## Thursday, April 9, 2015

### Applying Econ 101 Supply and Demand Models to Minimum Wage

A few days ago, I finally realized that minimum wage actually works.  But don't worry, I still hate it.  Let me explain.

I had opinioned for a long time that minimum wage wasn't even effective, meaning that its positive effects over time were bascially none.

To the layman it may seem obvious that a guaranteed pay raise should have positive effects, but I think for the mathematician or economist this should be less obvious.  At least it was for me, being an amateur mathematician and an infantile economist.

Basically, I assumed that fancy hand waving stuff happens and then we get some good old status quo ante bellum, or actually bad effects.

A few days ago I tweeted the following:

You see, I've never actually taken Econ 101.  For all my interest and mathematical training, the most exposure I got was sitting in on my brother's Econ 101 class a few times just after my mission before I resumed taking classes.

It was fascinating and exciting, but I never went further with that subject.

But I got to see some basics like the supply and demand model.

It's not complicated, but sometimes we dismiss elementary mathematics too quickly.  Math majors are notorious for forgetting how to do arithmetic, after a certain point you are working mostly with symbols.

I didn't work this out on paper, but I went over the details in my head.

My first challenge came in trying to visualize the axes.  I kept on reversing them in my head.  Then I settled on price being the input variable and supply and demand being response functions to the price.  That resolved the axes confusion, but unfortunately supply and demand graphs are often drawn the other way, with price on the vertical axis and quantities on the horizontal axis.  It's really irrelevant, except for the purposes of visualization.

The next problem was trying to describe the most relevant constraints that would affect the supply curve.

Applying Econ 101 supply and demand models to labor pricing has several significant challenges.

One of these is the main simplifying assumption used by such models.  These models assume uniform goods, every good is essentially the same.  This is definitely not true in the labor market.

I thought I could get around this, and still have a fairly plausible model, by pretending that labor was uniform except that it had an ordering that determined employment preference.

This simplifying assumption says that one person is essentially the same as the other, but certain people will be chosen first over other people.  The most employable person would get hired first, and then the second most employable etc.

Basically, people decide first that they want to hire someone, and then they choose the most employable available person to hire.  I realize this isn't completely accurate, but it seemed like a tolerable assumption that wouldn't mess up the model I wanted to use.

The next problem is deciding what you will use for the units of labor supply and demand.

Will you count jobs, man hours, or productive output?

I ended up counting jobs and workers.  At a certain point I was concerned this might be a poor choice of units for this problem, but it turns out I was being thrown off by other bad assumptions.  Any choice of these three different units is acceptable, though they all have their own strengths and weaknesses.  It took me a while to even get to this point, because initially I didn't evaulate the question of unit choice in a methodical way.

One challenge with modeling the supply of labor is people basically take the best paying job they can get, or at least close to it.  It's not like they're holding onto reserves of gold until someone makes the right offer.  Labor is a perishable commodity, and working, for most people, is a necessity.  It almost seems like the behavior on the supply side is completely dependent as to what happens on the demand side.

Perhaps we ran into this problem because we didn't completely satisfy the condition of uniform goods.

If the uniform goods assumption truly holds, then that should mean the supply and demand curves can be modeled completely independently, I don't see any mechanism that would make them interdependent.  Both jobs and workers must be completely uniform and indistiguishable.  Otherwise, econ 101 is of limited use in this situation.

What if we just focused on unskilled labor? That seems about as uniform as you can get.

Let's start by saying there is a fixed pool of unskilled labor, the value of everyone in this pool is identical, though they may have different prices they demand for their labor.

The question then becomes, at what point do people forgo having a job because it doesn't pay enough? What is the price needed to buy their labor?

This is a pretty crappy question because most people rely on the price of their labor to survive.  It's like playing chicken with the biological constraints of survival.

In this case it's okay to do this, because we are talking about hypothetical supply curves for the purpose of economic modeling.  If we had an economic system that functioned by testing the boundaries of these curves in real life in order to optimize itself, that might present some ethical issues.

I really hate the way I sound right now. It's all so liberal, but I promise I got here entirely based on my approach to the mathematical problem.  Whether or not it's correct is an entirely different issue.

So anyway, what a lot of people say happens, is that the supply curve for unskilled labor ends up looking a little like a cliff.  It drops off sharply at the point that people can't afford to survive.  The unskilled labor pool potentially has to dance right on the edge of this cliff.  Because the constraints of survival are close to uniform, there's not much of a curve to the labor supply curve.  There is one cutoff point at which unskilled workers can or cannot accept a job.  Above this point they will say yes to anything they can get, below it, they just can't survive.

If this is true, it may be cause for some concern.

But we still haven't talked about the demand curve yet, so we can't actually say that things are bad for unskilled workers.

What does the modern demand curve for labor look like?

One of the dominant trends of the past 20, 100, 1000, or ten thousand years is using tools to increase productivity. Whoa, crazy! Demand has risen as well, but the current demand increase seems to be driven by want more than need, and there's no guarantee we can sustain it to absorb our higher productive capacity.

With geometric productivity gains, what happens to the demand for labor?  That depends on the units you use.  If your unit is productive output, it's definitely increased.  However, if your unit is workers/jobs, the demand curve for unskilled workers has simply flattened.

Demand for unskilled workers seems to be relatively inelastic, meaning it doesn't respond to price.  This makes sense, worker productivity is high, even for unskilled work, and we tend to have a fixed number of positions in our supply chains to make them work.  Using the same number of workers and machines, we can scale the output to whatever level of production might be required.

