This is just a post for rearranging the equation of the effective demand real rate rule. It helps for understanding the equation better. Here is the equation...
Effective Demand real rate rule = z*(TFUR2 + ELS2) – (1 – z)*(TFUR + ELS)
z = (2*ELS + NR)/(2*(ELS2 + ELS))
TFUR = Total Factor Utilization Rate, (capacity utilization * (1 – unemployment rate)).
ELS = Effective Labor Share is Non-farm Labor Share: Business sector * 0.765. Equation for ELS = (7.5*previous quarter ELS + 2.5*2 quarters previous ELS)/10
NR = Natural real rate of interest of 3.0%. See highlighted in yellow at top of graph.
LRAS curve = ELS limit.
When z in substituted for its longer version in the equation, and then simplifed, the equation becomes this...
Effective Demand real rate rule = NR/2 + TFUR (z * TFUR + z -1)
NR/2 which is based on the ELS limit represents half of the natural real rate. The other half is calculated with the TFUR. I will take the equation and extend it out more.
NR/2 + (TFUR2 (ELS * NR + 2 *ELS2) + TFUR (NR - 2 *ELS2))/2(ELS + 1)
It's a complicated way to determine the other half of the natural real rate, but it determines the short term real rate in relation to where the economy is within the business cycle.