I don't understand how the thought experiment ends with The government covering all cost and Walmart paying little to nothing for employment. There is defined limit on cost of living and I would't see it change if a company payed a wage that provides above that line. Would you mind explaining more?
Sure. This is the hypothesis we want to test: When government provides benefits to workers, employers actually collect the value by paying lower salaries. So let's start by imagining a case where there are no government benefits. The employee works at Walmart for a salary of, say, $2000 per month. Now we introduce a government benefit worth $500 per month (to keep it simple, let's say it is a cash benefit). The employee now enjoys $2500 worth of income and life is better. But according to our hypothesis, Walmart takes advantage of the situation by lowering the monthly salary to $1500. Now it appears that the worker's situation is not changed from the start. While doing the same work the worker receives the same $2000 in income. Walmart has absorbed the benefit, and now pays only $1500 for work that is worth at least $2000. The worker has the same job and the same lifestyle. Then an additional $500 government benefit is introduced. Again, Walmart takes advantage by lowering the salary to $1000. The worker is indifferent about where the money comes from, and continues doing the same work and living with the same lifestyle. Two more government benefits and the worker's entire income comes from the government and Walmart has reduced the salary to zero, absorbing the entire value of the benefits. Obviously at this point it no longer makes sense for the employee to continue working. I conclude that, contrary to our hypothesis, the employer cannot take the entire value of a government benefit out of a worker's salary. It's not a very realistic scenario, but it does suggest that something will happen if the employer tries to lower salaries when an employee receives outside income. What I think will happen is that Target will see that Walmart is getting a great deal, paying $1500 for $2000 worth of work, and will offer the worker $1600 to do a similar job. Assuming there is competition in the market, the worker should be able to bid their salary up to something close to what it is worth. That is how the worker got a job paying $2000 to start with, and the employer's accounting does not change when the worker receives outside income.
This discussion got to be pretty extended, but the big idea I got was that when government (or a wealthy uncle) covers some of your living costs, you have less incentive to work for income. Employers have to make you a better offer before you will find it acceptable. The amount an employer is willing to pay for a worker is entirely based on how much value the worker can provide to the employer. The employer doesn't care how much wealth the worker and others in their household have.