This page was last updated on October 22, 2016.

My research into effective demand began in October 2012. The research has expanded to including economic growth models and monetary frameworks.

This page gives a brief synopsis of the effective demand research.

## What is Effective Demand?

Effective demand is a measure of the demand limit upon the utilization of labor and capital. This effective demand limit predicts when profit rates will begin to turn downward in a business cycle. This effective demand limit determines the output gap and spare capacity.

Keynes described effective demand as a point where the aggregate demand function and the aggregate supply function intersect, but where the aggregate demand function effectively limits aggregate supply. This point can keep utilization of labor and capital from reaching full-employment. This concept contradicts Say's law that says "supply creates its own demand". Effective demand rather says "demand ultimately creates its own supply". Effective demand ultimately determines the full utilization of labor and capital in a business cycle.

Keynes wrote about Effective Demand in the General Theory, chapter 3, which was entitled *The Principle of Effective Demand*. He did not give a specific equation for effective demand which left it up to future economists to figure out an equation. My work is an effort to figure out the models of effective demand.

## Basic principles of effective demand

The effective demand limit determines a maximum for the percentage utilization of labor and capital in production. Thus, the effective demand limit establishes a constraint upon the utilization rates of labor and capital. (T in the equations below)

The utilization of labor is represented by the unemployment rate. The utilization of capital is the capacity utilization rate.

The basic principle is that profits will be maximized at the effective demand limit.

The main principle behind an effective demand limit is aggregate capital income begins to consume itself beyond the effective demand limit. Capital will protect its position in the aggregate by limiting utilization of labor and capital. Capital income seeks to maximize its relative strength in the economy. The effective demand limit reflects that maximization.

Another principle is that Real GDP production tends to settle into an attractor state around the combined utilization of labor and capital. The attractor state points toward a stable level of Productive Capacity during the growth phase of the business cycle. Ultimately the combined utilization of labor and capital is limited by an effective labor share measure. Then Real GDP lifts off of the attractor state and starts heading toward a higher attractor state.

Another principle is that as labor share drops, the optimum utilization level of capital drops too. Capital utilization is optimized macro-economically at the effective demand limit established by labor share. Aggregate production can still increase beyond that point. Eventually, the combined utilization of labor and capital falls from optimum levels toward a recession. (see post on Circular Flow of Labor & Capital)

1. The utilization of available labor & capital depends upon the share that labor receives from total value-added income.

2. After a recession, when the utilization of labor and capital is below the effective demand limit, there is profit incentive for businesses in the aggregate to utilize more labor and more capital.

3. When the utilization of labor and capital hits the effective demand limit, the utilization of capital is optimized. Then there is profit incentive for businesses in the aggregate to utilize more labor and LESS capital.

4. After the utilization of labor and capital hits the effective demand limit, over time a recession will form. Profits have been maximized and start to decrease. Businesses in the aggregate will begin to utilize LESS labor and LESS capital.

## Equations for the effective demand limit

Basic Effective Demand Limit, L = LSI*0.76

LSI = labor share index (non-farm business sector), 2009 base year

Effective demand limit upon real GDP = rGDP*e*T/L* (1 - (1 - 1/e)*T/L)

T = capacity utilization * (1 - unemployment rate)

T is also called TFUR in the graphs below. (total factor utilization rate)

L = an effective demand limit function from above

e = (3.3*natural real rate + 3) ...(coefficient matches bottom of short-run real interest rate with unstable equilibrium and sets maximum of effective demand at the stable equilibrium in graph below. Link to post. )

The above equation for the Effective Demand limit upon real GDP has the following model with stable and unstable equilibriums. The straight up-sloping line goes to the economy's Productive Capacity at 100% TFUR. The red dot marks where effective demand caps aggregate demand which then limits aggregate supply in terms of the utilization rates of labor and capital.

UT index, UT = L - T

UT index stays above zero using Basic Effective Demand Limit equation.

As the utilization of capital and labor rise in the business cycle, past data shows that they eventually reach the effective demand limit (L). T stops rising and will fall.

