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.
1 dollar 600 units
4 dollars 4200 units
6 dollars 6600 units
9 dollars 10200 units
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 =
Pick (9, 400) to find k although you can pick something else such as (1, 3600)
Since 400 =
, k = 3600
In terms of demand (d) and price (p), we get:
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
s = 1200p + -600
The equilibrium point is the price at which the supply is equal to the demand
Multiply both sides by p
= p × (1200p + -600)
3600 = 1200p2
Divide both sides by 600
6 = 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.
Sep 11, 17 05:06 PM
Easy to follow solution to 100 hard word problems in algebra
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