(1) The city engineer in a city of the second class or village engineer shall, when requested by the mayor, city council, or village board of trustees, make estimates of the cost of labor and material which may be done or furnished by contract with the city or village and make all surveys, estimates, and calculations necessary to be made for the establishment of grades, the building of culverts, sewers, electric light systems, waterworks, power plants, public heating systems, bridges, curbing, and gutters, the improvement of streets, and the erection and repair of buildings and shall perform such other duties as the city council or village board of trustees may require. When a city of the second class has appointed a board of public works, and the mayor and city council have by ordinance so authorized, the board of public works may utilize its own engineering staff and may hire consulting engineers for the design and installation of extensions and improvements of the works under the jurisdiction of the board of public works. Whenever the mayor and city council have authorized the same, the board of public works may purchase material and employ labor for the enlargement or improvement of the systems and works under the jurisdiction of the board of public works.