# Calculating equilibrium price and the point elasticity of demand

Consider an economy with the following demand equation:

$Q_D = 100 - P$

and supply equation:

$Q_S = P$

1. The first thing you need to do is calculate the equilibrium price and quantity. To solve for equilibrium price and quantity you need to see $Q_D = Q_S$ such that:

$100 - P = P$

$100 = 2P$

$P = 50$

Now to solve for equilibrium quantity you just substitute the price back into either equation, since in equilibrium supply equals demand. This implies that $Q = 50.$

2)  Calculate 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:

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