I've heard anecdotally that Disney World raised its ticket prices but then attendance counterintuitively increased.
The most likely reason is the economy improved so more people went; the growth effect exceeded the decrease in demand due to price increase.
However, we can speculate that a different mechanism might be going on. Disney World -- or anywhere -- is populated by two kinds of people: rich people from all over the country and world who can afford the travel and vacation time off from work, and poorer people from the local surrounding area whose travel costs are very low and can make a day trip of it.
Rich people do not like to be around poor people. This may be especially true in the American South, where poor people include the subculture of rednecks and white trash, and rich people feel especially uncomfortable around places with lots of such people. Because of the high numbers of people visiting from the local surrounding areas, Disney World does have a bit of a feel of a white trash playground.
Increasing park entry fee prices would most increase the relative cost of the trip for those coming from the local surrounding area, whose travel costs are low: this will cause less poor people to attend. This would make the park more attractive in the eyes of the rich, causing the counterintuitive increase in demand.
Disney is not a fixed good: one's experience depends on who else attends.
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