Keep in mind that these posts are preliminary steps to forming a new model in economics.

This post will add 3 more equations to the monetary framework.

In the previous post, I presented the 3 price spaces of the AS-ED model (aggregate supply-effective demand). The equations of these price spaces determine the inflation rate and the spare capacity below and above real GDP respectively. Here is a graph...

The equations only need 4 input variables... unemployment rate, capacity utilization, effective unit labor costs and effective labor share. From these four variables one can calculate the current inflation rate and the spare capacity to utilize labor and capital. (unit labor costs is the nominal share of real GDP... labor share is the real share of real GDP.)

It does not matter what the real GDP is; Once one draws the aggregate supply and effective demand curves in the model, one can calculate these price spaces solely based on the dynamics between existing factor utilization and labor share of national income.

These equations determine price levels and interest rates. Also, these equations exist apart from any level of real GDP or even potential real GDP. They are universal to any economy.

We now take the monetary policy framework that was presented before...

On the y-axis we have the interest rate. On the x-axis we have the TFUR (total factor utilization rate). The effective range of monetary policy is bounded by the LRAS curve and effective demand to the right and by where the path of the Fed rate crosses into negative territory to the left.

A crucial concept of this monetary framework is that it must be positioned over the range where the TFUR is moving. The whole framework is positioned in relation to the effective labor share anchor, which in the above graph is 80%. The TFUR will move below that point through the business cycle. In order to have an effective monetary policy, the framework must be positioned correctly.

We are going to reinforce the position of the framework with the 3 equations presented in the first graph above. Those equations all use the TFUR and they all calculate interest rates (price spaces). Thus those 3 equations can be plotted into the monetary framework graph... It looks like this...

This framework moves with the 4 variables mentioned above... unemployment rate, capacity utilization, effective unit labor costs and effective labor share. The framework now incorporates the price spaces of the AS-ED model. Therefore the AS-ED model and this monetary framework model have been integrated. Information from one directly transfers to the other.

I want to emphasize something which may not be obvious. The 3 equations for price spaces confirm and reinforce the positioning of the monetary framework. I said before that the effective labor share anchors the LRAS curve and that the TFUR will move to the left of the LRAS curve. In this graph above, the 3 equations from the AS-ED model confirm the LRAS curve. How? The spare capacity line crosses the x-axis at the LRAS curve. The inflation rate line and the Price level of effective demand line cross at the LRAS curve. (Note also that these lines cross at the currently measured inflation rate.)

The framework itself does not depend on the z coefficient nor the inflation target. Those variables are only used for aligning monetary policy with the framework. The framework represents existing dynamics within the economy. If monetary policy is not functioning within this framework, it will be ineffective.

I will now add in the lines that determine the path of the Fed rate. I will use a z coefficient appropriate to establish a viable and effective monetary policy over the business cycle. And I will use a standard inflation target of 2%. And I will use current values for effective labor share and effective unit labor costs.

The two lines added are the violet line of the path of the Fed rate and the yellow line of the effective demand limit. These two lines also cross at the LRAS curve confirming the effective labor share anchor. We can see the effective range of the Fed rate extends from the LRAS curve to the point where the path of the Fed rate goes into negative territory. As long as the effective labor share stays steady around 74%, this will be the effective framework for monetary policy to regulate and stabilize the price spaces of the economy.

The red dot shows where the Fed rate would be right now if this framework were being used. The current TFUR is 72%. The Fed rate would be around 4%. Yet the current Fed rate is almost 0%, because economists think that the economy should return to where it was before the crisis. They are in a group delusion. They cannot accept the fact that the dynamics of the economy have shifted to a lower level and must now function at that lower level.

The current low Fed rate of 0% is destabilizing the economy. Safe assets are not desired. And we are now in the part of the business cycle where bubbles can form.

I will end by giving the equations for the lines in the monetary policy & framework and the equations for the aggregate supply and effective demand curves...

Path of Fed rate = z*(TFUR^{2}+els^{2}) - (1-z)*(TFUR+els) - inflation target

Effective demand limit = 2*z*TFUR^{2} - 2*(1-z)*TFUR - inflation target

Reflective Fed rate = els*(els-TFUR)/(1+TFUR)

Inflation rate for price space = (ulc_{e}-els)/TFUR (note: This inflation rate = measured inflation rate * (1 + spare capacity). When spare capacity is high at the bottom of the business cycle, this inflation rate includes a premium potential. This inflation rate will converge with the measured inflation at the LRAS curve.)

Price level of effective demand = (ulc_{e}-TFUR)/TFUR

Spare capacity = (els-TFUR)/TFUR

Inflation rate for price space = Price level of effective demand - Spare capacity

Aggregate supply curve = Potential real GDP + a * (cu - els)/els

Effective demand curve = real GDP * els/TFUR

els = effective labor share = (labor share: business sector, 2005=100) * 0.78

ulc_{e} = effective unit labor costs = effective labor share * (1+inflation rate)

TFUR = capacity utilization rate * (1 - unemployment rate)

z is a coefficient for positioning the Fed rate path

cu = capacity utilization

a = amplitude coefficient of business cycle in terms of real dollars according to a base year.

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