Except in Hennepin County, the board of county commissioners of each county may, by resolution, set a reasonable allowance for expenses or a per diem allowance in lieu of expenses and a mileage allowance to be paid the members of boards or agencies authorized by statute, and members of advisory boards or committees, performing duties for all or part of the county, when the board or agency does not itself have power to make expense allowances for its members. The allowances shall be paid from the funds under the administration of the boards or agencies. Members of the board of county commissioners shall not receive any per diem pursuant to this subdivision.
No member of a board, agency, advisory board, or committee shall receive an allowance for expenses, or a per diem allowance in lieu of expenses, or a mileage allowance pursuant to subdivision 1, if in another capacity the member receives from the county under authority of any other statute or resolution either:
(a) an allowance for or per diem allowance in lieu of the same expenses or mileage; or
(b) a fixed amount, whether as part of a salary or otherwise, for expenses of like kind incurred in the performance of duties in the other capacity.