The board of supervisors of any county in which a county free library has been established may enter into contracts with any city maintaining a free public library, and any such city, through its board of trustees or other legislative body, may enter into contracts with the county to secure to the residents of the city the same privileges of the county free library as are granted to, or enjoyed by, the residents of the county outside of the city, or such privileges as are agreed upon in the contract, upon such consideration named in the contract as is agreed upon, to be paid into the county free library fund. Thereupon the residents of the city shall have the same privileges with regard to the county free library as the residents of the county outside of the city, or such privileges as are agreed upon by the contract.