https://www.commondreams.org/news/2018/08/24/force-billionaires-welfare-sanders-tax-would-make-corporations-fund-100-public

https://www.washingtonpost.com/business/2018/08/24/thousands-amazon-workers-receive-food-stamps-now-bernie-sanders-wants-amazon-pay-up/?noredirect=on&utm_term=.684bf61efc4f

Sen. Bernie Sanders (I-Vt.) announced on Friday that he will introduce legislation next month that would impose "a 100 percent tax on large employers equal to the amount of federal benefits received by their low-wage workers" in an effort to pressure corporate giants into paying a living wage.

Under the new legislation, "if an Amazon worker receives $300 in food stamps, Amazon would be taxed $300," the Vermont senator's office noted in a press release. The tax would apply to all companies with 500 or more employees.

R1

Assumptions

1. Welfare is structured to give progressive payouts based on wage. Welfare payouts are highest for low wage earners and vice versa.

2. Labor can be divided into skill levels, and low skill labor presently pays lower wages than high skill labor.

3. We have a representative firm with Cobb-Douglas production; really what's important is diminishing returns to inputs and substitutability between them I could do all of this just assuming any demand function where the demand for labor slopes downwards.

Model

Suppose we have a representative firm operating with the production structure:

Y = K^α L1^β1 L2^β2 ... Ln^βn

where Y is output, K is capital, Li is labor, and (α, β1, ..., βn) are > 0. Labor is divided into discrete skill bins i = 1,...,n where Ln is the highest skill labor.

Solving for a budget constraint of B, we have Li^* = B*βi / w_i where w_i is the wage for labor of skill i.

Let f(i) be the wage subsidy given to labor of skill i where f(i) > 0 and f'(i) < 0. By assumption 2, this is equivalent to saying welfare declines with wage which is supported by assumption 1. We define f(i) in such a way that the welfare payout is w_i*f(i). So, for example, if skill j workers make a wage of $400/wk and receive $100/wk in welfare, we have f(j) = 0.25.

Adding the Sanders Tax

The tax means that firms must pay wages plus welfare; this means wages go from w_i to w_i * (1 f(i)).

The new optimal labor demand is equal to Li^** = B*βi / (w_i * (1 f(i)) )

Note that present demand relative to previous demand is Li^** /Li^* = (w_i)/(w_i*(1 f(i))) = 1 / (1 f(i))

This is a value that increases with i since f'(i) < 0. For workers who receive no welfare, their labor demand will not change. And, for instance, if f(j) = 1, demand for j skill workers will fall by 50%. Workers who receive a lot of welfare will experience a larger relative (%) shock in labor demand.

Therefore, labor demand experiences negative shocks that are, relatively, the largest for low-skill workers. In practice, this means that we expect, at least in partial equilibrium (holding supply constant), that the tax will reduce the wages and employment of low-skill workers. Firms will instead substitute their production needs with capital or higher skill labor which doesn't collect welfare.

In short, this policy is increasingly worse for workers who receive more welfare.

Won't the firm raise wages so it can pay less taxes? (Assumption 1)

For firms to actually save money by raising wages, we would need marginal effective tax rates above 100%. For instance, suppose someone who costs $400 wage $100 welfare could be upped to $450 wage $25 welfare. In this case, a firm would save money by paying more in wages. However, on the worker's end, this would mean that getting a $50 weekly wage raise would reduce their after-tax income by $25. Obviously there are broken welfare schemes in real life that may cause this, and assumption 1 might not hold. However, I doubt most welfare recipients face >100% MTRs.

What about cases of low skill labor being paid high wages and vice versa? (Assumption 2)

This doesn't change the point of the R1 - people who get more welfare will be hurt more by this tax. Setting up the CES by skill is useful as a simple classifier of different types of workers, but this could have also been done by splitting up labor by profession.

What if firms use a different production function? (Assumption 3)

As long as labor demand is downward sloping, taxing labor will shift demand down. I used CD, because Y = CD(Capital, Low Skill Labor, High Skill Labor) is commonly used and the math is simple.

edit:

Cobb-Douglas reeeeeeeee

None of this analysis really needs Cobb-Douglas, I already mentioned this.

Assume labor demand slopes downward. Taxing labor demand will reduce the demand for labor. Doing it more for workers who receive more welfare will cause a greater drop in labor demand for those workers. Hence, this tax hurts the poor the most, since their labor costs go up by the most.