Why not just go into our vast database of previous purchases and see what happened previously when toothpaste cost twice as much? The reason is that on the previous occasions, the price may have been higher for different reasons. For example, the product may have been in short supply, and every other store also had to raise its price. But now you are considering a deliberate intervention that will set a new price regardless of market conditions.
Given enough time, chances are that someone else will have tried doubling the price. You can just observe. (this assumes perfect information, or that hidden variables to not effect what you are about)
What interventions give us is data efficiency. Where observation required LOTS of data, intervention needs (possibly) a single action.
Want to formulate this! Under various types of model/noise what is the data efficiency of interventions versus observation!?
