All contracts made in pursuance hereof shall be for such period of time and upon such terms and conditions as shall be agreed upon. The contract shall fully set forth the amount of money to be contributed by the county and city towards the acquisition of such site and the improvement thereof and the manner in which the property shall be improved and the character of the building or buildings to be erected thereon. It may provide for the amount of money to be contributed annually by the county and city for the upkeep and maintenance of the property and the building or buildings thereon, or it may provide for the relative proportion of such expense, which the county and city shall annually pay. The contract may specify the parts of such building or buildings which shall be set apart for the exclusive use and occupation of the county and city. The money to be contributed by the county or city may be raised by a sale of bonds of such county or city or by general taxation. Any such county or city now possessing funds or having funds available for a county or city hospital from a sale of bonds or otherwise may contract for the expenditure of such funds, as herein provided. Such contract shall be made only after a proper resolution or ordinance of the county legislative authority and ordinance of the city have been passed specifically authorizing it. The contract when made shall be binding upon the county and city during its existence or until it is modified or abrogated by mutual consent evidenced by appropriate legislation. A site with or without buildings may be contributed in lieu of money at a valuation to be agreed upon.