Once again, I must point out that it is not supply and demand that increases unemployment in neoclassical, mainstream economics when wages go up. That makes no sense at all in any economics.
Employers hire workers to increase their production of goods or services. If wages go up it makes no sense for employers to lay off workers because not only will the employer see a reduced profit from the increased costs due to the wage increase for the workers that they retain, they will lose the profits and the fixed cost coverage from the lower production due to reduced workforce. They will see lower revenue and lower profits than if they had kept the workers.
You really don't have this right.
Let's assume that ex-ante economy-wide all firms have hired just enough people to maximize profits. In some cases this will involve paying someone, say $5 per hour whose marginal contribution is $5.50.
Now you pass a law raising the minimum wage to $10. At the margin there will be several negative impacts on demand for unskilled labor. First, all the people who have a marginal contribution to profit of less than $10 are immediately kaput unless prices can be raised enough to maintain a positive marginal contribution to profit at the new labor rate. Second, at the margin possible substitutes for unskilled labor become more attractive whether they be automation or hiring skilled people who are now relatively cheaper. Third, businesses that employ large amounts of unskilled labor will raise prices causing demand for their products to fall, causing these industries to hire fewer people.
You declare that what I said is not right and then ignore what I said, not giving me the courtesy of pointing out why. I will provide you with an example of what I mean.
Your explanation has a few problems. They are, in no particular order,
1) You say that owners had maximized profits
ex ante. This is means to me that they have set their prices to make the most profit that they can and maintain a sales volume that utilizes nearly all of their production capacity, giving them them the best chance to cover all of their fixed costs. Then the paternal government decides to destroy the economy by raising the minimum wage. Suddenly in your explanation the owners are no longer able to maximize their profits. They do everything wrong, they lay off workers and they raise their prices. They reduce their ability to produce products and they reduce the demand for the products, reducing their sales volume. Both actions reduce their ability to cover their fixed costs reducing their profits below the maximum that they could be making. Yet you don't explain why they would be so stupid. Why are they able to maximize their profits before the minimum wage increase and unable to do it afterward?
2) Maximizing their profits before the wage increase means that they have some control over price. The theory of marginal productivity, which you go on to offer in your explanation, depends on supply and demand setting price. You can't have it both ways.
3) Marginal productivity is a seriously flawed theory. There is nothing in it which would limit the higher unemployment to just an increase in the minimum wage mandated by the government. According to the theory any wage increase would result in an increase in costs and the necessity of laying off workers. In fact any cost increasedfor raw materials, rent, electricity, etc. would result in less employment. That obviously doesn't happen.
4) This is a thread about higher unemployment resulting from a minimum wage increase. I explained why this doesn't happen, because the maximum profit still would be to sell the same number of products at the same price as before. You presented an explanation that assumes that an increase in the minimum wage will result in higher unemployment and higher prices as givens. And then you leave it to us to imagine the problems that would result from the lower employment and the lower demand.
5) Wow, a third fallacious argument, the dark specter of automation, which naturally you believe haunts the very lowest paid workers in the economy, which in your view would be the first jobs to be automated. Yes, why automate the higher paid jobs when the ROI of automating the lowest paid jobs is available?
Increased wages lower profits. I suspect that this is the reason that so many fallacious arguments exist against raising wages. The profit takers won't more profits without having to work for them. Investing in real production facilities is risky, hard work. It is much easier to have the government suppress wages to increase profits. It is unfortunately bad for the economy, though. We need those people to invest in production facilities in the US.
I don't think that the desire to make a large amount of easy profits by suppressing wages would be very convincing, even on Fox News.
Over the last thirty five years corporate profits have doubled to ≈ 11% of GDP and wages have dropped by the same percentage that profits have decreased. Increased profits result from reduced wages.
That bastion of supply side, neoclassical economics, the Congressional Budget Office, estimates that increasing the minimum wage slowly over three years to $10.10 an hour will increase wages by 19 billion dollars a year and will decrease profits by 17 billion dollars a year, the two billion dollar difference resulting from the increased demand that the extra 19 billion dollars in wages will create. Increased wages decrease profits.