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That's wage compression: Wages came closer together, and the productive method became more cost-effective.

But what about the workers? If Firm B needs only 1 hour to do the work of 5 hours, then isn't that 1 worker doing the work of 5, leaving 4 workers unemployed?

Well not so fast. The empirical evidence has shown this not to be true…but why?

Imagine if everybody on the whole planet were infinitely rich. This can only be true if all things appear with zero human labor, and so the government sets up all the things to make all the things, and everything is free. That's not actually possible.

So people always face scarcity: they want more than they have. They have limited means to achieve their ends, and have to face trade-offs. They can't have everything they want.

So you have 4 workers now no longer needed to make the table. Well, they still have two working hands, right? They would like jobs because they really, really don't want to be unemployed and destitute.

You also have people who don't have everything they want. They would like things, and somebody has to make those things, ship those things, sell those things. You have a market: a meeting of buyers and sellers.

But what if no buying and selling is happening?

Well, to buy and sell, you need money. Without money, you have a money shortage: people looking to buy, people looking to sell, no buying or selling because there is no money to trade.

Now, if everybody is working and there is no way to make more tables, then adding twice as much money so people can buy twice as many tables won't work. There won't be twice as many tables, and people willing to spend more can get two tables. People will be willing to spend more if it means they can get a table, so prices go up: you have inflation.

But what if you want to buy more tables and you have all these unemployed?

In that case, creating money—and thus spending—activates labor. These unemployed are used to make tables, as the demand for tables has increased, the table market is hot, and sellers want to cash in on that. Jobs are created, and sellers compete for business by keeping low prices, wage permitting.

At this point we see a number of things: the increase in minimum wage caused technical progress, i.e. a change in process to become more productive. More productive means less labor is used to do the same thing, and the additional labor can be used to do something else. Unemployment doesn't change, but the amount available to purchase for each person does.

And there's the rub: the dollars go further. Minimum wages got closer together, prices may have gone up a little, and yet the people whose wages increased more slowly than minimum wage are still able to buy more. That last bit happens for a lot of complex reasons, such as that low wages are a small part of the total wage bill—higher wages affect price much more—and of course, because wages closest to the minimum wage move the most, while wages farther up move the least. 10% of $5 is only 50 cents, which is only about 3.3% of $15, and about 1.7% of $30. So put it all together: $5 wages increase faster than $15 wages; and $15 wages increase faster than $30 wages; and a small increase in a $30 wage is equivalent to a much larger increase in minimum wage; AND this compression causes replacement of larger amounts of unproductive labor with smaller amounts of productive labor, so there is a ceiling on the cost increase somewhere for various products.

That's right: all real wages go up. Buying power goes up.

It's tied to the relationship between minimum wage and per-capita GDP, technically, but that's another matter that gets into optimal policy and indexation. Research on that is here: https://arxiv.org/abs/2010.14669

And that's what happens when you step back from the micro perspective of "Firm A replaces labor with capital" and consider the macro perspective of "we have available labor to be applied to more productive work, but Firm B can't cost-compete with low-productivity Firm A if minimum wage is too low." Carrying this out further gets into things like trade—if productivity growth from moving Firm A to Firm B is much less than the growth in producing another product, then we import whatever Firms A and B were making, and alter the composition of industries by producing more of the other, more-productive thing. That, however, is another topic.

Yes, it is; it would also be good to cover how minimum wages interface with productivity, and the difference between the microeconomic and macroeconomic impacts of minimum wage.

In a microeconomic perspective, a minimum wage—in theoretical terms—reduces a firm's demand for labor. Notice the exact wording: "a firm's demand." That's an important distinction from the aggregate demand, i.e. the demand for labor in total across the economy.

To expand upon the microeconomic view—and I urge you to take this information in carefully, as studying microeconomics before macro is harmful to a student's understanding of either—one might consider two firms able to produce the same good, but using different processes. In Firm A, five hours of worker wage at $5/hr is used; in Firm B, one hour of worker wage in aggregate at $30/hr is used.

By "in aggregate," I mean that both these processes take in the same inputs, and both produce the same outputs; but in Firm B, they might use different tools, machines, and so forth. Human labor hours go into making those tools, maintaining them, fueling them, and operating them. Amortizing all those activities to get the average total wage paid for 1 hour of work, where 1 hour produces the same output as 5 hours by Firm A, gets you the aggregate hourly wage for 1 hour of aggregate work.

So that's a lot of words.

To simplify the model, just accept that Firm B uses a worker who's five times as productive. This wraps up all the above explanation and puts it into a black box which we understand logically, but no longer have to think about.

Well look closely: Firm A uses five hours, or $25 of labor, to produce what Firm B produces in one hour but at a cost of $30. Firm B will not be able to compete with the prices of Firm A, and so productivity will not grow, and the economy remains poorer than it would be if Firm B were more cost-effective.

We might ask questions like: what if Firm B became even more efficient and could produce in 1 hour the output of 7 labor-hours of work at Firm A? Then we could say well, without minimum wage, Firm A workers would lose their jobs unless they took a pay cut, and so wages will go down.

We can do even better.

What if there are two firms like Firm A, both unproductive?

Well supply and demand, that graph that shows the equilibrium point? It shows where quantity supplied equals quantity demanded. It also shows that below a certain wage price, some lower quantity is demanded.

That means workers are available at a lower price.

So imagine you buy tables. If the same table is available at $200, but also one for $175, which would you buy? The one for $175, of course. Now, will you buy two tables, spending $350 in total? No, of course not; or at least the vast majority of the market won't. In aggregate, the quantity demanded doesn't increase by as many tables as are sold at $175; instead, much of the purchase of $175 would have been $200 purchases, and there is a $25 consumer surplus—the consumer got the table for $25 less than they'd be willing to pay.

Well this is a problem.

The firm producing $175 tables hires 100 workers at $4/hr. The firm producing $200 tables loses customers, and experiences a reduction in sales equivalent to what is produced by 100 of their workers—who are paid $5/hr. Those $5/hr jobs go away.

This tightens the job market. Workers have trouble finding jobs because the demand for labor has fallen: the quantity demanded at $5 has decreased, as has the quantity demanded at $4. The workers, desperately in need of work, become more willing to take jobs at $4/hr, and the quantity supplied at $4/hr increases—supply increases, meaning wages decrease. Note that if the workers stubbornly refuse to take jobs below $5/hr, they will not find jobs, and they will remain unemployed, so unemployment will increase; but this is unlikely.

So without a wage floor, wages move downward and downward. Consumers have less money, and demand for products falls; but price also falls. There are a lot of reasons why prices don't fall as much, which have to do with wage compression.

So what is wage compression?

Consider again Firm A and Firm B. Firm A can produce a table for $25 using five worker hours at $5/hr; Firm B can produce a table for $30 using one hour of $30/hr labor. What if we raise the minimum wage to $5.50/hr?

Firm A can now produce a table for $27.5, but Firm B can't produce for less than $30. The wages at Firm A went up by 10%, but the wages at Firm B didn't.

At $6.50/hr minimum wage, however, Firm A has to pay $32.50 of wage to produce a table. Now Firm B can produce a table for $2.50 cheaper, right? Not so fast: the demand for more-productive workers increases because less-productive workers are expensive; and more-productive workers remain more cost-effective until an aggregate wage of $32.50. Wages at Firm A increased by a full 30%, but at Firm B they only increased by a maximum of 8.3%.

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