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