Some have said that involuntary unemployment is impossible in the free market (v.g. Mises, Hoppe, Block, Huerta de Soto) a discussion of such position can be found here http://www.uni-svishtov.bg/dialog/2008/1.08.WBII.WB.pdf
Such thing is false. Why?
In Human Action, Mises says "Unemployment in the unhampered market is always voluntary." What he is saying is that A->B. If Free market then unemployment always voluntary. That structure allows us to easily find a counterexample. If we find A and not B then A does not imply B, so we could have involuntary unemployment in a free market.
Here it goes:
Let E be a free market economy, a closed system composed by two plots of lands, owned by farmers Artir and Hoppe. Artir's plot is quite fertile and can yield crops the whole year. Hoppe's is not, and can only sustain him in summer. We assumme strict observance of property rights, so no theft is allowed and entering each other's property requires previous permission.
So in summer certainly there is no unemployment, as each inhabitant of E farms his own land. But winter comes and Hoppe basically can either choose to starve and die or ask Artir for some food:
H: Hey, you know my plot of land won't sustain me in winter, right?
H: So could you let me work in yours for a small fee. I will farm the entire plot, have the minimal amount of crop and you wouldn't have to work. My marginal productivity for you is above zero!
A: You see... food is nice and having to pay you would mean eating less... and maybe that deficit of food does not compensate me not having to work. Uncertainty and stuff.
H: But you are not really conscious of what you are just doing, right?
A: What am I doing?
H: You are creating involuntary unemployment.
H: Well. That cannot exist in a free market! You know! It's a priori, you cannot negate it.
A: I'm just doing so. You aren't working in my field this winter.
H: But I will starve! I will die. Working in your field is my only alternative.
A: Well, H, according to you if I'm not violating the so called Non Agression Principle, I'm not doing wrong. According to you, it's not wrong to let you die. Your ethics are truly funny.
H: True, but but.. this isn't about my ethics, it's about economics! Mises, the greatest economist of the twentieth century also believed that. Are you putting yourself above him?
A: Being Mises does not free you from the capacity to err. Or H, for that matter.
And so it is demonstrated.
Now, some people would now follow that because involuntary unemployment can appear in a free market, government should do something to avoid it. In my example, Artir is just plainly trolling Hoppe [and in doing so, trolling all those who believe in the now falsified proposition], and the government perhaps should force him to employ Hoppe, or tax Artir and subsidize Hoppe. Fun thing is that Hoppe would not accept that, but Artir [the real one, that is the one who writes this lines] would. Letting someone die in order to avoid a small disconfort is just plainly inmmoral. Hoppe (and government, community associations or whatever institutions are there for treating this issues) would be justified in forcibly taking the smallest plot of land from me in order to feed himself. But not all cases of involuntary unemployment are like that. How far an involuntarily unemployed would be able to go in order to secure means of living is a topic for another post.
Howevah, in a free market entrepreneurs are guided by profit and tend to put money over bastardry and trolling and so if hiring a worker would raise their profits, they will. But there are three problems with this:
a) Uncertainty. The so called marginal productivity cannot be known. At much, can be estimated. And margins of safety around it could perfectly put it below zero, so wouldn't get hired. Some could argue that the worker should offer to work for free, or even pay to work. Those who argue for that are just and simply trolling the audience. Such thing would be useful in the short run to earn experience, but in the long run would send you to the grave if no other sources of income are available, which is technically a possibility.
b)Problems of knowledge: There may be employers who are offering employment and employees who seek it, and provided that they meet would sign a contract and all solved. Unfortunately that is not always the case: not all agents have the same information, which is dispersed among the participants of the market. I can be offering a job in Spain, and my perfect employee could be looking for a job in Siberia.
c)Regulation: Of course, if there is regulation it could be said that it's not a free market anymore. True. In that case we'd be talking of government induced voluntary unemployment. There are certainly regulations that induce it and also difficult solving some cases of the main a) and b) problems. But regulation could also be present in a free market, in a certain way. (i.e. a gated community that does not allow for restaurants to be established inside it, resulting in a certain chef being involuntarily unemployed. Even if he perfectly knew that such business is profitable and he went to the community council and ask for a permission, there would be a period of time between the petition and receving the answer in which, if that was the only employment possibility, wouldn't be able to do nothing, and having to choose between being unemployed and being unemployed, which isn't quite voluntary). The key is to find what regulation minimizes such situations, without leading to more problems.
Now the good news: there are incentives in the market to solve the above mentioned problems. There are websites to find jobs, one can have savings so to mitigate the effects of temporal unemployment, and some regulation can be eliminated as to allow entrepreneurs to create more jobs, etc. In a healthy economy, involuntary unemployment would be minimized without need for intervention, I say. Some would disagree with this, as may argue that the economy may settle in a non-full employment equilibrum and blah blah (Or even more sophisticated variants of the argument that do not assume (and are correct in not doing so) equilibrium but end up saying basically the same). A refutation of that is not the topic of this post.
So to conclude:
Is involuntary unemployment technically possible in a free, unregulated economy? Yes.
Is there a solution? Yes. Moar free market.
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