Saturday, September 21, 2013

Impose a Living Wage and Reduce Unemployment?

What happens to unemployment when the minimum wage increases? What if a living wage is imposed, raising the minimum wage a lot?

The Standard Static Story

Here's the standard story from intro econ in one easy picture:



The difference between the amount of work people are willing to supply at the minimum wage and the labor demanded by firms at the minimum wage is unemployment. (Note that unemployment doesn't exist at the competitive equilibrium in this model. Unemployment exists at the minimum wage because at the higher wage people want to work or work more (i.e. are "underemployed") but firms are unwilling to provide that work opportunity).

So, an increase in the minimum wage would increase unemployment and decrease employment. If the minimum wage is increased a lot to impose a living wage, then unemployment and underemployment increase a lot.

A Crazy Alternative Story

The standard story is nice, but it's a story that actually makes MORE assumptions about the supply of labor than the standard labor supply curve in many neoclassical models. In the standard labor-leisure model (now were at intermediate econ!), an individual's supply of labor can be backward bending.

Imagine you are given a small raise and can choose the amount you work in a year. Would you work more -- or less? What if you were given a pay cut? Would you work less -- or more? What if you were given a large raise? What if you earned $1,000,000 an hour; how much would you work a year then?

If given a raise, it turns out that most people would work more if they have a relatively low wage to begin with, but would work less if they have a relatively high wage. This is the backward bending labor supply curve. If people who work "minimum wage" jobs exhibit this phenomenon and have relatively similar preferences, the aggregate labor supply curve will also be backward bending at some wage level.



Now if there is an increase in the minimum wage, unemployment may actually go down! This would happen if the minimum wage pushed the market well into the backward bending portion of the labor supply curve and labor demand was inelastic enough. Here, we get the interesting case where imposing a living wage doesn't increase unemployment, it decreases it! However, notice employment still declines, as before. So we have a regime of decreasing unemployment and decreasing employment.

Notice in both stories an increase in the minimum wage reduces the total surplus in the economy. In addition, workers as a whole are better off if the gains from increasing the wage on those who remain employed outweigh the losses to those to lose their job or otherwise work less than they would like at that wage. Firms are definitely worse off.

This is very close to an analysis of how unions affect the labor market in the simple classical model. It's usually a good deal for those who remain employed, but hurts workers who would be willing to work for a little less, hurts firms, and there is a net loss compared to the competitive outcome.

An Even Crazier Story

Suppose -- this is very much a hypothetical -- the aggregate labor supply is backward bending and it intersects the demand curve in multiple places like this:



I've also added the standard "dynamics" to the static model. The competitive equilibrium is "stable" in the following sense: if wages were slightly below the competitive wage, demand would exceed supply. In order to attract more workers, firms are willing to raise the wage offered to workers. At a higher wage, laborers are willing to work more, and more may enter the market. We move "up" the curves until we hit an intersection -- the competitive equilibrium. At wages just above the competitive equilibrium, the opposite happens; supply exceeds demand and workers are willing to accept a lower wage in order to get a job or work more. The wage declines until it hits the competitive equilibrium.

Notice that the second equilibrium up the demand curve does not have this stability property, but the highest wage one does. Now if a living wage is imposed, wages for the lowest skill workers could settle at ABOVE the living wage at a high wage, low work, no unemployment equilibrium. Again, this could be good for workers if the benefits to those who are working outweigh the costs to those who are not, but it's also likely that this could lead to a WORSE outcome for the workers, too! That is, if the surplus is small enough (as it in the figure), both workers and firms would prefer the economy to be at the low wage, high work equilibrium, but instead the economy is stuck in stagnation!

Is This Why Both Unemployment and Employment are Declining and the Economy is in the Doldrums; It's All About the Minimum Wage and Backward Bending Labor Supply?

Almost certainly NOT, so why did I bother with these crazy stories?

0) They're interesting! So what if it's not reality? It might describe some reality sometime.... Ok, you want some better reasons? Here you go:

1) It speaks to what MAY happen if there are LARGE changes in the minimum wage. The empirical literature on the minimum wage only talks about the effects on employment for small changes in the minimum wage around the levels we currently have (or have had in the past). In order to understand the effects of large changes, we have to have a model of the whole market. I just presented a couple. Crazy things can happen in less dubious models, too.

2) Unemployment is just an indicator. People aren't necessarily better off because it goes down. It depends on what else is going on in the economy. The crazy story above is one example of people being worse off when unemployment declines.

3) Multiple equilibria happen all the time. Often, some of the equilibiria are bad. If stuck in a bad equilibrium, even though everyone knows they are stuck in a bad spot, no individual actor (even perfectly rational ones!) can do anything to get out of it.

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