If the work of the improvement, or any part thereof, is executed by the city, then the amount appropriated and used from the special fund to pay the costs and expenses of the work or part thereof executed by the city shall not exceed the amount of the respective lowest valid bid received for such work or for such part thereof, or, if no bids have been received and the work of the improvement is executed by the city the amount appropriated and used from the special fund to pay the costs and expenses of such work shall not exceed the amount of the respective estimate thereof provided for in Section 18041 of the Streets and Highways Code. If such costs and expenses exceed the amount of the said bid, or of the said estimate in case no bids are received, then such excess cost and expense shall be paid out of any moneys in the general fund in the city treasury.