A paper in the Proceedings of the National Academy of Sciences reports on an experiment to test how pay-what-you-like pricing performs when compared with merchant-driven "discount" pricing, and suggests that people pay more when given the choice. Ironically, the paper isn't priced on a pay-what-you like basis (it's $10 for two days' access).
We investigate the role of identity and self-image consideration under “pay-what-you-want” pricing. Results from three field experiments show that often, when granted the opportunity to name the price of a product, fewer consumers choose to buy it than when the price is fixed and low. We show that this opt-out behavior is driven largely by individuals’ identity and self-image concerns; individuals feel bad when they pay less than the “appropriate” price, causing them to pass on the opportunity to purchase the product altogether.
Here's a summary from Science magazine:
...scientists tested pay-what-you-want (PWYW) pricing in three experiments. In the first, some boat tour riders were given the option to pay $15 for a photo of themselves, while others were asked for $5, and still others were asked for PWYW. More people bought photos under the $5 plan, about 64%, than when they could name their own price, about 55%. (Only 23% opted for the $15 photos.) Scientists think that when people have to decide on a fair price, fear of looking cheap keeps some from purchasing altogether, they report online today in the Proceedings of the National Academy of Sciences. In a second trial, researchers found that attendees at an amusement park paid five times more for a photo of themselves on a ride (such as the one above) under PWYW pricing if told that half the proceeds would go to charity. And in the third experiment, guests at a restaurant with PWYW pricing either paid someone directly for their meal or paid anonymously by slipping money into a box near the door on their way out. Customers paid about 13% more when they were anonymous than when they paid someone directly. In all cases, the team says, PWYW seems to work because we want to feel good about ourselves when doing it.