Hyena comments on A potentially great improvement to minimum wage laws to handle both economic efficiency as well as poverty concerns - Less Wrong
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I think you should replace "earnings" with "hourly wages". It makes more sense, given perfect information, to have a system which tops up hourly earnings rather than earnings generally because this incentivizes work rather than earnings.
We don't, for example, want to issue subsidies to people who work part time at high-payed work just because they'll be topped up by the scheme.
This seems to be a good idea. But the only problem with it is that the labor market is not as liquid as a financial market. It is in principle quite possible for a person in a free market to be commanding 1.5 * minimum_wage in a part time job or for part of the year, but unable to find work for the rest of the year or rest of the free time, which would push his annual salary below minimum wage. Theoretically there should be absolutely zero unemployment with no minimum wage laws. However in practice it would still be a couple of percent due to liquidity holes in the market, with people in between jobs, in the process of talking with multiple employers etc. In my method, there is still incentive for people earning above min wage to work as hard as possible, since the state subsidy is only (x-y)/2 and not (x-y). I agree with your point though, that the incentives would be stronger in the event of replacing earnings with "hourly wages", if only you could handle the issue of genuine unemployment due to liquidity holes that prevent the person from making min wage averaged across the year.
I don't think we need to handle liquidity problems, though, except through unemployment insurance. Designing its incentives would overcome most of its ill-effects (for example, creating a cash bonus for getting a job that diminishes the longer you on it, a la a shared savings model).
I actually live on UI, I know way too much about what unemployment looks like from the inside at this point.