The normal Taylor rule takes into account the difference between inflation and a target inflation, and output and a potential output. Economists are now dropping the output part of the rule because output is just not easy to measure for them.

But I will take a simple version of the Taylot rule and apply it to capital output and labor output.

First, capital output...

Interest rate of capital = N + p + a * (p - p*) + b * (c - c*)

N= natural rate of output growth

p= price inflation

p*= inflation target

c= capacity utilization

c*= target capacity utilization

a= coefficient, 0.5

b= coefficient, 0.5

Second, labor output...

Interest rate of labor = L + w + a * (w - w*) + b * (u - u*)

L= natural rate of growth in total labor hours

w= wage inflation

w*= target wage inflation

u= unemployment rate

u*= target unemployment rate (natural rate of unemployment)

a= 0.5

b= 0.5

In the first equation, the inflation and growth of production are considered.

In the second equation, the inflation and growth of labor income are considered.

How do these equations look over the years? Let's graph let next to the effective Fed funds rate...

Both of the equations echo the general path of the Fed rate which should be no surprise.

As the economy recovers from a recession, the interest rate of capital (orange) rises above the line for labor (green). In the past 2 recession, capital output makes a stronger initial comeback than labor income. Then labor income overtakes production before the next recession. We now see that labor income is overtaking capital which is a sign of the current business cycle coming to an end.