Using Linear
Equations
to find
Supply,
Demand, and
Equilibrium
This…
That’s right!
Did you know that
you don’t need a
table of values to
create a curve?
Quantity Supplied
20
30
Table of
Values
… can be represented by
this…
Equation
Qs = 10 + 2P
Supply Curve
Supply Curve
35
35
30
30
25
20
Supply
15
10
Price
25
Price
Price
5
10
20
Supply
15
10
5
5
0
0
0
5
10
15
20
25
30
35
Quantity
Quantity Supplied
5
10
0
5
10
15
20
25
30
35
Quantity
Price
5
10
Quantity Supplied = Price
Qs = P
1
Supply Curve
Supply Curve
35
35
30
30
25
20
Supply
15
Price
Price
25
20
10
10
5
5
0
Supply
15
0
0
5
10
15
20
25
30
35
0
5
10
Quantity
Quantity Supplied
10
20
Price
5
10
20
25
30
35
Quantity Supplied = 2 x Price
Qs = 2P
Supply Curve
Supply Curve
35
35
30
30
25
20
Supply
15
Price
25
Price
15
Quantity
20
10
10
5
5
0
Supply
15
0
0
5
10
15
20
25
30
35
0
Quantity
Quantity Supplied
20
30
10
15
20
25
30
35
Quantity
Price
5
10
The fact is, if we are given an
equation of a line…
Qs = 10 + 2P
we can form a table of values.
Quantity Supplied
20
30
5
Price
5
10
Quantity Supplied = 10 + 2 x Price
Qs = 10 + 2P
Or, if we are given a table of
values…
Quantity Supplied
20
30
Price
5
10
we can form our equation!
Qs = 10 + 2P
2
We’ll focus on using an equation to
form our table of values.
Qs = 10 + 2P
Qs = 10 + 2P
First, we’ll simply choose (at random)
any two values for our price. (Let’s use
simple numbers!)
Quantity Supplied
Then, we’ll solve for Qs by substituting our
chosen values for P!
Price
Quantity Supplied
Price
5
10
Watch this! We’ll substitute our first
price into the equation…
5
10
One more time! Now we’ll substitute our
second price into the equation…
Qs = 10 + 2P(5)
Qs = 10 + 2P(10)
= 10 + 20
= 10 + 10
= 30
= 20
And there you have it!
And that’s it!
Quantity Supplied
Price
Quantity Supplied
Price
20
5
10
20
30
5
10
Demand Curve
35
30
25
Price
Now let’s examine
some examples with
demand curves!
20
15
10
5
0
0
5
10
15
20
25
30
35
Quantity
Quantity Demanded
10
5
Price
5
10
3
Demand Curve
35
30
30
25
25
20
20
Price
Price
Demand Curve
35
15
15
10
10
5
5
0
0
0
5
10
15
20
25
30
0
35
5
10
15
20
25
30
35
Quantity
Quantity
Quantity Demanded = 15 - Price
Qd = 15 - P
Quantity Demanded
20
10
Price
5
10
Let’s use an equation to form a table of
values.
Demand Curve
35
30
Price
25
Qd = 50 - 3P
20
15
10
First, we choose two values for our
price. (Remember, use easy numbers to
work with!)
5
0
0
5
10
15
20
25
30
35
Quantity
Quantity Demanded
Quantity Demanded = 30 – 2 x Price
Price
5
10
Qd = 30 - 2P
We substitute our first price into the
equation…
Qd = 50 - 3P
Qd = 50 - 3P(5)
= 50 - 15
Then, we’ll solve for Qd by substituting
our chosen values for P!
= 35
And that’s it!
Quantity Demanded
Price
Quantity Demanded
Price
5
10
35
5
10
4
One more time! Now we’ll substitute our
second price into the equation…
The curve created by this equation
would look like this…
Demand Curve
35
Qd = 50 - 3P(10)
30
25
Price
= 50 - 30
20
15
10
= 20
5
0
0
5
10
15
20
25
30
35
Quantity
And there you have it!
Quantity Demanded
Price
Quantity Demanded
Price
35
20
5
10
35
20
5
10
Now let’s examine how we
can use these equations
to find equilibrium price
and quantity!
We know that equilibrium is the point
where Quantity Demanded equals
Quantity Supplied.
So, if we’re given an equation for
Quantity Demanded:
Qd = 50 - 3P
And an equation for Quantity Supplied:
Qs = 10 + 2P
Then we can express equilibrium by the
following equation:
50 – 3P = 10 + 2P
Qd = 50 - 3P
Qs = 10 + 2P
We can now solve for price (P):
50 – 3P =
– 3P =
-3P - 2P =
- 5P =
P =
P =
10 + 2P
10 + 2P - 50
10 - 50
- 40
- 40 / -5
8
5
Once we know what the price is at
equilibrium, we can then find the
equilibrium quantities by substituting
“8” for “P” in our equation:
50 – 3P =
50 – 3(8) =
50 – 24 =
26 =
Equilibrium
Quantity
Demanded
10 + 2P
10 + 2(8)
10 + 16
26
Equilibrium
Quantity
Supplied
6