I would like to model the following situation in the simplest possible way. First, a government imposes a proportional tax on the whole population, say, x% of income for each household. But then, it decides to return the collected amount of taxes back by subsidizing each household with a lump-sum amount of money, say, X USD.
Intuitively, there should be some efficiency loss due to redistribution for any type of subsidy other than a proportional one (because of incentives distortion). But it also seems to me that it should be possible to prove it with some simple model that illustrates that individual supply curves change in a way that the market supply curve never gets back to it's previous level, thus, causing DWL.
So far I couldn't come up with a way on how to plot this, so I would be happy to hear some ideas on that, as well as any alternative ideas that could illustrate such inefficiency.