Effective Demand Research

Limit of capacity utilization

 Capacity utilization has a limit expressed with this equation...

labor share index*0.76/(1 - unemployment rate)

The reason for this limit is found in the balance between labor and capital. The real share to labor is expressed by the limit. If capacity utilization goes over that share, then capitalists begin to consume their own income for production. The result is falling profits in the aggregate.

Answering a question about Effective Demand

On the Angry Bear blog, a commenter named Axt113 asked about effective demand. I referred him to Chapter 3 of Keynes' General Theory... He responded.

Okay, I found the section, it says:

“The value of D at the point of the aggregate demand function, where it is intersected by the aggregate supply function, will be called the effective demand.”

Okay, so effective demand is the equilibrium point of aggregate supply and aggregate demand, but that implies that shifts to aggregate demand and aggregate supply ( in the short run), will change effective demand.

So wouldn’t increasing aggregate demand, by higher wages shift effective demand upwards?

Here is my response...

Don’t confuse the AS-AD model that we normally learn with the model that Keynes is presenting in that section.
The normal model puts AS = AD at any point in time. The lines always cross. What is consumed equals what is supplied.
Now Keynes model puts demand above supply at any point in time. Demand above supply gives entrepreneurs incentive to employ more labor and capital. Yet, the difference between demand and supply gets smaller as more labor and capital are utilized. So imagine two lines that meet at some distant point. One line is demand above the other line of supply. The point at which these two lines meet is effective demand. If we see the point as stationary, then as you employ more labor and capital beyond the point, demand will go below supply. Then entrepreneurs will un-employ labor and capital.

So the normal model has AS and AD moving together. In Keynes model, the economy is moving toward a “fixed” long run equilibrium state between supply and demand.

Now, you are asking if increases in wages can shift that stationary point of effective demand… I would say Yes, as long as labor’s share of national income rises.
Let me explain my model… put price on the y-axis to show what is supplied and demanded. But on the x-axis put the utilization of labor and capital. The x-axis now represents how the economy grows by utilizing more labor and capital. As you move right on the x-axis, you utilize more labor and capital with the demand line higher than the supply line. Eventually you reach the equilibrium point between supply and demand. The equilibrium level of effective demand on the y-axis is the top side of potential GDP. That is the effective demand point that Keynes describes…. beyond which employment of more labor is not wanted by firms.
For me, that equilibrium point is determined by labor’s share of national income… Not by labor’s total income, but by labor’s % share. Very different concept.

Now what could shift that equilibrium point upward? There are many ways… I will give 2.
1. We could raise labor’s share. That would shift the demand up, sliding the equilibrium point up and to the right along the supply curve. ultimate potential GDP is raised and the natural rate of unemployment is raised.
2. We could just raise wages. But now that would shift the demand curve to the right, but also shift the supply curve to the left. So you may end up simply increasing the total amount at the equilibrium point as seen on the y-axis. Yet, the top limit for utilizing labor and capital seen on the x-axis has not changed. Your level of full employment has not changed.

What can cause that equilibrium point of effective demand to fall?
This is what happened after the crisis… labor share fell. The demand curve shifted to the left. The result was that the equilibrium point now reflects a lower total value of the economy (GDP on y-axis) and a lower full employment level of labor and capital (higher natural unemployment and lower capacity utilization on x-axis). Potential GDP also fell.

OK… now does raising wages raise the effective demand limit? That depends on how you measure the effective demand limit, either by the y-axis or the x-axis. You could see GDP increasing (y-axis), but the natural level of unemployment has not changed (x-axis).
For me, effective demand must be primarily determined by the x-axis. The x-axis reflects Keynes’ focus in Chapter 3 on the rate of employment of labor to describe the effective demand limit.

So when you say that raising wages should raise the effective demand limit, we need to study the effect to know how. Did potential GDP rise? Did the natural rate of unemployment rise? You could get different answers to those questions.

