Supply and demand
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.
Supply and demand equations
Use the information above to find the supply and demand equations.How to find the demand equation
Usually, the demand equation is modeled with an inverse variation.
Pick (9, 400) to find k although you can pick something else such as (1, 3600)
In terms of demand (d) and price (p), we get:
Demand equation
How to find the supply equation
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
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
Multiply both sides by p
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.