Public improvements may be made by the city government itself or by contract. The council shall award all contracts for such improvements; provided that the council may authorize the city manager to award such contracts not exceeding an amount to be determined by the council and subject to such regulations as the council may prescribe. Every contract for public improvements of more than $1,000 shall be awarded to the lowest and the best responsible bidder after such notice and opportunity for competitive bidding as the council may prescribe. All bids may be rejected, and further notice and opportunity for competitive bidding may be given.