# Market Equilibrium

The equilibrium level in a market is where the quantity supplied equals the quantity demanded. At this point, the supply and demand curves intersect, and the market forces of supply and demand are in balance. Consequently, no participant in the market wants to change their behavior.

## Market Equilibrium Graph

In the graph, point A is the equilibrium point, 50 is the equilibrium price, which balances the quantity demanded and supplied. Note that no other price does this, as the curves do not intersect at any other point. 300 is the equilibrium quantity, meaning the amount supplied and demanded simultaneously at the equilibrium price.

The equilibrium price is also known as the market-clearing price because, at this price, buyers purchase everything they want, and sellers sell everything they want to sell. This quantity is exactly the same in both cases. If the price is different from the equilibrium price, either buyers cannot buy as much as they want, or sellers cannot sell as much as they want. The equilibrium point is determined by supply and demand.

## Finding the Equilibrium Mathematically

In the following example, the equilibrium condition is used, meaning that both the price and the quantities supplied and demanded must be equal, to find the equilibrium point using the supply and demand functions.

To find the equilibrium between supply and demand, we need to equate the supply and demand functions and solve for the quantity \( Q \) and the price \( P \).

The functions are:

\[ \text{Supply: } P = 0.1Q + 20 \]

\[ \text{Demand: } P = 80 - 0.1Q \]

We equate the two equations to find the equilibrium:

\[ 0.1Q + 20 = 80 - 0.1Q \]

We add \( 0.1Q \) to both sides of the equation to combine like terms:

\[ 0.1Q + 0.1Q + 20 = 80 \]

\[ 0.2Q + 20 = 80 \]

We subtract 20 from both sides of the equation:

\[ 0.2Q + 20 - 20 = 80 - 20 \]

\[ 0.2Q = 60 \]

We divide both sides of the equation by 0.2 to solve for \( Q \):

\[ Q = \frac{60}{0.2} \]

\[ Q = 300 \]

Now we substitute \( Q = 300 \) into one of the original equations to find \( P \). We will use the supply function:

\[ P = 0.1(300) + 20 \]

\ [ P = 30 + 20 \]

\[ P = 50 \]

Therefore, the equilibrium point is:

\[ Q = 300, \; P = 50 \]

Note that it is also possible to use the equilibrium quantity of 300 in the demand function to find the equilibrium price, which is 50 whether using the supply function or the demand function.