This refers to the aggregate demand and supply interaction based on the simplified IS-LM interaction influencing the aggregate demand (AD) and the labour market and the capital cost influencing the short-run aggregate supply (AS). These curves are composed of the two main parameters, the aggregate income level and the price level, as well as the money supply (MS) basing the IS-LM, and the wage index (W) basing the labour market.
# Default Parameters
import random
Y=[20,30] # The aggregate income level: Change here to see each effect
P=[100,102] # The price level: Change here to see each effect
W=[10]
WB=0.2
MS=[100]
rHD=10
CapCost=[10]
# Function representing the price inflation
def PrInf():
return ((P[-1]-P[-2])/P[-2])
PrInf()
# Higher function
# The aggregate demand influence
def Y_Inv(MSlmis,Ylmis,dp):
r_MS=pow(MSlmis/10,-1.05)+rHD*(PrInf()) #LM side
return pow(Ylmis,-1*(r_MS-PrInf())) #IS-side
Y_Inv(MS[-1],Y[-1],PrInf())
# A part of the short-run aggregate supply influence (The Labour Market).
def Y_Lab(Wlab,Plab):
return (50-(50/(Wlab/Plab)))/100
Y_Lab(W[-1],1+PrInf()+0.000001)
def AggregateDemandCurve(Ydd):
Pd=Y_Inv(MS,Ydd)/Ydd
return Pd
def AggregateSupplyCurve(Wlab,Plab,Css):
Ps=Css+Y_Lab(Wlab,Plab)
return Ps
def AggregateSupplyCurveShift(Y1,Y2,Pinv):
dp=(Y_Inv(MS[-1],Y1,Pinv))-(Y_Inv(MS[-1],Y2,Pinv)) #AggregateDemandCurve(Yd1)-AggregateDemandCurve(Yd2)
return dp
print(Y_Inv(MS[-1],Y[-1],PrInf()),Y[-1],PrInf())
print(Y_Inv(MS[-1],Y[-2],PrInf()),Y[-2],PrInf())
AggregateSupplyCurveShift(Y[-1],Y[-2],PrInf())
def AggregateDemandCurveShift(Y1,Y2,Wlab,Plab,Csd):
dp = (Csd+(Y_Lab(Wlab,Plab)*(1+WB*(Y1-Y2)/Y2)))-(Csd+Y_Lab(Wlab,Plab)) #AggregateSupplyCurve(Yd1)-AggregateSupplyCurve(Yd2)
return dp
print(CapCost[-1]+(Y_Lab(W[-1],PrInf())*(1+WB*(Y[-1]-Y[-2])/Y[-2])))
print(CapCost[-1]+Y_Lab(W[-1],PrInf()))
AggregateDemandCurveShift(Y[-1],Y[-2],W[-1],PrInf(),CapCost[-1])
# Calculating the average aggregate income level across all over the time period to generate the long-run aggregate supply interaction
def Ymean():
Ysum=0
for i in range(len(Y)):
Ysum=Ysum+Y[i]
return Ysum/len(Y)
Ymean()
# Main function: The interaction of the aggregate demand and the short-run aggregate supply
def Shift1(MSlmis=MS,Y1=Y[-1],Y2=Y[-2],Wlab=W,Plab=PrInf(),Csd=CapCost[-1],Pinv=PrInf()):
OutputGap=Y[-1]-Ymean()
PriceInflation=((P[-1]-P[-2])/P[-2])
if (OutputGap>0.05) & (PriceInflation>0.0001): # Positive Inflation
dP=AggregateDemandCurveShift(Y1,Y2,Wlab,Plab,Csd)
P.append(P[-1]*(1+dP))
print(dP)
MS.append(MS[-1]*(1+OutputGap/Ymean()))
print(MS[-1])
Y.append(Y[-1]*(1+(Y_Inv(MS[-1],Y[-1],dP)-Y_Inv(MS[-2],Y[-1],PriceInflation))))
W.append(W[-1])
CapCost.append(CapCost[-1])
elif (OutputGap<-0.05) & (PriceInflation>0.0001): # Negative Inflation
dP=AggregateSupplyCurveShift(Y1,Y2,Pinv)
P.append(P[-1]*(1+dP))
print(dP)
W.append(W[-1]*(1+Ymean()/OutputGap))
CapCost.append((1+dP)*CapCost[-1])
print(W[-1])
Y.append(Y[-1]*(CapCost[-1]/CapCost[-2]+(Y_Lab(W[-1],dP)-Y_Lab(W[-2],PriceInflation))))
MS.append(MS[-1])
elif (OutputGap<-0.05) & (PriceInflation<-0.0001): # Deflation
dP=AggregateDemandCurveShift(Y1,Y2,Wlab,Plab,Csd)
P.append(P[-1]*(1+dP))
print(dP)
MS.append(MS[-1]*(1+OutputGap/Ymean()))
print(MS[-1])
Y.append(Y[-1]*(1+(Y_Inv(MS[-1],Y[-1],dP)-Y_Inv(MS[-2],Y[-1],PriceInflation))))
W.append(W[-1])
CapCost.append(CapCost[-1])
elif (OutputGap<-0.05) & (PriceInflation<-0.0001): # Dereguation
dP=AggregateSupplyCurveShift(Y1,Y2,Pinv)
P.append(P[-1]*(1+dP))
print(dP)
W.append(W[-1]*(1+Ymean()/OutputGap))
CapCost.append((1+dP)*CapCost[-1])
print(W[-1])
Y.append(Y[-1]*(CapCost[-1]/CapCost[-2]+(Y_Lab(W[-1],dP)-Y_Lab(W[-2],PriceInflation))))
MS.append(MS[-1])
else:
print("Nothing")
print(OutputGap,P,Y)
# See the result
Shift1(MS[-1],Y[-1],Y[-2],W[-1],PrInf(),CapCost[-1])
print(Y)
print(P)
print(MS)
print(W)
print(CapCost)
This is the mathematical and statistical model referring to a physics theory. Originally, this was invented to predict the randomly floating atoms' movement. This is applied to financial modelling to predict the random walk movement of stock prices. 
