# Calculate the equilibrium price and quantity from math equations

In this post, I will cover how to find the equilibrium quantity and price when given an equation representing the supply and demand curves. Consider the following equation:

Find the equilibrium quantity and price given the inverse demand equation $P_D = 10 - 3Q$ and and the inverse supply function $P_S = 2P$

Firstly, let's look at what the inverse demand and supply equations are actually representing. These equations simply represent the relationship between price and quantity in 'maths language'. For example, the supply equation $P_S = 2Q$ says that the price of supply will always be twice the size of the quantity of goods being supplied. Suppose that the quantity supplied was 1 unit. In this case, the price of supply would be $P_S = 2*(1) = 2$. If the quantity supplied was 2 units, the price of supply would be $P_S = 2*(2) = 4$.

## Constructing a supply and demand schedule

In an early post, we saw how the supply schedule can be used to draw a supply curve. We can actually use these supply and demand equations to construct a supply and demand schedule presented in the table below.

 Qty supplied Price of supply Qty of demand Price of demand 1 2*(1) = 2 1 10 - 3(1) = 7 2 2*(2) = 4 2 10 - 3(2) = 4 3 2*(3) = 6 3 10 - 3(3) = 1