Earlier quoted context omitted.
I don't think this is such a terrible thing, although clearly this adversarial approach to testing ideas isn't for you, or everyone. Enrico Fermi used to challenge grad students with similar questions, the famous example being 'how many piano tuners in Chicago?'. I don't think it's a stupid or impossible question, but one that seeks to establish how you go about estimating tricky things and thus identifying fruitful…
Maybe it's the traditionally educated engineering in me (I was trained as a mechanical engineer), but I don't see a point in this purely theoretical hand-wavy math. There are established ways for us to get good estimates of a great deal of information - including your hairdresser problem - that involve seeking out real data. Sitting in a void of zero knowledge and postulating wildly, even if it gets you in the ballpa…
Ah, but the most lucrative questions are about products not yet invented, for which there are few facts. They are lucrative because there is not yet any competition. If there were lots of facts available, ripe for the picking, then by definition the net margins would be terrible.
For instance, suppose you were a grad student at the MIT Media Lab in 1995. Does it make financial sense to join the work on an electronic ink product? The answer to that question could only have been derived from a series of guesses and wild deductions. You cannot just look up how efficient planar electroluminescent backlights are going to be in 10 years. Or how expensive and power-hungry non-volatile memory devices are going to be in 10 years.
For a research organization to invent and capture a new market, they have to be good at making and using wild guesses about the future. (Looking up answers is valuable too, but for different reasons.)