## Equation for center of business cycle… another economic mystery??

I was up late last night tinkering in the “equation workshop” to calculate the center of the business cycle (potential GDP). The equation is opening up my eyes to some new insights.

The center of the business cycle is an important concept. It is the core foundation of the real GDP business cycle. Ultimately the level of real GDP is determined by its center. So, what drives the center? How does it move? A model and an equation is needed to answer these questions.

The idea is to calculate the business cycle center as a % of productive capacity. (Productive capacity is the total output that can be generated with 100% utilization of labor and capital.) The economy does not reach full productive capacity because of production and demand constraints.

There is a brute way to calculate the center of the business cycle. First find the productive capacity of the economy. There are two equations for this.

Productive capacity = Real GDP/T

Productive capacity = Effective demand/effective labor share

T = TFUR, multiplying labor utilization by capital utilization

Then to figure the center of the business cycle, this equation…

Center of business cycle = Real GDP – Biz cycle amplitude constant * (c/e – 1)

c = capacity utilization… e = effective labor share… Biz cycle amplitude constant is given in 2009 $$ as $3.4 trillion.

Then to find the % of productive capacity for the center of the business cycle…

% of productive capacity = center of business cycle/productive capacity

This equation does not give insights into what drives the center of the business cycle. So I searched for a more elegant equation.

Here is what I found…

Center of business cycle as % of productive capacity =

T * (1 + g * (1 – c/e)) ….. or ….. T * (1 + g – g * c/e)

g is a variable between 0 and 1. It seems that g has changed over the years. I will explore g in the rest of the post because it is the mystery of the equation. Finding the equation for g itself would open new insights.

I present a video to explain the equation. The video proposes that the variable g has declined over the years. The result is that capital utilization is now the preferred way to raise real GDP, instead of raising labor share. (link to video if not seen well.) The orange line in the graph on right keeps the other variables constant while changing labor share. The blue line on the right changes capacity utilization while holding other variables constant.

The center of the business cycle has been declining over the years as a % of productive capacity. The cause of that decline is the steady drop in labor share (effective demand). However, business now sees the way to generate growth is through capital utilization, even though capital utilization is suppressed by lower demand.

It is unlikely under this proposed dynamic that labor share will be rising any time soon.

Here is a graph for 3rd quarter data… Lines change holding all other variables constant.

Related articles:

Lambert, Edward. *Building a growth model with effective demand*. 4/6/13

Lambert, Edward. *When labor share does not rise in the growth model*. 4/6/13

Lambert, Edward. *Super macroeconomic potential real GDP*. 4/7/13