How to price museum visits

So you come across a museum and wonder whether it is worth visiting. The entrance price is rather steep, and given the uncertainty of your future enjoyment, you decide to pass on the opportunity and walk on. Could the museum have found a way to still attract you? One way would be to give you free entry, but this would oviously lead to loss of revenue and overuse of the museum.

Bruno Frey and Lasse Steiner claim it can attract casual visitors by asking for an entrance fee that depends on the time spent in the museum. This would allow for a cheap "sneak peek," and true lovers would pay much closer to their marginal utility. This is more efficient than exit donations, as those are voluntary and thus lead to loss of revenue and overuse of the museum. Keeping in mind that a museum's mission is often to spread knowledge and enjoyment, this scheme is much more likely to attract visitors with lower marginal utility and possibly expose them to arts or sciences they may learn to appreciate. Instead, museums typically emphasize club memberships, who cater to visitors who would have come anyway and offer them deep discounts that bring revenue loss.