Said cities may, with or without petition of abutting property owners in the manner provided by law for the paving and improvement of their streets and highways, provide for the payment of their share of the cost of any original paving, construction or improvement of any portion thereof, and the entire cost or any portion thereof of any additional width not thus paid for by the Commonwealth by an equal assessment on the foot front rule, including the expenses of the necessary drainage, against the owners of property abutting on the line of the improvement, or the city may pay the entire cost of any such improvement, construction or reconstruction not thus paid by the Commonwealth.