Analysis of Wage Rates Scenario in Elliot Temple’s Educational Materials on Reisman’s Marxism Book

Previously, I posted my discussion of Elliot Temple’s educational materials on George Reisman’s most recent book on Marxism. That compilation of discussion does not contain my analysis of the extended wage rates scenario Elliot offers in his materials. I have posted that analysis below. This is only lightly edited (to correct one misstatement I caught through a quick pass through) and I have not yet reviewed the answers he provides.

Hypothetically suppose there are 20 businesses. This will be a simplified scenario so we can look at how wages are determined. After presenting the scenario, I ask some questions.
Currently the businesses have no employees, but they have the factory floor space and tools to hire up to 100 workers each (and they won’t expand).

So there is factory floor and tool capacity to hire 2000 workers.

There are 800 workers available to take jobs.

So lots of the factory floor and tool capacity is going to go unused (60%).

All work is unskilled – any worker can do any job. All jobs have the same number of hours and equally good working conditions. Workers must make $25/hr or more to have a good standard of living in this society, and $1/hr or more for minimum subsistence. The average rate of profit is 5%/year, so any use of capital with a lower return is inefficient and the capital could be more gainfully used elsewhere (basically you’d be better off investing in stocks and bonds rather than in the business). The business owners take salaries, so all profits of a business are a return on capital.

So the owners have their earnings deducted from sales revenues as expenses of the business like other wage-earners.

As a further simplification, the rate of return on capital from each business is unaffected by the number of workers employed, it only depends on the hourly wage paid – but, nevertheless, each business wants to hire as many workers as possible (up to 100 max) as long as the hourly wage is low enough to get 5%/year profit or more. Additionally, the capital in the businesses is totally liquid – it can instantly be converted into stocks and bonds, or back into a business, for free. Also, everyone lives in the same town and has the same commute to every business, and every worker knows about the job openings at every business, and every business knows about all the available workers. And everyone (both businessmen and workers) are equally good at salary negotiation.
All the workers are equally productive, but the businesses are not equally productive. Some businesses use workers and capital in better ways to create more valuable products. We’ll rank them from 1-20. The best one, #1, can pay workers up to $100/hr and still make a profit of 5%/year on the capital invested in the business. The #2 business can only pay $95/hr, at most, in order to have a profit of 5% or more. The #3 business can only pay $90/hr for workers or else its capital would be better invested in stocks and bonds. And it keeps going down by $5/hr for each business, until the 20th business can only pay up to $5/hr for labor and still make a 5% profit per year.
All the employers are selfish and greedy individually, but they don’t form a cartel or a conspiracy of employers, they just act in their own interests without coordinating with other employers. They try to pay the lowest wages they can and to maximize their profits. And the workers try to get the best wages they can, but they don’t unionize, they just act as individuals. Also, no one starts a new business and no one is self-employed.
Questions
What optimally happens in a free market, and why?

The various employers will bid against each other for the available pool of employees. The more productive ones, able to pay more due to their ability to maintain high rates of profit while paying high wages, will outbid the less productive ones.

How many workers are hired by which businesses, and what are their wages?

(Note that I do not think I would have had the same analysis if not for prior discussion on this topic on the FI list.)

The wages the businesses will pay is determined not by the max they are willing to pay, but what is necessary to outbid their next nearest competitor.

Let’s suppose that the “bidding” for employees happens in dollar increments. Business #1 (B1) is able to pay up to $100/hr. But nobody else is offering $100/hr, so it doesn’t actually need to pay that much. (Note that for brevity I’ll refer to the businesses as “B1”, “B2” etc from now on). B2 is willing to pay $95/hr. Assuming, as the scenario specifies, that the workers are all equally productive, B1 doesn’t actually have any incentive to outbid B2 for the workers, since there are sufficient (and equally productive) workers to fully staff both businesses. B1 just has to make sure that it’s bid is high enough to ensure it has a part of the “lot” of 800 workers that is sufficient to staff its business enterprise.

