It shall be the duty of the municipal building commission to prepare a detailed statement of the estimated expenditures of such commission for the then ensuing year and transmit the same each year to the Board of County Commissioners of Hennepin County on the date specified by the board. The estimate shall specify what portion of the total expenditures of the commission shall be borne by the county and city, respectively, and it shall be the duty of the county commissioners to levy a tax at its proper meeting sufficient to meet the county share of the final statement of estimated expenditures. A like estimate shall be transmitted each year to the city council of the city of Minneapolis on the date specified by the council, and it shall be the duty of the city council to levy a tax at its proper meeting sufficient to meet the city’s portion of the final statement of estimated expenditures. If the dates specified by the city and county are different, the commission shall transmit its budget estimate to both the city and the county on the earlier of the two dates. The commission shall submit a final statement of estimated expenditures ten days before the date Hennepin County and the city of Minneapolis are required to certify their tax levies.