The contract shall provide:
(1) for the proposed expenditure for the construction, purchase, or lease of the city-county building and the proposed cost of equipping and operating the building;
(2) for the management of the building by a method which will provide that the city and county shall each be represented and have an active part in the management of the building;
(3) that the management of the joint institution shall have such powers as will be necessary to accomplish the purposes of this part.