# Supply and demand

The goal is to find supply and demand equations using some given informations and then use the equations to find equilibrium point. After doing some market research, a manufacturer notices the following pattern for selling an item.

Supply

Price                                Supply

1 dollar                             600 units
4  dollars                          4200 units
6  dollars                          6600 units
9 dollars                          10200 units

Demand

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.

### Supply and demand equations

Use the information above to find the supply and demand equations.

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

Usually, the supply equation is modeled with a linear 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

s = 1200p + -600

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 = 1200p2 + -600p

Divide both sides by 600

6 = 2p2 + -p

2p2 + -p - 6 = 0

(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.

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