I am going to build the growth model now based on the principles of Effective Demand. The starting point is the graph of the model. Let's look at it and explain it...

We see capacity utilization as the dependent variable (y-axis) and effective labor share as the independent variable (x-axis). We draw a line where capacity utilization is equal to effective labor share. The line represents potential real GDP where capacity utilization is equal to effective labor share. This comes from the equation for potential real GDP...

Potential real GDP = real GDP - a * (cu - els)/els

When cu = els, potential real GDP = real GDP. This is the center of the business cycle. (cu=capacity utilization... els=effective labor share. a=constant for the amplitude of the business cycle.)

There is another important view of this line. It also represents the limit to capacity utilization if there was 100% employment. This comes from the equation for Effective demand.

Effective Demand = real GDP * els/(cu * (1-u))

If u (unemployment rate) is equal to 0%, then when els = cu, Effective demand is equal to real GDP.

Thus, the green line in the graph above represents the line of equilibrium at 100% employment, where real GDP, potential real GDP and Effective demand all meet in unison. It is this point of reference of total equilibrium that we can judge the growth, the maturing process if you will, of an economy.

Ok let's use this graph...

First, we have to look at a graph from a previous post...

The pink line is potential real GDP and uses the equation given above. This pink line is the derivative of the upsloping blue line. Therefore, the pink line represents the rate of change of the blue line. Where they meet, the rate of change of the blue line equals the output of Potential real GDP.

What is the blue line? It shows the Super Macroeconomic Potential real GDP. The explanation is... As capacity utilization increases for any given real GDP, the economy has diminishing returns as far as potential real output. Here is the equation of the blue line...

Y^{!}=Super Macroeconomic real GDP. ... a=constant for the amplitude of the business cycle... cu=capacity utilization... els=effective labor share... Y=real GDP. (The derivative of this equation again is the equation given above for potential real GDP.)

Y^{!} is a measure of true potential real GDP. When Y^{! }is below potential real GDP, the economy is not living up to its real potential as far as utilization of its capital and labor. When Y^{! }is above potential real GDP, the economy is over-utilizing capital and labor. Both scenarios are in effect, inefficient.

Where the Super Macroeconomic potential real GDP crosses potential real GDP, you find the optimal utilization of capital for any given real GDP. Labor is optimally utilized by association.

So now, let's solve for the capacity utilization rate where the two lines cross. This equation will give us the optimal capacity utilization for any given real GDP. Here is the equation...

Keep in mind, this equation calculates the optimal capacity utilization rate for any given real GDP. But we can see in the equation that we can make els (effective labor share) the independent variable in a graph, holding both Y (real GDP) and a (business cycle amplitude) constant.

We can therefore plot this equation on our basic graph for the growth model given at the beginning above. Here is what the plot looks like...

We are looking at the optimum utilization rates of capital depending on effective labor share. When we follow the blue line, optimal capacity utilization falls as effective labor share falls. Likewise, optimum capacity utilization rises as effective labor share rises. Where the two lines in the graph meet, the business cycle is optimized in terms of utilizing capital and by association labor.

The business cycle will revolve around the green line. The business cycle will rise above it and then fall below it, as the green line represents potential real GDP. Yet, the business cycle moves within an upper limit effectively set by the rate of unemployment (the utilization rate of labor). The business cycle cannot move above that upper limit, which is imposed by Effective demand. The limit on real GDP is established when Effective demand is equal to real GDP. At that point, the real output does not have incentives to increase.

So if we look at the equation for Effective demand...

Effective Demand, ED = Y * els/(cu * (1-u))

and then solve for cu, capacity utilization, we get...

cu = Y * els/(ED(1-u))

The upper limit of cu happens when Effective demand, ED, is equal to real GDP, Y. Therefore we get...

cu = els/(1-u)... Now we can plot the upper limit of capacity utilization on the graph...

This graph uses an unemployment rate of 7% to calculate the red line. Imagine the economy revolving around the green line and staying below the red line. Well, no need to imagine, I will show you actually data since 1967 using a constant of 6% for the unemployment rate, so that you see this is true...

Now we need to go back and remember that this is a growth model. Growth is determined by real GDP. If we look at the graph right above here, we see that the US economy has been in the 80% range of capacity utilization and effective labor share for some decades.

But then you wonder about a country like China, where it is reported that their capacity utilization rate is in the 60% range. The position of the blue line in this graph would represent where the economy of China is. Effective labor share would be around 60% too, which seems like a low level to pay labor. But then you realize that their country is growing fast and they need to put more income into capital share of income. By giving more share of national income to capital, China can grow.

The most important question of a growth model is this... What happens as the real GDP of China grows. In other words, how would the blue line change on this graph as the real GDP of China grew? Well, let's look at it...

We can see that for the economy of China to grow in equilibrium, effective labor share must increase. The workers must be paid more. The benefit of this is better optimal use of capital. In essence, the economy of China will mature in a stable way as long as they follow the green line. As their real GDP grows, so must their effective labor share.

The pay of labor is an issue in China and they are taking steps to allow labor income to rise. They have a plan for the minimum wage to rise by 13% over the next 5 years. But if China was to use this model, they would be able to increase labor income with more certainty that they are growing in balance. They would calculate where they are in the model by ascertaining their amplitude of the business cycle, a, their real GDP and their effective labor share of income. Then, they will know they are growing in balance if effective labor share moves up the green line as real GDP grows. It is quite simple.

The main problem when countries grow in real GDP is that they do not raise the effective labor share of income enough. The result is that the country cannot continue to grow. I will use this growth model to explain this process in a later post.