## Minimum Wages

In response to my two earlier posts on “Understanding Economics” and its followup, the matter of minimum wages has come up in the comments. Some ideas have the peculiar characteristic that they appear to be good at first glance but lose much of their shine upon closer inspection. Minimum wages is one fine example of that set.

To start our close inspection, let’s first understand what wages are. It’s a transaction involving two parties — one party is selling labor and the other buying it. The price at which the sale and purchase of labor takes place is determined through a bargaining process. If there is no coercion involved in the transaction, as in all voluntary transactions, both parties stand to gain.

Is there a case for a third party to intervene in this? The answer is yes only if the intervention could make at least one party better off without making any other person worse off. To use a technical term here, this is what is called a “Pareto improvement.” Otherwise the answer is no.

This involves a general principle and we should pay particular attention here. A situation is “Pareto optimal” if you cannot make someone better off without making at least one person worse off — which is that you cannot make a “Pareto improvement.”

Is anyone being made better off while simultaneously ensuring that no one is made worse off by intervening in a simple labor transaction?

Let’s take one case at a time. Suppose the seller and the buyer of labor voluntarily agree on \$10 as the wages. That is what we will call the “free market” wage rate — both parties arrived at a rate voluntarily and without any coercion from third parties.

As a third party, suppose you step in and force a different wage rate. You side with the seller and impose \$9 as the wages. You make the employer better off and the employee worse off. Or say you impose a \$11 wage rate. In this case you have made the seller better off and the buyer worse off. In either case, you have only helped one party at the expense of the other.

There is a range of wages at which a transaction takes place. The lower end of the wage, say is \$8 — below which the seller will not sell; and the upper end, say \$12 — above which the buyer will not buy. If your intervention is between these two limits, you are just changing how the “surplus” — which is the difference between the two limits — is divided.

The total surplus in this transaction is \$4, the difference between \$12 (the maximum the buyer is willing to pay) and \$8 (the minimum the seller is willing to accept). Since the buyer and seller have arrived at a voluntarily negotiated \$10 as the wage, the seller enjoys a surplus of \$2 (\$10 – \$8) and the buyer enjoys a surplus of \$2 (\$12 – \$10). In this case the \$4 total surplus was equally divided. Had the negotiated wage been anything else within the range, it would have yielded the same total surplus but the division of that total would have been different.

When you intervene to set a wage rate within the rage, your intervention moves the situation from one Pareto optimal to another, but it is not a Pareto improvement. It is pure meddling but you can actually do much worse. Here’s how. By imposing a wage rate outside the feasible range.

Suppose you impose a \$7 wage rate. The buyer is willing to buy at that rate but the seller is unwilling. Trade does not take place. That makes both the seller and the buyer worse off. Similarly, if you impose \$13 — the seller is willing but the buyer is not. Trade again does not take place and both are worse off. Through your intervention in the market, you have imposed losses.

Let’s examine what you are doing: you are imposing your will on others. You decide how much the seller’s labor is worth (in case you impose a wage lower than the free market wage) or how much the buyer should value labor at (in case you impose a wage higher than the free market wage.) There is no justification for you to do so in either of these cases.

Note that I have introduced the terms “surplus,” “Pareto optimum” and “Pareto improvement” here because it is useful vocabulary. Vocabulary helps us reason efficiently and present out arguments compactly.

To summarize the above, the free market wage of \$10 arrived at by the buyer and seller is Pareto optimal. Your intervention within the range \$8 – \$12 leads you to another Pareto optimal but it is not a Pareto improvement. It is not a Pareto improvement because one party gains only at the expense of the other.

Your intervention outside that range leads you to a situation where the trade does not take place — and this is not Pareto optimal since at least one or both parties can benefit (a Pareto improvement) if the wage is allowed to be freely set within the range.

In this simple example, the \$10 free-market wage rate is Pareto optimal. But it is not the only Pareto optimal wage. As pointed out above, wage rates of \$8, \$9, \$11, and \$12 are also Pareto optimal. But an imposed wage rate below \$8 or above \$12 is Pareto inferior because you can make both parties better off — a Pareto improvement — if you just let them get on with their business and not interfere.