Labor Share affects the potential of investment to raise GDP

The circular flow is a model used to show how money and products move in the economy. I am going to use a simplified version to show the effect of changes in labor share of income. Many people think that labor income is not quantitatively different than capital income. I will show that GDP is affected by labor share of income.

Basic Equilibrium

Let's start out with a basic model. It will only involve owners of labor, owners of capital, firms and a financial sector. The only injection into the circular flow will be investment. The only leakage from the circular flow will be savings. The model does not include the government sector nor imports and exports.

Graph #1

Start at the out-going income from firms. Firms are paying out $1 million in income. 80% will go to labor (labor share of income of 80%). 20% will go to capital (capital share of 20%). The GDI (gross domestic income) of the economy is $1 million. Capital takes all of their income and saves it for investment. Labor takes 85% of their income and consumes production (marginal propensity to consume of 85%). Labor takes the remaining 15% of their income and puts it into savings.

Capital savings and labor savings then add together for the total of savings in the economy. Then those savings are invested in firms to maintain and increase the means of production. Consumption is directed at the finished goods and services produced from the capital used in the means of production. The in-coming money to firms is the sum of investment and labor's consumption.

In the graph above, the economy is in equilibrium. (Savings = investment) (In-coming = out-going)

In equilibrium...

GDP = consumption + investment

GDI = labor income + capital income

GDP = GDI

Investment rises

Money increases in the economy when banks make loans using a fractional reserve system. The banks can lend out more money than they have in reserves. This is how money is created in the economy. Banks can just create money when they make loans. So now we can change the graph above to show an increased level of investment by banks.

Graph #2

Look in the green boxes. Investment has risen to $520 thousand from $320 thousand. Investment is injecting an extra $200 thousand into the economy. Maybe QE is finally providing liquidity. The result is that there is now $1.2 million in-coming to the firms. Consumption has not changed because the extra investment has not been paid out as income yet.

The economy is going into a disequilibrium. (Savings ≠ investment) (In-coming ≠ out-going)

Firms now pay out that in-coming $1.2 million as income maintaining the same labor share of 80% and capital share of 20%. We allow that money to flow through the economy. Let's see what we end up with.

Graph #3

We see the out-going $1.2 million go through the circular flow and leads to a total savings of $384 thousand, which is still less than the investment level. Consumption has risen to $816 thousand. Total in-coming into firms from the increased level of investment and the new increased consumption is now $1.336 million.

The economy is still not in equilibrium. (Savings ≠ investment) (In-coming ≠ out-going)

Firms now pay out the increased in-coming money of $1.336 million in another round as income to labor and capital.

Graph #4

We see that total savings continues to increase and that consumption continues to increase. The in-coming money to firms continues to increase. And so the economy goes through numerous rounds with the increased investment until equilibrium is reached. Here is what the economy will look like once it reaches equilibrium, where (Savings = investment) and (In-coming = out-going).

Graph #5

The important thing to see in this moment is that GDI (gross domestic income) has increased to $1.625 million from the original increased investment of $200 thousand.

But now let me ask you... What equilibrium level of GDI would this model have reached if labor share of income had fallen to 75%? If you think there is no quantitative difference between labor and capital income, then the resulting GDI should be the same.

Lowering labor's share of income

I will now lower labor's share of income in the model. Why? Because labor's share of income has fallen 5% since the crisis. This fall is unprecedented. And I present a simplified simulation of how that fall in labor share affects investment... and how it affects the efficacy of quantitative easing... cough cough.

I will simply change labor's share to 75% using the increased level of investment of $520 thousand. Then I will solve for the equilibrium level of GDI. Here it is...

Graph #6

GDI has fallen from $1.625 million to a lower equilibrium of $1.434 million. We can see that the economy is in equilibrium (Savings = investment) and (In-coming = out-going). The only difference was lowering labor's share to 75%.

