(a) General rule.--The original cost of the site and buildings of the joint detention facilities and the equipment thereof, all additions thereto and all fixed overhead charges in conducting the joint detention facilities shall be paid by the counties constituting the districts in the ratio of their population according to the last preceding United States census.
(b) Inmate expense.--
(1) The cost of the care and maintenance of the inmates in the districts shall be certified monthly to the counties from which inmates have been committed. The cost shall be paid by the counties in proportion to the number of inmates committed from each county.
(2) All payments shall be on warrants of the county commissioners, countersigned by the county controller in counties where that office exists.