There don't appear to be any direct studies on revenue, but the GrubStreet article mentions a study by Lynn (2018)[0] which looks at the impact of eliminating tipping on online reviews, which have an impact on revenue (but of course it's difficult to judge, since perhaps not all declines in Yelp scores are equal; maybe in that study declines/improvements in score had more to do with the quality of the food):

> This study examines the effects of such moves away from tipping on restaurant’s online customer ratings. The results indicate that (i) restaurants receive lower online customer ratings when they eliminate tipping, (ii) online customer ratings decline more when tipping is replaced with service-charges than when it is replaced with service-inclusive-pricing, and (iii) less expensive restaurants experience greater declines in online customer ratings when replacing tipping with either alternative than do more expensive restaurants.

> ...

> Given the already ubiquitous and increasing popularity of online reviews, and the influence that such e-word of mouth has been shown to have on consumers’ purchasing/patronage behaviors (see Kim, Li, and Brymer, 2016; Ong, 2012; Zhang, Ye, Law, and Li, 2010), our results also have important implications for restaurants’ bottom-line that warrant being underscored. For instance, in a longitudinal analysis (2003- 2009) of Yelp online reviews and revenue data for every restaurant in the city of Seattle Luca (2016) recently estimated that restaurateurs can expect a 9% increase in revenue for every one-star Yelp rating improvement. Thus, if the results of our study are shown to be reliable and Luca’s (2016) estimate generalizable then it follows that low and moderately priced restaurants that decide to replace voluntary tipping with either automatic service charges or service inclusive pricing can expect to experience a nontrivial loss in profits as a function of lower online satisfaction ratings.

The paper notes that raising prices whether through services charges or what will be a price increase for a significant percentage of the clientele:

> Additionally, tipping is a form of voluntary pricing and price discrimination that results in approximately 25 percent of customers tipping less than 15 percent of bill size and 65 percent of customers tipping less than 20 percent of bill size (Lynn, 2017a), so replacing tipping with service charges or service inclusive pricing will raise dining costs for a quarter to half of restaurant customers and this is likely to reduce the overall satisfaction of those customers.

One restaurant that had switched to no-tipping before abandoning had tip averages of 21%.[1] I don't know anybody who tips that much, but apparently they exist. But if you increase prices by 21% on all clientele, then the restaurant becomes more pricey compared to restaurants that do tipping. Someone who would have tipped 15% might just go to another restaurant and tip that much, whereas a particularly generous tipper who would have paid 25% to make the average about 20% between these two is now just paying that 21% price hike - that's an overall decline in revenue. And the restaurateur said his mistake was not raising prices high enough to cover both the waitstaff wages that they had been getting from tipping ($25-40/hr) and raises for the back-of-house staff; he says he should have raised them 40%! Perhaps he could have done so, but it seems likely he would have been doing less business and had to downsize.

But OK, let's assume that somehow restaurants earn the same amount of income as before with hiked prices and no tipping, and that extra income is paid to the staff. If any money goes to the back-of-house staff, that means that the waitstaff would be making less than they did before. Do you think it's reasonable for waiters to be making $25-40/h while the kitchen staff is making $13-20?[1] I don't particularly think it is, and if tipping culture eventually ends (which, make no mistake, I am no fan of tipping), we would see waitstaff being paid less because now they can't switch to a restaurant where they can make more than tips, but we might see kitchen staff make more. However, this would necessarily mean that waitstaff are making less money.

[0]: https://static.secure.website/wscfus/5261551/7004898/ijhm-ti...
[1]: https://www.npr.org/sections/thesalt/2016/05/15/478096516/wh...