Solving for equilibrium price and quantity mathematically - YouTube

[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