Here is the graph to show the UT index of the effective demand limit. The combined utilization of labor and capital stays below the effective labor share limit.

## Better Model for the Output Gap

In this effective demand research, I calculate the output gap by comparing capacity utilization to the effective labor share.

Output Gap = 2800*(capacity utilization/L -1)

This equation gives a reliable view of when the output gap is peaking in a business cycle.

As the official output gap has been continuously revised up since 2009, the effective demand model has stayed within its normal range without revision. In real terms, the output gap peaks between $100 and $200 billion.

## Equation for a Monetary Rule

Effective Demand Monetary rule, ED rule rate = z(T^{2} + L^{2}) - ( 1 - z)*(T + L) + (1+a)C + aCv - 2aCt

z = (2*L + Natural real rate)/(2L^{2} + 2L)

This effective demand monetary rule is divided into two parts. One for the short-term real rate and one for the central bank's reaction function to inflation.

Short-term real rate = z(T^{2} + L^{2}) - ( 1 - z)*(T + L)

Inflation reaction function = (1+a)C + aCv - 2aCt

Ct = long-term desired core inflation target. Also, NGDP price level target.

Cv = core inflation averaged back over time. I use the previous 3 years.

C = current core inflation rate

a = weighting coefficient. I use a = 0.5. If a is zero, then a central bank has no response to manipulate inflation. The central bank would add the value of current inflation to the short-term real rate. As a increases, a central bank would react more strongly to manipulate inflation back to its price level target, Ct.

Effective Demand Monetary rule is designed to maintain a nominal GDP target over time. (see this post).

This graph compares the actual Fed rate with the prescribed rate from the Effective Demand Monetary rule.

## Cobra Equation relating Utilization of Labor and Capital

As the business cycle recovers after a contraction, both the utilization rates of labor and capital increase. But there comes a point where the utilization of capital will stop increasing or fall, while the utilization of labor keeps increasing or falling. This point reflects an optimum use of capital as I show below.

How can this relationship be put into an equation?

The following 3-dimensional equation which looks like a cobra in 3-dimension, gives a value for a z-vertical.

As the z-vertical rises the business cycle keeps progressing. The goal is to keep increasing the z-vertical as long as possible through a business cycle. The maximum of the z-vertical shows another version of an effective demand limit.

z-vertical = (m + k - am^{2}k^{2})/L

m = (1 - unemployment rate)

k = capacity utilization rate

a = 1.46 - L ... (L = 0.76 * labor share index)

The maximum of this equation in terms of employment of labor is...

Max of z-vertical = √1/2ak

In 2015, capacity utilization fell while the utilization of labor increased (unemployment fell). The equation predicted this.

The following is a graph measuring the height of the z-vertical which becomes associated with the after-tax corporate profit rates.

Here is the z-vertical regressed and fitted to actual after-tax corporate profit rates.

Calculated regressed z-vertical for after-tax corp profit rate = 0.344*(m + k - am^{2}k^{2})/L - 0.524

The derivatives of the z-vertical equation show optimization of capital and labor. A derivative at zero means optimum utilization.

First, the derivative in terms of capital.

Capital utilization is always brought to its optimum during a business cycle in a developed country. That is the priority of capital income at the center of the circular model. Capital has the advantage over labor. The 2 preceding graphs imply that after-tax corporate profit rates are maximized when capital is optimized.

(Note: In an undeveloped country which does not have enough capital for the labor force, the model predicts that labor would be optimized more than capital. This is due to the cobra's head having a left side and a right side.)

Now, the derivative in terms of labor.

Unlike capital, labor never reaches its optimum utilization since it never reaches zero in the graph. **Capital comes first in capitalism.** And since the 1990's, the utilization of labor has been getting worse as seen by the plot steadily trending upward. The increasingly unmet potential of labor utilization coupled with lower labor share is a problem. The US is becoming over-capitalized in relation to the labor force. Supply-side economics can be partly blamed for this?

Capital has not lost its advantages while labor has.