This analysis is the same as we carry on all the way through B8, which pays $65 an hour. B8 does indeed need to outbid B9, which pays $60 an hour. In fact all the business enterprises from B1 to B8 need to outbid B9. If any one of those enterprises only offered $60, then the workers would be indifferent between working for that business enterprise and working for B9. This would be a dumb result, since B1-B8 are more profitable than B9 and thus more able to pay higher wages.

So B1-B8 will pay the wage necessary to keep workers from going to B9 or below. Assuming dollar wage increments, they will bid up the wage for all their workers to $61/hr. Note this is way higher than subsistence 😉

What is the unemployment rate?

The involuntary unemployment rate is 0%. Because of the number of profitable business enterprises relative to the number of workers, there is full employment.

In what ways does worker need matter (like the minimum wages needed for a good standard of living, or for minimum subsistence)?

Minimum subsistence plays no role in the determination of wages. The market wage is in fact way way above minimum subsistence, but could have been below or at subsistence given different market conditions.

Likewise, the minimum needed for a good standard of living plays no role in the determination of wages.

In what ways does employer greed matter?

Employer greed matters in that the employers act in order to maximize their own profit. One way to look at labor is an input to the production process. With other inputs (like steel or electricity), the business owners want to make sure they pay enough to outbid their next nearest competitor for a given resource. Doing so allows the business owners to maximize their own profit. So rather than driving down wages, employer greed causes wages to be bid up to the point where the next nearest competitor can’t afford the labor.

A new business is created. It’s able to offer wages of up to $25/hr for up to 100 workers (while still making a 5% return on his capital or higher). What affect does this have on wage rates and how many workers work at each business?

I believe this would have no effect on wage rates. There’s already a business (B16 I think?) that offers that wage rate and is currently being outbid by businesses 1-8. The addition of another business offering below-market wages when there is full employment at the market wage.

Another new business is created. This businessman invented a really great new product which is easy to make. He’s able to offer wages of up to $500/hr for up to 100 workers. What effect does this have on wage rates and how many workers work at each business?

This new business (BN) would be paying at the top of the market, and would hire the “first” 100 of the fungible employees specified in the hypo. The BN + B1-B7 would collectively hire the entire labor pool.

B8 wants workers and is willing to pay $65/hour. BN + B1-B7 need to outbid B8 but not each other. Assuming dollar bidding increments, the entry of BN results in the market wage being bid up to $66/hr.

What happens to wages if another 200 workers enter or exit the situation?

According to general economics principles, an increase in the supply of something, all things being equal, should lower the price. Let’s look at the details.

The entry of 200 workers into the original hypothetical situation means that enterprises B9 and B10 will be able to staff their enterprises. This means that B1-10 need to outbid B11 and below (but not each other). B11 pays $50/hr. So assuming dollar bidding increments, the entry of 200 workers lowers the market wage to $51/hr.

What if the #1 business expanded in size and could now hire up to 400 workers instead of 100?

Collectively, B1-B5 would be able to hire the entire labor pool. This means they would need to outbid B6, which pays $75. Assuming dollar bidding increments, the expansion of B1 would result in a market wage of $76/hr.

What if the #20 business expanded to be able to hire up to 400 workers?

No effect on the market wage, since they’re being outbid.

In the original scenario, what happens if the government passes a minimum wage law of $25/hr?

No effect, since the market wage is higher.

What about a minimum wage law of $80/hr?

I think one way to look at this is that employers who are below the minimum wage cannot participate in the auction for labor. If they did participate, then the bidding process to beat the next-nearest competitor for the available pool of labor would be driven below the minimum wage.

The cut off point here is B5. B5 is the business that pays exactly the minimum wage. In the original scenario, B6-B8 also participated in the auction for labor. Now, they cannot.

Since the employees are fungible, each concern has no incentive to pay higher than the minimum wage. So the government-controlled wage winds up being $80 for those still employed. However, only 500 of the original labor pool of 800 are employed in the new situation. There are now 300 people unemployed. The unemployment rate has gone from 0 to 37.5%. The government has effectively outlawed the employment of these people.