If the improvement is not objected to or is not completed or commenced, as the case may be, within the time prescribed in the notice, or if the improvement specified in the notice consists of the maintenance of a boulevard or some improvement thereon, the city, in the event that the owner does not inform the city auditor in writing, within ten days after the service of the notice, that the improvement will be made, shall make the improvement or shall order the same to be made by such person as the city may have contracted with, under the direction of the street commissioner, at the expense of the lot or parcel of land adjoining the improvement. The expense of the improvement shall include the expense of giving all notices in connection with the work, of making assessments, and of any other nature incurred in doing such work.