Labor Market Disequilibrium

With President Obama's call for an increase in the minimum wage to $9 per hour, there has been a flurry of discussion about labor market disequilibrium.   Economics 101 suggests that an effective minimum wage creates a surplus in the labor market.   That is what I teach.  That is what I believe.

 Increasing that minimum wage, ceteris paribus, will make the surplus of labor larger.    The result should be both an decrease in quantity demanded and an increase in quantity supplied.   In a disequilibrium market, the short side rules, and so the actual employment of labor should be the quantity of labor demanded.   Basic economics suggests that a higher minimum wage will reduce employment.

Of course, both the supply and demand for labor are shifting over time, likely both increasing.   If demand was rising faster than supply, the quantity of labor demanded and employment would rise faster than quantity supplied and the surplus of labor would shrink.   Unfortunately, if demand was growing more slowly than supply, employment would rise, but so would the surplus of labor.  

Raising the minimum wage, then, could cause employment to rise more slowly or even fall for a time.   The surplus in labor markets would worsen at least temporally, or if demand is growing more slowly than supply anyway, the surplus would just get worse.

Rather than think of the problem in that conventional way, consider a scenario where the wage rate is at equilibrium, but actual employment is below the equilibrium quantity of labor.   The equilibrium quantity of labor is both the quantity of labor demanded and the quantity of labor supplied at the equilibrium wage.  

The quantity of labor demanded is the amount of labor that firms are able and willing to buy--really rent and utilize for production.   It can be divided in to two parts, the amount of labor that firms are actually utilizing and the additional amount of labor that firms would like to utilize.    Measuring this in full-time worker equivalents rather than man-hours of labor, this would be employment and vacancies.    The quantity of labor demanded is the sum of employment and vacancies.

The quantity of labor supplied is the amount of labor households are able and willing to sell.   It can also be divided into two parts--how much the households are working and how much additional labor they would like to provide.   Again, using full-time worker equivalency, that would be employment and unemployment.    The quantity of labor supplied is the sum of employment and unemployment.   Leaving aside measurement issues, that is the labor force.

The equilibrium wage is defined as the wage where quantity of labor demanded equals quantity of labor supplied.   In other words, the sum of the employed and vacancies must match the sum of the employed and the unemployed.    With the number of employed being the same for both quantity supplied and quantity demanded, that means that at the equilibrium wage, the vacancies must match the number of unemployed.   

Again, the equilibrium quantity of labor is both the quantity of labor supplied and the quantity of labor demanded at the equilibrium wage.    Assuming that the wage is at equilibrium, actual employment will equal the equilibrium quantity of labor if both vacancies and unemployment are equal at zero.     However, again, with the wage at equilibrium, if there are positive (though equal) amounts of vacancies and unemployment, then actual employment will be less than the equilibrium quantity of labor.

As firms search for additional workers and households search for new employment opportunities, the matches move actual employment towards the equilibrium quantity of labor.   With the equilibrium wage being below the firms' demand price, the marginal revenue product of labor, and above the households' supply price, the marginal evaluation of leisure, gains from trade occur when actual employment increases towards the equilibrium quantity of labor.

Clearly,  all gains from trade will always be exhausted and actual employment will always equal the equilibrium quantity of labor.

Right..

Another portion of Economics 101 explores the concept of frictional unemployment.   At the very least, because man is mortal, workers most separate from their employers at death.   Fortunately, we also reproduce and children grow up to be new workers.   In reality, there is a tremendous amount of movement in and out of the labor force.   Firms come and go.   Vacancies are constantly being created and constantly being filled.   Unemployed workers are constantly finding jobs and new people are becoming unemployed, often by entering or reentering the labor force.

Suppose that actual employment is 95% of the equilibrium quantity of labor.   At the equilibrium wage, the unemployment rate would be 5%.   The vacancy rate would also be 5% of the labor force.  There are enough jobs for everyone who wants to work.   The unemployed find jobs within a reasonable period and firms fill their vacancies.   But there are new people becoming unemployed and new vacancies being created.    That is the Econ 101  version of frictional unemployment.

However, at the current level of employment, the marginal revenue product of labor would be higher than the households' supply price for labor.    This creates a range of possible wage rates where quantity of labor supplied and demanded both remain greater than the current level of employment.  

Considering solely firms, at the equilibrium wage there appears to be a shortage of labor.   The firms want to hire more labor than they currently are employing.   Increasing the wage above equilibrium, up to the point of the marginal revenue product of those currently employed would simply reduce this "shortage."  In other words, vacancies would decrease.

