The tax levied in this article shall be effective upon each and every purchase in the city of such utilities service. In all cases where the seller shall collect the price thereof for monthly periods, the monthly periods shall be computed on the basis of the calendar month. However, any seller may elect to compute the tax on the basis of a monthly period other than a calendar month, if such seller shall file with the city treasurer a written designation of the monthly period to be used by the seller. Upon such designation the seller may use the monthly period so designated as the basis for the computation of monthly charges. The period may be changed by such seller from time to time by fixing a different monthly period. If by such change the period shall be lengthened or extended, the maximum tax for any period of less than or more than one month resulting from the change of period shall be computed by increasing or reducing the maximum proportionately to the excess or fraction of a month resulting from such change.