The Wage Bill

First, we can look at total wages paid in the labor market, sometime called the wage bill. By looking at the wage bill, we can find out if the additional wages earned by the working poor exceed the wages lost by those who find themselves unemployed.

Total wages are equal to the total hours worked multiplied by the hourly wage:

total wages = real minimum wage × hours worked.

Because we are measuring the wage in real terms, total wages are likewise measured in real terms. Figure 10.13 "The Wage Bill" provides a graphical interpretation of the wage bill: total wages paid are given by the shaded rectangle.

From this equation it can be shown thatTo derive this equation, we first apply the rules of growth rates to obtainpercentage change in total wages = percentage change in real minimum wage + percentage change in hours worked.Then divide both terms by the percentage change in the minimum wage and use the definition of the elasticity of demand:$$\begin{array}{c}\text{percentage}\text{ change }\text{in total wages }\\ =\text{percentage change in real minimum wage}\times \left(\text{1+ }\frac{\text{percentage change in hours worked}}{\text{percentage change in real minimum wage}}\right)\\ =\text{percentage change in real minimum wage}\times \left(1-[-(\text{elasticity of demand)]}\right)\text{.}\end{array}$$

percentage change in total wages = percent change in real minimum wage × (1 – [–(elasticity of demand)]).

The elasticity of demand is a negative number: if wages increase (that is, the change in the wage is positive), then hours worked decreases (that is, the change in hours worked is negative). It is therefore easier if we use –(elasticity of demand) because this is a positive number. The equation tells us that the change in the total wage is positive if the percentage increase in wages is greater than the percentage decrease in hours worked—in other words, if –(elasticity of demand) is less than 1.

If the demand for labor is relatively sensitive to changes in the wage, employment will decrease significantly following an increase in the minimum wage. Total wages paid will decrease. This is shown in part (a) of Figure 10.14 "Effects of an Increase in the Minimum Wage on the Wage Bill". Before the increase, total wages are given by the sum of areas A and B. After the increase, total wages are given by the sum of areas A and C. We get the opposite conclusion if labor demand is inelastic. In this case, an increase in the wage increases the total wages paid. The conclusion is intuitive: if employers do not change their hiring very much when wages increase, then total wages will increase. But if an increase in the minimum wage leads to a big decrease in the demand for labor, total wages paid will decrease.

Seller Surplus

The wage bill tells us how much workers are paid in total. A better measure of the benefits obtained by workers is the total sellersellers’ surplus#8217;s surplus in the market. We cannot measure this exactly unless we know exactly what the labor supply curve looks like, but we can conclude that just looking at the wage bill understates the benefits to workers of the increased wage. The reason is simple and does not even need any diagrams. Following an increase in the minimum wage, workers work fewer hours in total. Everything else being the same, people prefer leisure time to working. For example, suppose that total wages increase following an increase in the minimum wage. Then workers gain twice: they are being paid more, and they are working less.

Even if total wages decrease, workers might still be better off. They might be more than compensated for the lower wages by the fact that they don’t have to work as many hours. We are not saying that having a job is a bad thing; those who are working prefer having a job to being unemployed. But those who are working also prefer working fewer hours.

Expected Wage

So far, we have looked at the minimum wage through the lens of a competitive labor market. This is not a bad approach: as we have argued, the unskilled labor market is probably a reasonably good example of a competitive market. It is, however, a static way of thinking about the labor market, when the labor market is in fact highly dynamic.Chapter 8 "Growing Jobs" contains more discussion. People move in and out of jobs: they quit or are laid off from old jobs, and they search for new jobs. A worker who is employed this month may find herself unemployed next month; a worker with no job this month may be hired next month.

Earlier we claimed that an increase in the minimum wage has no direct effect on the unemployed. This is true in the static labor market picture, but once we take a more dynamic view of the labor market, it no longer makes very much sense to draw a hard-and-fast distinction between the employed and the unemployed. Over time, they will include many of the same people. So when we look at the distributional effects of the minimum wage, it is better to draw the distinction between unskilled workers (that is, the employed and unemployed together) and the relatively rich. With this in mind, let us now consider whether the unskilled as a group are likely to benefit from the minimum wage.

We might expect that unskilled workers will spend some of their time employed and some unemployed. When employed, they earn the minimum wage, but when unemployed, they receive much less. To keep things simple, suppose these workers earn nothing when unemployed. On average, the fraction of time that workers spend employed rather than unemployed is given by

$$\text{fraction of time employed = }\frac{\text{quantity of labor demanded}}{\text{quantity of labor supplied}}\text{.}$$

We can think of this as the probability that a typical unskilled worker will be employed at any given time. Combining this with the idea of expected value, we can calculate the expected wage of such a worker. If a worker earns nothing when unemployed, then the expected wage is as follows:

$$\begin{array}{c}\text{expected real wage}=\text{fraction of time employed}\times \text{real minimum wage}\\ =\frac{\text{quantity of labor demanded}}{\text{quantity of labor supplied}}\times \text{real minimum wage}\text{.}\end{array}$$

How does this expected wage change when there is an increase in the minimum wage? The answer, as you might expect by now, depends on the elasticities of demand and supply. Specifically, it turns out that the expected wage will increase if

–(elasticity of labor demand) + elasticity of labor supply < 1.

If both demand and supply are sufficiently inelastic, the average wage will increase. Conversely, if they are both relatively elastic, then expected wages will decrease.

There are some things missing from this story. In a more careful analysis, we would take into account the fact that workers are probably risk-averseBeing willing to pay more than a gamble’s expected loss in order to avoid that gamble. and dislike the randomness of their earnings. We would likewise take into account that unemployed workers obtain some income—perhaps from unemployment insurance. This actually makes it more likely that an increase in the minimum wage will increase the expected wage. These are details, however. We can draw two big conclusions from our discussion so far:

1. Under some circumstances at least, an increase in the minimum wage will have the effect of redistributing income from the relatively rich to unskilled workers. Policymakers may wish to reduce inequality in society, and the minimum wage is one possible tool that they can use. At the same time, the minimum wage comes at a cost to society: it distorts decisions in the labor market and leads to deadweight loss. This is an equity-efficiency trade-offTrade-off that arises when policies that deliver a more equitable distribution of resources also generate deadweight loss..
2. The distributional impact of a change in the minimum wage cannot be deduced from economic theory. It depends on the elasticities of labor demand and supply in the market for unskilled labor and is an empirical question. In the next section, therefore, we turn to the evidence on minimum wages.