The claim would be that prices rise, offsetting the cost to the consumer who are also workers. It does not do much if that is how it shakes out. The stated hope of those arguing for the raise is that the people at the top of the company make a lot of money and that money would be diverted to the workers. While I am sure that happens sometimes, I am not aware of evidence that this is often the case.

The $10 a burger price increase would be a stupid prediction unless the worker just sells one burger an hour and nothing else. If an employee's share of the selling amounted to, say, 10 burgers an hour on average, then a $1 price increase on burgers would counter the wage raise.