Do 9-ending prices really work?

Are people really so stupid that they perceive a price of 99.99 euros as so much cheaper than a price of 100 euros? And do 99-ending prices really lead to more sales and profits? These questions have been studied for many years by researchers in the field of business psychology (or price psychology).

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Studies (only a small selection):

Anderson, E. T., & Simester, D. I. (2003). Effects of $9 price endings on retail sales: Evidence from field experiments. Quantitative marketing and Economics, 1(1), 93-110.

Asamoah, E. S., & Chovancová, M. (2011). The influence of price endings on consumer behaviour: An application of the psychology of perception. Acta Universitatis agriculturae et silviculturae mendelianae Brunensis.

Bizer, G. Y., & Schindler, R. M. (2005). Direct evidence of ending-digit drop-off in price information processing. Psychology & Marketing, 22(10), 771-783.

Bray, J. P., & Harris, C. (2006). The effect of 9-ending prices on retail sales: A quantitative UK based field study. Journal of Marketing Management, 22(5-6), 601-617.

Felser, G. (2015). Advertising and consumer psychology. Springer Verlag.

Felser, G. (2013). Consumer psychology. Kohlhammer Verlag.

Parsa, H. G., & Njite, D. (2009). Psychology of pricing: A review and suggestions. Handbook of Hospitality Marketing Management, 375-402.

Schindler, R. M., & Kibarian, T. M. (1996). Increased consumer sales response though use of 99-ending prices. Journal of Retailing, 72(2), 187-199.

Schindler, R. M., & Kibarian, T. M. (2001). Image communicated by the use of 99 endings in advertised prices. Journal of Advertising, 30(4), 95-99.