They started at the beginning of 2006 with an index of 100. As of May, 1 2016 the index was just a touch over 180. This means that theme park ticket prices overall have increased by 80% in that time span.
I inserted RED bars (month and year on top) that show all of the Disney price increases (they had no price decreases) in this time period.
At the beginning of 2006 a single one day ticket to a Disney park was priced at $63.00 (see link above). Today a single day ("regular" price) is $110.00. That is a 75% increase!
Remember, theme park (Six Flags et al) tickets increased by 80% overall. Disney accounts for a disproportionate amount of that change.
If Disney admission tickets had just kept up with inflation during that time (using the CPI), ticket prices should only be $75.05, a 19.1% increase.
Seems clear that Disney is a "Price Maker" as opposed to a "Price Taker" and they are a "Price Leader" as well. However, the latter is harder to discern without doing the math.
When Disney raised prices did other theme parks follow suit at the same time? If you look at the times in-between Disney price increases (gotta look really close) there seems to be a bump up in the line indicating a lag (sometimes short, sometimes longer) when other theme parks followed with price increases.
I did find it interesting that Disney elected to increase prices in the dead middle of the Great Recession (noted on graph in gray area).
Pricing power, indeed!