I'd argue it's a great indicator, as expenses are necessarily tied to the wages of the population. An example like yours simply doesn't happen.

This means you have to come up with a representative example of how to calculate expenses, and I haven't seen a better approach for that than median wage, which seems to correlate highly with expenses.

Of course it's possible. The minimum wage doesn't directly affect the median wage (unless more than half the population only gets the minimum wage).

If you think it's impossible, please explain why.