Are welfare payments a subsidy to employers?

Over at the Forbes website Tim Worstall writes an interesting article making the basic point that Welfare Payments Really Are Not Subsidies To The Profits Of Walmart And McDonald's

A week back we had the shocking news that of the various welfare payments made in the US some $153 billion of them went to families in which there was at least one person working. This is true by the way, those do look to be about the right numbers. However, this was immediately leapt upon as evidence that this means that the welfare system subsidises the profits of those companies that employ low wage workers. Make the capitalist plutocrats pay up fair wages and that bill will fall, meaning that we’re no longer subsidising said capitalist plutocrats. And that’s the part of the argument that fails. As I’ve said several times around here. Such welfare payments are indeed subsidies but they’re subsidies to the low wage workers, not to their employers. Not that many people believed me but there you have it. And interestingly enough I gain support from Arindrajit Dube on this very point. The EITC is in fact a subsidy to employers but as that’s what it is designed to be that’s fine. Other welfare payments like food stamps and so on are not subsidies to employers: far from it they actually raise the wages that employers must offer.

Another way, I think, to see Tim's point would be to think in terms of bargaining theory. In particular the Nash bargaining solution. In a Nash bargaining problem we have a set of possible outcomes that the players of the game can agree on, we have the preferences of the players over these outcomes and, importantly, we have what is sometimes called the disagreement point. The disagreement point is the outcome is what will happen if the parties can not reach an agreement.

To apply this to the welfare as a subsidy argument note that what what welfare payments do increase the disagreement point for (would be) workers. Assuming that without welfare the disagreement for workers is to get nothing then having welfare increases the disagreement point to whatever the welfare payment is. This can increases the bargaining power of the worker thereby forcing the employer to increase his wage offer. In effect the employer has to make an offer over and above the disagreement point for the worker to get the worker to agree to the outcome and thus the higher this point, the higher the offer from the employer must be.

See, you can make the simple complicated if you put in just a little effort.

If you want the really complicated stuff try William Thomson, "Monotonicity of Bargaining Solutions with Respect to the Disagreement Point", Journal of Economic Theory, 42: 50-58, 1987.