In the previous post, I showed a graph of productivity against effective demand. In this post I want to explore the relationship between real compensation per hour, labor share and effective demand. Real compensation per hour is one of the two components of productivity, the other being labor share of income.

Productivity = real compensation per hour/labor share

Here is the plot of real compensation per hour against effective demand, 1967 to 2013. (note: In the following graph, real compensation per hour is given as an index, 2005=100, instead of a $ amount. The graph would look the same if we converted it to a $ amount.)

Graph #1

The relationship is a very close one. For instance, the plot is so close to the trend line between $10 trillion and $13 trillion that one can hardly see the plot because of the trend line.

Why are they so close?

Let's look at the equation for effective demand.

Effective demand = real GDP * effective labor share/(capital utilization * labor utilization)

Let's pull out the part... "real GDP * effective labor share". We will write it like this... Y*e. This represents labor income. There is another way to represent labor income. We multiply real hourly wages by total hours worked, W*L... Thus, Y*e=W*L.

We can re-write the equation for effective demand.

Effective demand = real hourly wage * total labor hours/(capital utilization * labor utilization)

This form of the equation says nothing about labor's share of real GDP. Yet, effective demand would in theory be the same regardless of what labor's share is. You just need to know real hourly wage and total hours worked. However, labor share is necessary if we calculate effective demand from real GDP. Also, labor share is important when we want to incorporate productivity, since productivity = real hourly wage/labor share. Let's rearrange the equation Y*e=W*L...

W/e = Y/L

Both sides of the equation determine productivity per hour. However, the effective demand equation will not tell us directly what productivity per hour is. Yet, the factors of productivity, W and e, both determine effective demand in their own way. So will we see the same close relationship if we plot e, effective labor share, against effective demand? Let's see...

Graph #2

Yes, we do see a close relationship between effective labor share and effective demand.

Both of the two lines in graph #2 will determine effective demand differently. Effective labor share is multiplied by real GDP, and real hourly compensation is multiplied by total labor hours.

To get productivity, we simply take the ratio of these two lines with real hourly compensation in the numerator, W/e. I now add the line to give us productivity.

Graph #3

Sometimes changes to effective labor share change productivity. And sometimes changes to real hourly compensation change productivity. Productivity wants to grow while effective labor share and real hourly compensation try to balance each other. It's like one or the other is always on its trend line.

One question for graph #3 is whether rising productivity in the face of declining labor share has reached its limit as far as aggregate demand for production? We are producing more, but less able to demand product. So, productivity has been stagnant for 3 years. And real GDP has been growing very slow lately too. The stagnation of both productivity and effective demand lead to the conclusion that we have reached the limit of being able to demand increasing production.

The economy has entered stagnation mode... unable to progress. Inflation is dragged down from low demand. Unemployment stays high. Here we sit waiting for something to change, while monetary easing makes the situation tolerable for owners of capital.

High productivity in the face of low labor share of income. Expansionary monetary policy keeps owners of capital investing and active. But what do you think will happen when the Fed starts tapering quantitative easing? There is no solid real demand upon which to continue business. The reality will set in and there will be a collapse.

The solution is to steadily raise labor share of income.