The manager shall be the chief purchasing agent of the city. All purchases for the city and all contracts shall be made or let by the manager when the amount of the purchase or contract does not exceed $20,000 unless a lower limit is provided by the city council; but all claims resulting therefrom shall be audited and approved by the council as provided in section 412.271. All other purchases shall be made and all other contracts let by the council after the recommendation of the manager has first been obtained. All contracts, bonds, and instruments of every kind to which the city is a party shall be signed by the mayor and the manager on behalf of the city and shall be executed in the name of the city.