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# -*- coding: utf-8 -*-
# This script describes how truncated and fully compounded fiscal multiplier
# scenarios can be consider to be equivalent. It is described in the accompanying
# iPython Notebook and at
#
# http://misunderheard.org/monetary_economics/2017/04/10/modelling_the_fiscal_multiplier/
#
# %%
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline
G = 100 # government spending
theta = 0.2 # tax rate
rounds = 5
# solve equation 1 for the 5th spending round
sum_y = G*(1-(1-theta)**(rounds+1))/(1-(1-theta))
print(sum_y)
# calculate the total tax paid after the 5th spending round
T = theta*sum_y
print(T)
# solve equation 2 for the 6th spending round
y = G*(1-theta)**(rounds) # gross income
# subtract the tax paid
y_d = (1-theta)*y # disposable income
print(y_d)
# derive the implied alpha value
alpha = (1-(G/sum_y))/(1-theta)
print(alpha)
# calculate the total income with saving
sum_y = G/(1-alpha*(1-theta))
print(sum_y)
# calculate the implied savings and tax revenue
s = (1-alpha)*(1-theta)*sum_y
T = theta*sum_y
print(s)
print(T)