Considering the households, at the equilibrium wage there appears to be a surplus of labor.   There are unemployed workers seeking jobs.   Decreasing the wage below equilibrium, down to the point of the households' marginal evaluation of leisure for the current level of employment, would just reduce this "surplus."  In other words, unemployment decreases.

Of course, considering the entire market, if the wage rises above equilibrium, there is a surplus of labor--the unemployed exceed vacancies.   There are not enough jobs for all the workers.   And if the wage is below equilibrium, there is a shortage of labor.  The vacancies exceed the number of unemployed.   There are not enough workers to fill all of the jobs firms want done.

This suggests that there is a range of minimum wages above the equilibrium wage that will not reduce actual employment.  

Most importantly, no one currently employed would lose their job.    Yes, the quantity of labor demanded would fall, but since actual employment is below that amount anyway, the decrease in quantity of labor demand would solely result in fewer vacancies.   There would also be an increase in the quantity of labor supplied, so there would be a larger number of unemployed workers.

If the firms have constant 5% vacancy rate, then employment must fall with the quantity of labor demanded.   Obviously, 95% of a smaller number is also a smaller number/  An increase in the minimum wage would seem to decrease employment.  

However, as long as the minimum wage is not raised above the marginal revenue product of the initial level of employment, then this would occur solely by attrition.    The firms never would have more workers than they find profitable, it is just that their procedures for replacing those workers that leave from time to time  are such that their actual employment is 5% below what would maximize profit.  

Interestingly, with the wage being pushed above equilibrium, the resulting surplus of labor might make it possible for firms to reduce the vacancy rate.   The typical firm has more applications, it has more applicants that  look like obvious good choices, and it has fewer situations where the preferred potential employee has already taken another job.    There is  a "buyers" market.  

Suppose the minimum wage rose 5% and the quantity of labor demanded fell 2%.    Actual vacancies would fall to 3%.   Further, suppose the quantity of labor supplied rose 4% and that the large surplus of labor makes it so much easier to fill vacancies, so that the firms procedures for hiring results in a 4% vacancy rate relative to the quantity of labor demanded.   Actual employment would only fall 1%, even though the quantity of labor demanded fell 2%.   

For example, suppose the relevant market had quantity demanded and supplied of 10 million.   Actual employment is 9.5 million.   The unemployment rate is 5% and vacancies are equal to 5% of the labor force.   The increase in the minimum wage decreases the quantity of labor demanded to 9.8 million.   The quantity supplied rises to 10.4 million.   However, actual employment falls to approximately 9.4 million, reflecting the 4% vacancy rate (approximately.)   Actual employment fell 100,000, even though the quantity of labor demanded fell 200,000.   There is a surplus of labor of 600,000, much higher than zero.  

Now, it is easy to see that if the surplus of labor improves the ability to fill vacancies enough, then actual employment might not decrease at all.   It is even possible that actual employment would increase!     If the quantity of labor demanded fell 2% and the quantity of labor supplied rose 10%, then firms might find that they can fill vacancies much faster than usual, and actual employment might be only 1% below the quantity of labor demanded. 

For example, suppose quantity of labor demanded (and supplied) was 10 million.   Actual employment was 9.5 million.  Because of the increase in the minimum wage, quantity of labor demanded falls to 9.8 million.   But the number of workers seeking work rises to 11 million.     It is so easy to fill vacancies, that the firms employ 9.7 million, nearly as much as the quantity of labor demanded.    Total employment increases by 200,000!

For free market economics (like me,) there is something right about equilibrium prices, including the equilibrium wage.   Given my framing, having enough jobs for everyone who wants to work seems right.   Having large numbers of workers competing for a few jobs seems wrong, even if the greater ease in recruitment for the firms results in more employment.

Like most free market economists, I would celebrate technological innovations that would improve the matching process so that both vacancies and the number of unemployed shrink, frictional unemployment falls, and employment moves towards the equilibrium quantity of labor. 

I think there is something horrid and offensive about creating an economic order where there just aren't enough jobs for all the workers.  

But then, the politicians who favor a higher minimum have a solution to the problem too few jobs.   They propose government jobs programs.   Having unemployed workers who want to work and are frustrated by the lack of jobs might help their political agenda.   While the frustrated unemployed workers are an obvious potential source of support, perhaps more important would be all of those who feel compassion for those suffering because there just aren't enough jobs.

Of course, the notion that politicians will increase the minimum wage only when it has no negative impact on employment is a pipe dream.    In the real world, there are a variety of labor markets.     Any increase in "the" minimum wage will almost certainly be increasing wages above the marginal revenue product of firms in some markets. 

 Still, it should not be  too surprising that an increases in some minimum wage has been found to have little impact on actual employment in some markets at some times.    It is easy to see.  Just think off the curves.   Think about disequilibrium.