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:
where represents the quantity demand and is the equilibrium price and:
where 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, . Therefore, we set the equations for the supply and demand curve equal to each other, such that:
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
Point elasticity of demand
Calculating the point elasticity of demand. To do this we use the following formula
The first part is just the slope of the demand function which means
And then we use the equilibrium value of quantity and demand for our values of and . Thus our point estimate is as follows:
The point elasticity of demand at the equilibrium quantity of 50 units and equilibrium price of $50 is -1 which is the unit elasticity.