Circular Flow of Labor & Capital

In the study of economics, one learns the circular flow of the economy between firms and households. This post however presents another circular flow model based on capital and labor. (It is a closed economy with no government for simplification.) There are 4 pools within this circular flow related to the income and utilization of labor and capital.

cap lab circ flow

In the center of the model is the percentage of national income from production that goes to owners of capital. We do have a capitalistic economy. The control of capital is at the center of the economy. Capital income is central to determining the pools around it… the percentage of national income going to labor and the percentage utilizations of labor and capital.

This circular model is different because we do not see money going back and forth between entities. Instead we see dynamics of utilization and distribution between one pool and another.

Share of Income between Capital & Labor

At the top of the circular flow is the relationship between how much of national income goes to capital and labor. For the most part, this is determined by owners of capital because they control the equipment, investment funds and other capital used for production. Then they hire labor to work with the capital.

There is a historical power struggle between capital and labor for sharing the income from production. Strikes, walk-outs and killings define the history. When labor loses bargaining power, labor share of income tends to fall. What effect then do changes in labor share affect the utilization of labor and capital?

Relationship between Labor Share & % Utilization of Labor (Green line in model)

In production, labor needs to be hired. The amount of available labor supplied depends on labor’s share of income from production. Here are some graphs to show this relationship. (update: The following graph presents the Unemployment rate as the percentage employed, instead of unemployed.)

update ls unrate

As the labor index rose to over 112 in the 1950’s and 1960’s, unemployment increased. The utilization rate of labor looked to be limited by the demand of capital owners.  Since then, labor share has fallen. Now it looks as though labor is limiting its own supply. The implication is that labor is less willing to supply its labor when its share of income is low.

We see this relationship also in the Labor Force participation rate.

update ls LF participation

When labor share was higher, the percentage of labor participating in production was higher. The steep decline in labor share since 2003 was accompanied by less labor participating in production. Granted there are other demographic influences. Still there looks to be some effect of lower labor share on the LF participation rate.

Relationship between Labor Share & % Utilization of Capital (Red line in model)

This relationship triggered by personal economic research in Effective Demand back in 2012.

As labor share of income falls, so does the upper limit of the utilization of capital (lower red line in the following graph.)

update ls cap util

Since the 1960’s, the maximum of capacity utilization in business cycles has fallen to lower levels with lower labor share. The effect of lower labor share upon capacity utilization is how I define Keynes’ concept of Effective Demand.

Relationship between Labor Share & both the % Utilization of Capital and Labor

This relationship involves the 3 circles around capital share in the circular flow model above.

Upon seeing how labor share limits the utilization of capital, I noticed an effect from the utilization rate of labor. So I developed a simple equation…

Labor share index * 0.76  >=  capacity utilization * (1 – unemployment rate)

The equation basically says that a labor share conversion (* 0.76) would set an upper limit to the value of multiplying together capacity utilization and (1 – the unemployment rate).  (0.76 was the slope of the midline tendency above in the plot between labor share and capacity utilization that zeros in on the limit.) So, in effect, the unemployment rate established the limits of capacity utilization in relation to labor share.

We see this in the following graph. (link to Fred data)

fred ut

The plot tends to stay above the zero line showing that the equation holds from business cycle to business cycle, including the current strange one. The converted labor share rate is seen to set a limit upon the multiplied utilization rates of labor and capital.

The Relationship between the % Utilization of Labor and Capital (Violet line in model)

As the business cycle recovers after a contraction, both the utilization rates of labor and capital increase. But there comes a point where the utilization of capital will stop increasing or fall. This point reflects an optimum use of capital as I show below. The utilization of labor may keep increasing or fall at that point.

How can this dynamic be put into an equation?

The following 3-dimensional equation gives a value for a z-vertical. As the z-vertical rises, capital and labor is used more optimally and the business cycle keeps progressing. The goal is to keep increasing the z-vertical as long as possible through a business cycle. A rising z-vertical shows optimum utilization of labor and capital.

z-vertical = m + k – am2k2
m = (1 – unemployment rate)
k = capacity utilization rate
a = 1.46 – 0.76 * labor share index

 The maximum of this equation is…

Max of z-vertical = √1/2ak … (square root of 1/2ak)

Here is a graph.

update path cobra

In the last year, capacity utilization has been falling while the utilization of labor has been increasing (unemployment falling). The equation predicted this. Yet has the z-vertical continued to rise? (link to following FRED graph)

update z-vertical

Yes, the z-vertical has continued to rise in this business cycle. However, the z-vertical is at lower levels in relation to the past which reflects the poor economic environment currently. A low z-vertical ultimately reflects under-utilization of both capital and labor which is a result of the lower than optimum labor share.

Now, I look at the derivatives of the above equation in terms of both capital and labor. A higher derivative means lower than optimum utilization.

First, the derivative in terms of capital. (FRED link)

in terms of capital z-vert

Capital utilization is always brought to its optimum during a business cycle. That is the priority of capital income at the center of the circular model. Capital has the advantage over labor.

Now, the derivative in terms of labor. (FRED link)

in terms of labor z-vert2

Unlike capital, labor never reaches its optimum utilization since it never reaches zero in the graph. Capital comes first in capitalism. And since the 1990’s, the utilization of labor has been getting worse as seen by the plot steadily trending upward. The increasingly unmet potential of labor utilization coupled with lower labor share is a problem.

Capital has not lost its advantages while labor has.

The utilization of labor has also been decaying since the end of 2014. So when economists say that the labor market is looking hopeful, I have seen the labor market getting progressively worse and heading toward an economic contraction.


The rise in power of the monopolies that Joseph Stiglitz writes about is giving more power to capital income. The above dynamics between labor and capital show the adverse impact upon labor. The result has been lower labor force participation, higher unemployment, lower capacity utilization, a weakening utilization of labor and an ever more sluggish economy.

Something needs to be done to give power back to labor.