The city board of education shall have the full and exclusive rights within the revenue appropriated for such purposes, or accruing to the use of the public schools, to purchase real estate, furniture, appropriated libraries, fuel and supplies for the use of the schools, and to sell the same, and to make expenditures for the maintenance and repairs of the school grounds, buildings and other property, to establish and build new schools, to superintend the erection thereof, to purchase sites therefor, to make additions, alterations and repairs to the building and other property erected for school uses, and to make necessary and proper notes, contracts and agreements in relation to such matters. All such contracts shall inure to the benefit of the public schools, and any action brought upon them and for the recovery and protection of money and property belonging to and used by the public schools, or for damages, shall be brought by and in the name of the city.