This post is going to be one of the most important posts in all of the Effective demand blog posts. Please scrutinize.

There is a need to start laying out the proof of how effective demand works. I have been posting equations and graphs for over two months. But is there really a solid logic, a solid truth underneath it all? Does labor share really determine capacity utilization? etc...

## First, What is Capacity Utilization?

Capacity utilization is the level of utilization for the capital goods used in the production of goods and services, whether sold to consumers or businesses. Capacity utilization measures the use of the "means of production".

From a paper entitled "Capacity Utilization", published in 1997 by Carol Corrado and Joe Mattey.

"Capacity utilization is a ratio of the actual level of output to a sustainable maximum level of output, or capacity... The output figures are monthly indexes of industrial production, and each industry utilization rate is equal to an output index divided by a related capacity index. The capacity indexes are designed to embody the concept of sustainable practical capacity, defined as the greatest level of output each plant in a given industry can maintain within the framework of a realistic work schedule, taking account of normal downtime and assuming sufficient availability of inputs to operate machinery and equipment in place. The concept generally conforms to that of a full-input point on a production function, with the qualification that capacity represents a realistically sustainable maximum level of output for a given industry, rather than some higher unsustainable short-term maximum."

It is important to know that capacity utilization is calculated for individual industries and sectors of the economy. Each industry has its own level of capacity utilization. Thus, there is a separate capacity utilization calculated for consumer goods, business equipment, durable goods, non-durable goods and so on. Ultimately there is an aggregate level of capacity utilization calculated for the whole economy.

Capacity utilization also measures goods from the 3 stages of production... finished, semifinished and crude. (source)

The fact that capacity utilization is presented for different sectors of the economy becomes essential to understanding how labor share affects capacity utilization. As you will see in the simulation below.

## A world of 100% labor share of income

We start with an economy that has 100% labor income share. All income from production is taken and spent on finished goods and services. Let's simplify the economy to a tribe of 10 households. Between the 10 households all needed goods are produced... food, clothes, furniture and housing. Each household produces $100,000 of production per year at 100% capacity utilization. Thus, total real GDP is $1 million.

Each household receives $100,000 and spends $100,000. Here is a graph of the economy...

The economy is completely stable at full-employment (LRAS curve). All output is bought. We are at the effective demand limit. There is absolutely no spare available capacity. All effective income buys output at 0% inflation.

Then something happens... the tools are wearing out for each family at a rate that causes their production to fall by 2% in a year. Then we see this...

Each family can now only produce $98,000 per year. And their income drops to $98,000 too. Therefore, both aggregate supply and effective demand shift left to a new LRAS curve of a real GDP of $980,000.

(note: One might think inflation would appear due to the same amount of money chasing fewer goods. In this model, there is no inflation because the velocity of money is assumed to slow down by 2% according to the equation MV=PY. Otherwise there would be 2% inflation, if the velocity had stayed the same and the aggregate supply curve slides up the effective demand curve. Here is a graph to show how inflation might develop.)

## 90% labor share, 10% capital share

The families come together to discuss what to do. They decide that one of the families will dedicate itself to making new tools for the other 9 families to replace the tools that wear out. The cost to each family will be 10% of its income. So of their total income, they will pay themselves 90% and hold 10% for replacing capital tools. (90% labor income, 10% capital income)

We see this the next year... (note: this preliminary graph is incorrect. I only use it as a teaching device to distinguish the change in labor income from output. The correct graph resolves the error farther below.)

The two red dots show the result at 0% inflation. The economy is now producing real GDP of $1 million again because two years of depreciating tools were replaced (brown aggregate supply curve). The red dot of the effective demand line shows only $900,000 of labor income. The economy is producing $900,000 of finished goods and $100,000 of capital goods. Since the economy has created another industry for maintaining the means of production, they have less overall production of finished goods.

From the difference between the red dots, it looks as though there is more supply than demand. Will there be deflation? Will output be cut? Is the graph even correct? Is effective demand really just labor income?

What is the problem? In fact, the graph #3 above is incorrect. So, let's look more closely...

The 9 families that produce finished goods are working at 100% capacity utilization of their capital tools. Thus they can produce no more than $900,000 worth of finished goods. However, even though each family is running at 100% capacity utilization, the tribal economy as a whole is only running at 90% capacity utilization for the industry sector of finished goods. We realize that the 10th family still has the tools to produce finished goods. They now also have tools to produce capital goods. Therefore, 10% of the capacity to produce finished consumer goods is going unutilized by choice.

And we know from the definition of capacity utilization that it is calculated for given industry groups. In this light, we will see that the family/industry producing capital goods is also at 90% capacity utilization. That family receives 10% from the total real income of $900,000 of the other families. This $90,000 of income is only 90% of the 10th family's capacity to produce $100,000.

Now we can correctly re-draw the above graph...

Thus, the total GDP of the tribal economy is $990,000 ($900,000 finished consumer goods +
$90,000 capital goods) and it is running at 90% capacity utilization in aggregate for its various industry groups .... all with a labor
share of 90%.

## A change in labor share is automatically matched by capacity utilization

The above shows that when the economy created 10% capital share causing labor share to go from 100% to 90%, capacity utilization also dropped to the exact same level as labor share of income, 90%.

It is important to realize that this is the fundamental dynamic from which the equation for Effective demand is derived. If labor share can determine capacity utilization, then there is an effective demand limit based upon labor share that limits utilization rates of capital resources in any given industry.

Capacity utilization could fall below this new level of 90% implying that the tribal economy could go into recession, but capacity utilization would not rise above the 90%.

In graph #4, we see that the tribal economy is in a new equilibrium at the effective demand limit (the aggregate supply curve is crossing the effective demand curve at actual output, red dot). Even though there is 10% spare capacity, that 10% is unavailable to use because everyone is working (100% employment). I will do a future post to show the dynamic of how unemployment allows capacity utilization to rise above the labor share rate but still within the limit of effective demand.

(note: You may be thinking... What if the 10th family trashed their unneeded tools for producing finished goods. Then the economy would be running at 100% capacity utilization. On the contrary, they would most likely hold or even transfer their tools to the other 9 families. Those tools would become a 10% reserve capital capacity. If those reserve tools were used in production without being replaced, then the capacity utilization of the capital goods' family would go down from not having to work. The result would still be an overall capacity utilization of 90% for the tribal economy as a whole.)

(note: The equation for the Effective demand curve is... Effective demand = real GDP * labor share/(capacity utilization * employment rate)... The final effective demand above is ... ED = 990,000 * 90%/(90% * 100%) = 990,000. Thus effective demand equals real GDP output.)