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...

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

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