At this point you may say that all this is very tedious and simplistic. It is tedious but necessary. If we have to understand the big issue we have to proceed slowly one small step at a time. We need to do this only once to establish the basic principles. Once only and then we can simply use the results we get to move on to the apparently more complicated bits. I say “apparently” because a complicated case is nothing more than a collection of simpler bits. If we understand those simple bits, the complicated bit does not appear to be all that complicated.

So now the next simple bit is to ask how are the range limits — \$8 and \$12 in our example — determined. That’s done by the availability of “substitutes.” The employer is willing to pay a maximum of \$12 for the job because for \$12 he can get the job done by using alternative means. Suppose he can hire a machine and thus avoid hiring a worker.

In the case of the worker, for \$8 he is willing to do the work but for less than that, he will not do the job — because his best available alternative is a job that pays \$7.99. So the principle here is that the wage that a person can demand depends on the person’s available alternatives.

So what determines what alternatives a person has? That depends on the skills of he person — a characteristic intrinsic to the person — and on the demand for that skill — a factor that is extrinsic to the person.

The wage rate for C++ programmers is determined by demand for C++ programming and the supply of C++ programmers. If there are very few people with C++ programming skills and there is a high demand for C++ programming, the wage rate will be high. Prices in free markets are determined through the interaction of supply and demand. If the free market wage rate is high, then it sends a signal to people to learn C++ programming. Conversely if the wage rate is low, then people will not learn C++ and move to acquire other skills.

Suppose the government imposes a high wage rate for C++ programmers which is higher than the free market rate, then employers will at some point move their C++ programming centers to where the wages are lower than the government mandated wages. Fewer people would be employed as a consequence of the imposed minimum wages if the minimum wages are higher than the free market wage.

The basic principle here is a very broad one. People respond to changes. If prices go up, people buy less of that and use substitutes. If the price of coffee goes up, people drink less coffee and perhaps drink a bit more of tea. If the price of apples go up, people switch to oranges.

You cannot raise the minimum wages and expect the same number of people to be employed at the job. Those who get to have the jobs are of course better off but there are many others who would be worse off.

One of the more important lessons one can learn by thinking systematically (which is what economics demands — thinking systematically) is that you should not only look at what happened as a consequence of a proposed policy but also look at what other things were prevented from happening as a consequence.

Yes, raising the minimum wage looks great when you consider that no one will get paid less than the minimum wage — and immediately think that all those who are currently earning minimum wages will benefit. But one of the absolutely predictable and unavoidable consequence will be that some people who are currently employed at the lower minimum wages will be let go. They will have no job at all.

Why is that? Because wages, by and large, are determined by how much a person’s labor is worth to the employer. The technical term is the “marginal product of labor.” I will go into that the next time I take up this topic of minimum wages.

### 3 thoughts on “Minimum Wages”

1. SV Thursday December 6, 2012 / 1:03 pm

Thanks for the revelation, never thought minimum wages could be harmful too! But in reality why is the minimum wage enforced? Why don’t they just remove that policy?

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2. allwyn Friday December 7, 2012 / 4:55 am

Recently, in his TOI article chetan bhagat talked about minimum wages for people who do house work in India, maybe according to him they are paid very less and to some extent I agree. I also think(not sure though) that people who do construction work – buildings, roads, bridges etc are paid very less plus the work conditions also look horrible to me again not sure about – they could be getting paid more.
My question how would it work out if the government was to formulate policy regarding wages for certain types of labor. Maybe give tax incentives to builders and fix a min wage there for the people working in construction but then as you said some people will just lose their jobs – another way would be to just give tax incentives and “hope” the builders pay them a little better salary!

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3. JP Sunday December 30, 2012 / 5:33 pm

SV,

Minimum wage policies are lobbied for by big businesses, specifically retailers and such in US. This is to prevent small businesses from competing with them. Big retailers (say Walmart) can afford to pay more and they also have efficiency of scale, even if they pay a bit more, it doesn’t matter at all; labor costs are minimal at the level they operate. However, small businesses have a significant cost of labor and any increases makes it difficult to survive.

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