A local exposition district under subch. II of ch. 229 may impose a tax at the rate of 3 percent of the sales price on the rental, but not for rerental and not for rental as a service or repair replacement vehicle, within the district’s jurisdiction under s. 229.43, of Type 1 automobiles, as defined in s. 340.01 (4) (a), by establishments primarily engaged in short-term rental of passenger cars without drivers, for a period of 30 days or less, unless the sale is exempt from the sales tax under s. 77.54 (1), (4), (7) (a), (7m), (9) or (9a). If the state makes a payment under s. 229.50 (7) to a district’s special debt service reserve fund, a majority of the district’s authorized board of directors may vote to increase the tax rate under this subchapter to 4 percent. A resolution to adopt the taxes imposed under this section, or an increase in the tax rate, shall be effective on the first January 1, April 1, July 1, or October 1 following the adoption of the resolution or tax increase.