Conclusions

1. After the crisis, labor's share of income fell 5%. The result is that the ability of investment to increase GDI or GDP output is muted. Investment has had less power to boost GDP. 
2. Investment returns to firms in smaller amounts. Firms receive less in-coming money.
3. Labor's consumption and labor's savings have decreased. This would be obvious from lower labor share and lower GDI.
4. Look closely at the capital income in graphs #5 and #6. In graph #6, capital's income has actually risen, in spite of GDI falling. This model shows how capital income and corporate profits can reach record heights while Main street struggles.
5. A lower labor share affects the efficacy of loose monetary policy. How can you expect loose monetary policy to put money in the hands of people when the falling labor share is taking money out of their hands? And any increased investment results in more upside for capital income with more downside for labor's income.
6. Loose monetary policy is heading toward a lower equilibrium level of GDP due to the lower labor share. Why has the economy responded so poorly to loose monetary policy? We can clearly see above that a lower labor share mutes the potential of investment to raise GDP.

Note: There is more that can be done with this model.

1. Effective demand limits can be incorporated.
2. The adjustments of monetary policy to these dynamics can be incorporated.
3. We would also find that unemployment's natural rate would be higher if we associate the rise in real GDP with utilization of labor and capital. Once GDP is limited to a lower level by a lower labor share, employment also gets limited. (My view is that the natural rate of unemployment has risen to around 7% due to the fall in labor share.)

The Proof of Effective Demand: Incorporating Unemployment & the NAIRU

Effective demand, as presented in this blog, needs a proof. I have shown equations, a growth model, a framework for monetary policy, a rise in the natural rate of unemployment and more. But underneath all that is still the question/doubt... Does Effective demand really exist in the economy? Is it a fundamental dynamic? Or is it just a figment of a wild imagination?

The goal now is to present a basic model to prove Effective demand. I will use the Effective demand - Aggregate supply model, which offers dynamics not present in the traditional Aggregate demand - aggregate supply model... dynamics like the NAIRU, the Phillips curve, self-correcting mechanisms around the LRAS curve.

It would obviously be helpful for the wolves of economics to detect weakness in the argument and attack. Then we try to resolve the weakness if possible. But this is a natural process of developing new models. Some hold water, some don't. So let's go...

I gave a simple preliminary proof involving just capacity utilization and labor share of income. That proof showed how a decrease in labor share was matched by a decrease in capital utilization due to a portion of production being retained for capital maintenance. Yet, Effective demand is based not only on utilization of capital, but also on utilization of labor... namely unemployment. So now I need to incorporate unemployment into the proof.

Looking at Unemployment in relation to Capacity utilization and Labor share

 In the preliminary proof involving only capacity utilization and labor share, I showed a model where changes in labor share are matched by a changes in capacity utilization. But we know that capacity utilization moves up and down through the business cycle, while labor share stays more constant. So they don't walk hand in hand, but rather capacity utilization orbits around labor share. I use the following equation to measure how capacity utilization orbits around labor share...

% swing of Cap. Util. = (cu - els)/els

cu = capacity utilization... els = effective labor share, (Labor share: business sector, 2005=100) * 0.78. By multiplying labor share by 0.78 we obtain the central tendency line. (See previous post.)

Let's graph this relationship for data since 1967...

Graph #1

Normally capacity utilization rises above and below the level of effective labor share by less than 10% both ways. This relationship shows a view of the business cycle. I have already shown a proof that capacity utilization stays close to labor share... but what limits the movement of capacity utilization to within 10% of effective labor share?

The model of effective demand says that the limits of capacity utilization are determined by the unemployment rate. So now let's graph the unemployment rate against the values in the above graph.

Graph #2

The blue dots show the plot before 2010. The pink dots show a higher unemployment rate since 2010, but I am not interested in why the pinks dots shifted in this proof. I want to show that unemployment increases as capacity utilization falls below effective labor share (move to left) and falls when capacity utilization rises above effective labor share (move to right). Specifically, I want to focus on the data to the far right, in the Effective demand limit zone. The principle of Effective demand says that as the economy utilizes more labor and capital, a limit is reached where further utilization of labor and capital is not profitable and has costs that limit further utilization of labor and capital.

