What is the impact of a price ceiling on a market equilibrium?

Define a price ceiling as a maximum price that a seller is allowed to charge for a good or service. Examples include rent controls and medication.Assume that we are currently at an equilibrium where p=p* and q=q*. If p^m (the maximum price) is above p* there is no equilibrium changes. However if p^m<p* then there is excess demand. Supply contracts to a new equilibrium where q^d>q*>q^s. This is elementary to show on a simple supply/demand diagram. The original equilibrium is where the supply and demand curves cross. The price ceiling can be visualised by a horizontal line beneath the original price equilibrium. q^d and q^s can be visualised by intersection with the price ceiling and the demand and supply curve, respectively. The excess demand is the difference between q^d and q^s.The greater PES and PED the greater the excess demand.