The Council shall have power to do any public work or make any public improvement by the employment of the necessary labor and the purchase of the necessary supplies and materials with separate accounting as to each improvement so made, or to do such work by contract duly let after competitive bidding. Where competitive bids are secured, the city, or any city department qualified to do the work, may enter a bid on an equal basis with other bidders. The Council shall also have the power to do any public work or make any public improvement under any legally constituted plan under which the labor is furnished by any other governmental unit, department, or agency of the United States or by the State of Michigan, or which is wholly or in part financed by them or either of them.