Playing Games with Numbers

Note: What follows is a discussion mostly grounded in theory, not empirical data. It is also very drafty. Caveat lector.

In light of the President's proposal for an increase in the minimum wage (and the ensuing debate), I decided it'd be worthwhile to delve into some of the relevant economic theory.

The most common argument against the minimum wage tends to go something like this: The market is efficient. It correctly determines the value of a person's work, and pays them something less than or equal to this amount. A minimum wage interferes with this process. If the work done by an employee is worth less than what minimum wage says that employee should be paid, then a company would lose money if it hired that worker. Therefore, the company will not hire that worker (or others of a similar productivity).

The argument goes on to claim that, as the employees that produce the products of the least (monetary) value are generally the poor, a minimum wage law disproportionately harms the worst off in society.

While this argument appears solid at first, it conceals several assumptions. These assumptions, once violated, can lead to a very different conclusion than the one intended by opponents of the minimum wage.

Unfortunately, in order to discuss these hidden assumptions, I must get slightly technical.

The Technical Part:

In economics, there are a number of different theories used to explain when companies hire workers. The one I will be discussing, is known as Search-Matching theory. In order to avoid being too technical, I will be simplifying. For full details, see this link.

Imagine we have two parties playing a game. One is a worker named Karl. The other is a company named The Very Big Corporation of America (henceforth referred to as TVBCA). TVBCA is attempting to rebuild after being defeated by The Crimson Permanent Assurance (footage available here).  Karl has recently fallen on hard times, and is applying for a job with TVBCA.

Karl is willing to accept any wage that leaves him better off than unemployment. However, he prefers to be paid as much as possible. TVBCA is willing to pay Karl any amount less than the total value of what he produces for them. They prefer to pay him as little as possible.

Given these preferences, it is clear that Karl and TVBCA are bargaining over a wage between the minimum Karl is wiling to accept, and the maximum TVBCA is willing to pay. In other words, they are bargaining over a point (the wage) within an interval. It is here that the first hidden assumption in the anti-minimum wage argument is revealed, and shown to be false.

The anti-minimum wage argument assumes that any deviation from the market wage (a point), will lead to unemployment. However, as has been demonstrated, unless something strange happens (i.e., the interval contains only one point), there are any number of possible wages where employment will occur. Unemployment will only occur if the increase in wage goes beyond the maximum TVBCA is willing to pay Karl.

The Key Assumption:

Having established that increasing the minimum wage doesn't inevitably result in an increase in unemployment, I move to the next (and most important) hidden assumption. Namely, that there would be more jobs lost due to the increased minimum wage than jobs gained from putting money in the pockets of the poor.

This assumption is more difficult to discuss intelligently, as determining its accuracy requires empirical data. It is also likely that the effect of the minimum wage on unemployment will not be constant. For instance, a minimum wage set during good economic times may have little to no negative effects, but during a future recession could lead to an increase in unemployment (as the value of what a worker produces decreases below the minimum wage).

Nevertheless, the minimum wage is not being set during good economic times. Quite the opposite, in fact. The world has barely stabilized after the worst economic crisis since the recession. Wages have stagnated, while corporate profits are the largest since records began.  Worker's wages should therefore average towards the low end (as their bargaining power is very low), whilst the maximum wage tolerable to employers should be very high (as implied by record corporate profits, workers are very productive following recessions).  All of this suggests that if there is any time where increasing the minimum wage won't lead to an increase in unemployment, it is now.

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