step here is to solve for [p]
Or equilibrium price
And the last step in this method is to plug in your equilibrium price
To your quantity supplied in your quantity demanded functions
to solve for equilibrium quantity
and
Then by plugging it into both of these and checking you'll make sure that you did your math right and that you didn't mess anything up
so it's a good way to check your answers, too
So let's go through [an] example
Let's imagine that our quantity demanded
is equal to
10,000
minus 80 p
So this is already solved for in terms of Q
It's possible
That this isn't solved for in terms of Q so for that method you would have to do some
Manipulation to get this solved in terms of Q so as an example. Let's take this function and solve for p
To solve this for p. We would have to add
80 p to both sides so we would get 80 p
equal
80 p plus our Qd equals
10,000 and
then subtract Qd from both sides and then
[divide] both sides by this 80 and that would give us p equals
10,000 over 80 minus Qd over 80
So if you were given something that looks like this you would want to solve for this qD
so to do that you would want to get qd by itself so you could add qd over 80 to both sides so
[you'd] get qd over 80 plus p
equals 10,000 over 80
You would then subtract p from both sides to get rid of it here and subtract it over there
And then you would multiply everything by 80 to get Qd equals
10,000 minus
80 P
And so that's how you would get your demand function in terms of Q instead of in terms of p
So this is our demand function
Our supply function in this example is going to be
20 P and
So note [that] these both confirm the law of demand and the law of supply, so this price goes up quantity
Demanded goes down as price goes up quantity supplied goes up
So for a typical graph we would get downward sloping demand
and
upward sloping supply
so we've solved for these two guys in terms of q we now have to set these quantities equal to each other and
The reason we do this is because in our typical supply and demand graph
we only have one equilibrium point and
that occurs at equilibrium price and
equilibrium quantity
So we know that we're going to be at the same equilibrium quantity on both the supply curve
represented by [our] supply function and the demand curve
represented by our demand function
So if we set those two guys equal to each other we'll have 10,000
minus 80 p
equals 20 p
so now we can add 80 p
to both sides and we [will] get
10,000
equals 100 p
so we get 10,000 equals 100 p if we divide both sides by a hundred we get a
Hundred equals p. So we now know that our equilibrium price is a hundred
And we know this represents the price where these two guys cross, so if we plug in this p-value now into our supply
function and our demand function
We should get that same quantity back out, so let's test it and see what happens
We know the equilibrium price
equals 100 our supply function
equal 20 times p
So if we plug in our equilibrium price we get 20
times
120 times 100 is 2,000
So our equilibrium quantity
should be 2,000
But let's plug it into our demand function just to make sure so [our] demand function was 10,000
minus 80 p
so if we plug in that hundred
for the p we get 10,000
minus 8,000 we got the 8,000 by multiplying 80 times p and
10,000 minus 8,000 is
Again 2,000 so our quantity demanded equals our quantity supplied. Which is good it means
We did it right and so our equilibrium
Quantity is 2,000 and our equilibrium price is 100
So remember these steps when solving for the equilibrium?
First solve your supply and demand function in terms of quantity so q equals something
Then set your quantity supplied equal to your quantity demanded
Once you've done this solve for p that will be your equilibrium price
Then plug those peas back into your quantity supplied and quantity demand functions to solve for equilibrium
quantity
You can do it for one if you're confident in your math, but I recommend doing it for both
Just to double-Check your methods and make sure you did your Algebra correctly