In the Effective demand limit zone, the data is tighter. Are the dynamics of capacity utilization and unemployment constrained when capacity utilization nears the limit of an expansionary phase of the business cycle? The following model will seek to explain unemployment's role in the effective demand limit zone.

100% labor share, 6% unemployment, 100% capacity utilization

I will start with a scenario with 100% labor share of income and 100% capacity utilization. This scenario is similar to the preliminary proof, but the difference is that now we have 6% unemployment. Why 6%? In graph #2 above, the tendency line shows that when capacity utilization is equal to labor share, unemployment has a "natural rate" of 6%. We see this from the y-intercept of the tendency line equation. The implication is that... in the middle of the business cycle, when capacity utilization is between its high and low in relation to effective labor share, there is a natural rate of unemployment of 6%.

6% unemployment will respresent the normal natural rate of unemployment in this model. It includes structural, frictional and some cyclical unemployment. It is not the natural rate of unemployment when the economy reaches the effective demand limit. That is another rate that I will include in this proof later.

So let's start the proof... We have a tribe of ten families (businesses) that produce finished goods and services for needs of individuals, like food, clothing, ritual items, etc... Each family produces $100,000 worth of goods or services. Thus, the real output is $1 million. All capital is being used in the production. 6% of the population which is able to work is unemployed for various normal reasons. Here is a graph of the economy using the Aggregate supply - Effective demand model (AS-ED). (inflation rate of 0%)

Graph #3

The bottom red dot shows that the tribe is producing $1 million of output at 0% inflation. Income and output are equal for finished goods and services. The upper red dot is showing that there is spare capacity of 6.4%, which comes from 6% of the able-bodied workers unemployed. Thus, there will always be spare capacity in the tribe, as long as there is natural unemployment.

We can see the LRAS zone stretching from the crossing point of the two lines to where the effective demand curve crosses the x-axis. The LRAS zone drops a little below the effective demand limit curve because if real GDP gets close to the effective demand limit, the dynamics of LRAS curve (long-run aggregate supply) begin to show effect.

At this point the tribe will never reach the LRAS zone because in essence they are running at full-capacity. They are running at Productive full Capacity (full employment) because capacity utilization is at 100%.

Then the families realize that their capital equipment is wearing out causing their productive capacity to decrease by 2% year over year. They see that they are producing less, $980,000.

Graph #4

The families come together and discuss what to do. They decide that one of the families will devote itself to fabricating and maintaining the capital equipment for the other 9 families. The 9 families will retain 10% of their income to pay the 10th family for capital upkeep. The result is that...

1. The decline in capital equipment will stop and returns to its previous level of productive capacity.
2. 10% of the productive capacity of finished goods & services will go un-utilized.
3. $100,000 productive capacity for an industry of capital goods is added to the tribe.
4. Labor share will drop from 100% to 90%.

90% Labor share, 6% unemployment, 100% Capacity utilization

If we tried to keep all capital at 100% utilization, the tribal economy would look like this...

Graph #5

Output is $1.1 million, but we see that output is over the effective demand limit. The Model of Effective Demand states that real output doesn't rise much over the effective demand limit. So what is happening in the tribal economy to confirm this?

This scenario is impossible, because in order for the tribe to utilize 100% of their capital maintaining with 6% unemployment, the 10th family would have to be producing finished goods and capital equipment. Without lowering unemployment, they cannot do that.

So, let's decrease capital utilization to 90%, since in fact, 9 of the 10 families is now producing finished goods. 10% of the capital capacity for the industry of finished goods is not being utilized. The economy actually looks like this.

Graph #6

Productive capacity for the tribe is now $1.1 million, but they can only utilize 90% of the productive capital. The real output is now $990,000. Of the $900,000 income of finished goods, 10% or $90,000 goes to the 10th family bringing total output for both industries to $990,000 (as seen in graph #6). $810,000 of the income from the 9 families is kept as labor income for purchasing finished goods for their personal needs. The $90,000 income of the 10th family is now spent on finished goods for them. Thus, the finished goods industry made and sold = $900,000. The capital equipment industry fabricated or maintained $90,000 worth of real output.

