## Calculating equilibrium price and the point elasticity of demand

The equilibrium price and quantity is the point where the supply and the demand curves intersect.

Consider the economy with the following supply and demand equations:

$Q_D = 100 - P$

where $Q_D$ represents the quantity demand and $P$ is the equilibrium price and:

$Q_S = P$

where $Q_S$ is the quantity supplied. These two equations are illustrated in the diagram below.

The equilibrium price is determined by finding the point where both supply and demand are the same value, i.e, $Q_D = Q_S$. Therefore, we set the equations for the supply and demand curve equal to each other, such that:

$100 - P = P$

$100 = 2P$

$P = 50$

We can solve for the equilibrium quantity produced by substituting the price back into either the supply or demand equation, as supply equals demand in equilibrium. This implies that

$Q = 50$

## Point elasticity of demand

Calculating the point elasticity of demand. To do this we use the following formula

$E_D = -1*\frac{\Delta Q * P}{\Delta P * Q}$

The first part $E_D = \frac{\Delta Q }{\Delta P }$ is just the slope of the demand function which means

$E_D = \frac{\Delta Q }{\Delta P } = 1$

And then we use the equilibrium value of quantity and demand for our values of $P$ and $Q$. Thus our point estimate is as follows:

$E_D = -1*\frac{50}{50} = -1$

The point elasticity of demand at the equilibrium quantity of 50 units and equilibrium price of \$50 is -1 which is the unit elasticity.