So demand for unskilled labor is inelastic, it doesn't respond to price.

It doesn't seem too complicated to say that inelastic labor supply makes workers vulnerable to price manipulation, and that inelastic demand makes countermeasures like minimum wage effective.

This has all been incredibly fun, but it's also an oversimplification, so it would be worth our effort to try to figure out what we are missing.

The biggest change from our original statements that we were forced to make is the uniformity of labor.

Every worker is different, and more importantly, the performance of the same worker can vary drastically depending on the environment in which he finds himself.  Happy workers are more productive, it's not rocket science.  Whistle while you work.

This means that the statements we made about the supply curve for labor may be inaccurate or misleading.  People have a million possible pathways for responding to changing labor prices, and what people get paid really does affect productive output.

Many people are suggesting that raising wages increases productivity, reduces theft and turnover, and improves employee and customer satisfaction.  They use this to argue for the minimum wage, but in my mind, this also confirms the view that minimum wage is unnecessary overreach, and labor supply curves really do respond to price.

This page perfectly states what I am trying to describe: The supply of labor is not actually inelastic.  An inelastic labor supply is the primary market property that leaves low wage workers vulnerable to wage price manipulation.  Again, understanding this requires methodical evaluation of the units of labor supply, so it's understandable that people might miss it.

Corporations may figure out policies or practices that would increase the inelasticity of labor supply, because this gives them more control over labor pricing.  However, people will unconsciously find ways to fight back.

One of these ways of fighting back has been supporting minimum wage.  But I think it ultimately works against the interest of workers in the long run.

So long as people have viable options, or create these options through natural civil disobedience, like not working as productively when you are abused or underpaid, market outcomes will reward responsible and ethical wage levels.

But the market alone is not always enough.

It is important to hold abusive individuals and corporations accountable for their inappropriate labor practices.  But minimum wage does nothing to target an abusive company versus a business that is labor intensive and has a low level of productivity.  Labor intensive businesses create more jobs, but inherently have lower pay, that is what labor intensive means.

Price protections like minimum wage can work when the demand for labor is inelastic, but is that what we want?

I am advocating that we lower the minimum wage and introduce a higher tier of wage subsidy benefits that supplement worker incomes directly when necessary.

Such a wage subsidy could be highly affordable because it supplements employer paid wages instead of paying all of someone's expenses.  The benefits go directly to the worker, not the company that employs them, unlike current wage subsidy programs.  It preserves natural market incentives because employer pay raises will increase total take home pay even while gradually reducing benefits.

It opens up entrenched businesses to competition by increasing the diversity of low wage jobs available, which is good for everyone.  Local businesses are more labor intensive and sensitive to wage price than corporate chains.  This is also what we want, because that makes them more responsive to employee needs as well.  I suggest taking a look at this article closely.

Every other aspect of the modern marketplace has increased the diversity, flexibility and quality of its offerings.  But the diversity and quality of low skilled and low pay jobs available has experienced no such improvements.  This is because we have limited our options.  If we did the same to any other product we'd experience the same kind of limitations.  High tech jobs are great and important, but they're actually less essential than the jobs that fulfill your everyday needs.

Fancy explanations cannot fix a broken, unconstitutional, and abusive policy like minimum wage.

I seriously wanted to enter the commercial unskilled job market.  I found it to be a toxic and unaccomodating place.  Instead of assuming I was broken and psychologically damaged, I decided to try to evaluate what led me to respond to my environment in the way that I did.

We need to stop shouting about how minimum wage works in our broken marketplace and actually fix our marketplace.  Minimum wage maintains the broken market conditions that make the policy effective in the first place.  It ultimately gives us a distaste for low productivity but essential job options.  If we want to disrupt corporate power, local, labor-intensive jobs are essential, and the best long term viable way to do this.  Read that last sentence twice.  It's probably the most important statement I've ever made on this subject.

Labor intensive jobs may sound like a bad deal, except when you realize that you have more control over the outcomes of your labor.  Over time you will become more efficient and can upgrade your tools and techniques, but you need the option of starting small if you want to take ownership of your own destiny.

Starting your own business is one option, but there is an entire spectrum here.  This is why locally owned, labor intensive businesses are such a great option for new and upcoming workers.  They may be tough at first and not pay a lot, but if the only person above you is the business owner, the possibility that you will be able to take over or branch out on your own is much greater, because you have observed the business management first hand.

Minimum wage forces the same constraints on these local labor intensive businesses that were designed for large, money grubbing, capital-intensive behemoths.  I feel like I am finally able to articulate my dissatisfaction with these rules.

If corporations are the only ones allowed to participate in purchasing labor, then demand for labor will become more and more inelastic moving forward.  If, on the other hand, we are all involved in employing each other, then demand for labor will have a nice gradation and path for self-improvement and advancement.

Which scenario do you want?

To stop playing chicken with the constraints of biological survival, let's focus on improving our social programs that provide direct assistance to people who desperately need it.  Let's stop trying to manipulate market outcomes in a maladaptive way.

A better profile of social programs might include the low wage subsidy program I really want to see, but it definitely involves improving programs like SNAP and housing programs.  We need to eliminate unnecessary or patronizing and presumptious obstacles.  We need to evaluate if these programs create adverse incentives.  We should integrate opportunities for participants to pay their benefits forward.

Eliminate obstacles, evaluate incentives, integrate opportunities.  C'mon people, even an unemployed neckbeard can think of that.

But what do I care?  Y'all do what you want with your country.  I'm done with authority.