We still see spare capacity of 6.4% because of the 6% unemployment. But wait, we have un-utilized capital, and we have un-utilized labor. What if some of those unemployed workers could be employed to produce with the un-utilized capital?

90% Labor share, 5% Unemployment, 94% Capacity utilization

The tribal economy now employs 1% of the 6% unemployed. In so doing they are able to utilize 4% more of their capital capacity. The equation used to determine the increase in capacity utilization from lowering unemployment is found in graph #2 above...

Unemployment = - 21.3 * (cu - els)/els + 6.00

Unemployment = -21.3 * (0.94 - 0.90)/0.90 + 6.00 = 5.05  ..... 5.05%

cu = capacity utilization (94%)... els = effective labor share (90%).

The equation is based on observed data from the United States from 1967 to 2010. Now we graph the tribal economy with this increased utilization of labor and capital.

Graph #7

As you can see, almost all of the spare capacity was used up according to the Effective demand equation.  The real output has now increased to $1.034 million. If this tribe were the United States between 1967 and 2010, a 5% unemployment rate would signal the NAIRU (Non-Accelerating Inflation Rate of Unemployment). Unemployment below 5% would trigger accelerating inflation without lasting growth in real output. The NAIRU sits in the LRAS zone. We can see in Graph #7 that the red dots are entering the LRAS zone.

(note: There are 2 natural rates of unemployment in this model. One corresponds to the middle of the business cycle, when capacity utilization equals effective labor share. The second corresponds to the NAIRU, when the utilization of labor and capital hit the LRAS zone. The dynamics are different at each natural rate.)

The graph shows very little spare capacity, but we know that there is much more spare capacity because there are 5% unemployed workers and 6% unemployed capital equipment. So then why does the model show very little spare capacity? The effective demand limit curve shows the spare capacity up to the LRAS zone where we find the NAIRU. The Effective demand curve shows available spare capacity that is natural to the economy. Once you use up more than the effective demand spare capacity, we begin to see the dynamics of the Phillips curve (see video by Chris Rodda). There will be wage inflation and lower employment in the short run, but unemployment will return to the NAIRU leaving the wage inflation in place.

Effective Demand model shows dynamic of Phillips curve

We can see how the Phillips curve can manifest in this model by pushing the unemployment rate below the 5% NAIRU to 4%? The economy would move to the blue lines in the following graph...

Graph #8

In graph #8, we see that the tribe is almost producing at the productive capacity of $1.1 million (98.5% capacity utilization). However, the equilibrium limit of effective demand and aggregate supply goes negative to around -4% (see crossing point of blue lines). In effect, the economy is pushing beyond its "natural" limits... beyond the "Effective Demand" limit. As the equilibrium point goes negative (or below the expected inflation rate if not 0%), pressures of wage inflation progressively build ultimately raising inflation expectations. Ultimately in graph #8, the consequence for going below the 5% NAIRU is an inflation rate that builds up to at least 4% in order to keep the equilibrium price dynamic above 0% (or the expected inflation rate if not 0%). The brown lines show the 4% shift upwards. The equilibrium between aggregate supply and effective demand goes back above 0% (see where brown lines cross).

Taking unemployment so low requires nominal wages to rise to induce some unemployed to work and to bid good workers away from other enterprises. Prices will also rise.

If inflation does not develop, the velocity of money will have to increase. However, if the velocity stays constant, then there will be inflation.

Why is it important to keep the equilibrium point of the AS-ED model above the current inflation rate? In this situation, spare capacity goes negative. There is pressure to raise wages, which will cut into aggregate profit rates. There is a reason why unemployment rates lower than 5% create wage inflation and price spirals.

