This paper uses observations on visitation rates to estimate Clawson demand functions for a non-priced recreation commodity, namely, the Milford Track located in the Fiordland National Park of New Zealand. Different classes of user with potentially different demand elasticities are identified, and shadow prices consistent with revenue maximization of a discriminating and non-discriminatory monopolist tourist authority are estimated. Alternative maximum revenue and consumers' surplus valuations are presented which correspond to different concepts of measures of willingness to pay for use, including travel costs and the opportunity cost of time.