In supply (and demand) problems, [tex]$y$[/tex] is the number of items the supplier will produce (or the public will buy) if the price of the item is [tex]$x$[/tex].
For a particular product, the supply equation is
[tex]$y=2 x+525$[/tex]
and the demand equation is
[tex]$y=-5 x+700$[/tex]
What is the intersection point of these two lines?
What is the selling price when supply and demand are in equilibrium?
price = $ [ ] /item
What is the amount of items in the market when supply and demand are in equilibrium?
number of items = [ ]
Answer (2)
Set the supply and demand equations equal to each other: 2 x + 525 = − 5 x + 700 .
Solve for x (equilibrium price): x = 7 175 = 25 .
Substitute x back into either equation to find y (equilibrium quantity): y = 2 ( 25 ) + 525 = 575 .
The intersection point is ( 25 , 575 ) , so the equilibrium price is $25 and the equilibrium quantity is 575. ( 25 , 575 )
Explanation
Understanding the Problem We are given a supply and demand problem where we need to find the equilibrium point. The supply equation is y = 2 x + 525 and the demand equation is y = − 5 x + 700 . Here, x represents the price of the item and y represents the number of items.
Setting up the Equations To find the equilibrium point, we need to find the intersection of the supply and demand equations. This means we need to solve the system of equations:
y = 2 x + 525
y = − 5 x + 700
We can set the two equations equal to each other:
2 x + 525 = − 5 x + 700
Solving for x (Equilibrium Price) Now, we solve for x :
2 x + 5 x = 700 − 525
7 x = 175
x = 7 175
x = 25
So, the equilibrium price is $25.
Solving for y (Equilibrium Quantity) Now that we have the value of x , we can substitute it back into either the supply or demand equation to find the equilibrium quantity y . Let's use the supply equation:
y = 2 x + 525
y = 2 ( 25 ) + 525
y = 50 + 525
y = 575
So, the equilibrium quantity is 575.
Stating the Answer Therefore, the intersection point (equilibrium point) is ( 25 , 575 ) . The equilibrium price is $25 per item, and the equilibrium quantity is 575 items.
Examples
Understanding supply and demand equilibrium is crucial in economics. For instance, imagine you're selling handmade bracelets. By analyzing the supply equation (how many bracelets you're willing to make at a certain price) and the demand equation (how many bracelets customers want at that price), you can find the price point where supply meets demand. This ensures you're not overproducing or underpricing your bracelets, maximizing your profit and satisfying your customers' needs.
The intersection point of the supply and demand equations is (25, 575). The equilibrium price is $25 per item, and the equilibrium quantity is 575 items in the market.
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