"Workers would be better paid, and the assumption is that they would consume more. But they would also produce more output, which would tend to depress prices for goods. The loser, in this scenario, would be profits. Companies would be unable to raise prices, as competition for sales would prohibit it. They would be unable to cut wages, as competition for workers would prohibit it. Therefore, their profits would shrink. This would reduce the amounts they were willing to pay for capital goods, and tend to reduce demand for labor in those industries which primarily produce such goods. Thus, high economic growth with a stable money supply would lead to high wages, low profits, more resources allocated to production of consumer goods, and fewer resources allocated to production of producer goods. This should be a self-liquidating phenomena." (source, wikipedia)

As more production goes into producing finished goods in our tribal society, there is an associated raise in effective labor share, which cuts into profits as well. In order for labor share to stay in balance with rising capacity utilization, nominal wages would want to rise by 5% in graph #8. Businesses will not tolerate this situation for long if there is not extra money being pumped into the economy.

According to the dynamics of the Phillips curve, unemployment below the NAIRU and its associated increase in output will be temporary but the resulting inflation from increased nominal wages will remain. So eventually in the above graph #8, unemployment will return to 5% and real output will return to $1.034 million. But the new expected inflation rate will remain. Here is a graph showing the return to the NAIRU with two possible outcomes, an inflation rate of 0% and one of 4%.

Graph #9 

We can see in this graph that real output and unemployment fell back to the other side of the effective demand limit curve. Thus the effective demand limit curve reflects the dynamics of the Phillips curve. There is a self-correcting mechanism to keep real GDP below the effective demand curve.

There are reasons for real output to stay below the effective demand limit curve. Two principle reasons are that unit labor costs rise and aggregate profit rates decrease.

Summary

We started the tribal economy with a natural unemployment rate of 6% based on the cyclical movement between capacity utilization and labor share of income. The 6% natural unemployment at full capacity with 100% labor share kept their economy from experiencing inflation from competing workers. The capital equipment began to wear out, so the families decided to retain 10% of their profits as capital income to maintain their capital equipment. The result was a 10% drop in the capacity utilization of the whole economy from 100% to 90%. With the appearance of spare capital equipment, some of the unemployed were induced to work. There were not enough unemployed to raise capacity utilization back up to 100%. But the tribe was able to lower the unemployment rate to 5% to achieve a higher capacity utilization rate of 94%. The tribal economy could sustain that level without inflation sitting on the edge of the LRAS zone. But then they induced more workers to work with higher nominal wages. The unemployment rate dropped to 4% and the capacity utilization rate went to 98.5%, but the cost of entering into the LRAS zone was ultimately an inflation rate of 4%.

So where is the proof? The proof is that the dynamics of the Effective demand model describe actual data from the United States economy from 1967 to 2010.  I simulated data from the US economy. I used a hypothetical tribal economy with a different level of real GDP, capacity utilization and labor share. But the model still worked by describing the effects as increased utilization of spare capacity turns into inflationary pressures as described by the Phillips curve. If the numbers had changed, the dynamics would still have been the same.

Here are the equations for the curves in the model. The price level is isolated for the graphs.

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

Since, effective labor share = effective unit labor costs/(1 + price level)...

Effective demand = real GDP * (eulc/(1 + price level))/(cu * (1 - u))

Also...

Aggregate supply = Productive capacity * els + a * (cu - els)/els

Aggregate supply = Productive capacity * (eulc/(1 + price level)) + a * (cu - eulc/(1 + price level))/(eulc/(1 + price level))

u = unemployment...
cu = capacity utilization...
els = effective labor share, (Labor share: business sector, 2005=100) * 0.78. By multiplying labor share by 0.78 we obtain the central tendency line. (See previous post.)...  
Effective unit labor costs (eulc) = nominal labor income/real GDP output...
a = business cycle amplitude constant in terms of real $$ from a base year. $300,000 was used for the above graphs. A higher constant gives the aggregate supply curve a less steep slope.

Other cited source...

Rodda, Chris. The NAIRU.mov, Youtube channel, 6/2/2013, http://www.youtube.com/watch?v=zajMQzFTCNA

Effective Demand Basics: Capacity utilization adjusts with Labor share

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.)