When there is increase in demand in a situation where supply is constant the equilibrium price as well as equilibrium quantity will increase at the dame rate.
In the diagram, demand and supply of good are equal at point E. So E is equilibrium point. At this point OP is equilibrium price and OQ is equilibrium quantity. When demand increases, demand curve shifts to right i.e. D 1 D 1 , then at OP price there is EF excess demand. This results competition among buyers which will raise the price. At a higher price, quantity demanded will fall and quantity supplied will increase, resulting in upward movement along new demand curve and given supply curve. This reduces the gap between quantity demanded and quantity supplied. These changes will continue till we reach the new equilibrium point E1 where quantity demanded is equal to quantity supplied. Now OP1 is new equilibrium price. Since new equilibrium price [OP1] is higher than the old equilibrium price [OP] which shows that equilibrium price has increased.