The goal is to find supply and demand equations using some given information and then use the equations to find equilibrium point.

After doing some market research, a manufacturer notices the following pattern for selling an item. The graph for the following situation is shown below.

**Information about the supply based on the price**

**Price ****Supply**

1 dollar 600 units

4 dollars 4200 units

6 dollars 6600 units

9 dollars 10200 units

Information about the demand based on the price

**Price ** **Demand**

1 dollar 3600 units

4 dollars 900 units

6 dollars 600 units

9 dollars 400 units

Notice that for the supply, as the price goes up, the number of items goes up too. This is so because it will cost the manufacturer more money to produce more items.

However, for the demand, as the price goes up, the number of items goes down. People have a tendency to buy less when the price goes up.

Usually, the demand equation is modeled with an inverse variation.

The inverse variation equation is y =

k
x

Pick (9, 400) to find k although you can pick something else such as (1, 3600)

400 =

k
9

Since 400 =

3600
9

, k = 3600
y =

3600
x

In terms of demand (d) and price (p), we get:

d =

3600
p

**How to find the supply equation**

The linear equation is y = mx + b

Use (4, 4200) and (9, 10200) to find m

m =

10200 - 4200
9 - 4

m =

6000
5

= 1200
y = 1200x + b

Use (4, 4200) to find b

4200 = 1200 × 4 + b

4200 = 4800 + b

4200 - 4800 = b

-600 = b

y = 1200x + -600

In terms of p and supply ( s ), we get

**Supply equation:**

s = 1200p + -600

**How to find the equilibrium point**

The equilibrium point is the price at which the supply is equal to the demand

3600
p

= 1200p + -600
Multiply both sides by p

p ×

3600
p

= p × (1200p + -600)
3600 = 1200p

Divide both sides by 600

6 = 2p

2p

(p - 2) × (2p + 3) = 0

p = 2 and p = -3/2

p = 2 since the price must be positive

The equilibrium point is 2 dollars.