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component	household	production	government	$\Sigma$
planned government spending		$+G$	$-G$	0
transfer payments	$+G_{transfers}$		$-G_{transfers}$	0
final consumption	$-C$	$+C$		0
sales tax		$-T_{sales}$	$+T_{sales}$	0
income tax	$-T_{income}$		$+T_{income}$	0
factor income	$+W$	$-W$		0
interest	$+i$		$-i$	0
[output]		$[Y]$

stock	$-\Delta H$		$+\Delta M$
$\Sigma$	$0$	$0$	$0$

$$Y = C + G$$$$Y_{taxable} = W + i$$$$T_{income} = \theta Y_{taxable}$$$$Y_{disposable} = Y$$$$T_{sales} = vC_0$$$$C_0 = \frac {C}{1+v}$$



In [1]:

    
# import required Python libraries
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline  

# set the number of time steps
N = 300

# initialise containers for endogenous variables
C = np.zeros(N) # consumption
Y = np.zeros(N) # income
Y_t = np.zeros(N) # taxable income
Y_d = np.zeros(N) # disposable income
T_i = np.zeros(N) # tax revenue
T_s = np.zeros(N) # tax revenue
i   = np.zeros(N) # interest
H_h = np.zeros(N) # private savings
H_g = np.zeros(N) # government debt
W   = np.zeros(N)

G = 20
G_t = 5

theta = 0.25
omega = 0.1

r = 0.02

alpha_y = 0.8
alpha_h = 0.2


for t in range(1, N):
    # calculate consumer spending
    C[t] = alpha_y*Y_d[t-1] + alpha_h*H_h[t-1] 
        
    # calculate total production 
    Y[t] = G + C[t]
    
    T_s[t] = (omega*C[t])/(1+omega)
    
    W[t] = Y[t] - T_s[t] 
    
    i[t] = r*H_h[t-1]
    
    Y_t[t] = W[t] + i[t]
    
    # calculate the tax take
    T_i[t] = theta * Y_t[t]
    
    # calculate disposable income
    Y_d[t] = Y_t[t] - T_i[t] + G_t
    
    # calculate the change in private savings
    H_h[t] = H_h[t-1] + (1-alpha_y)*Y_d[t-1] - (alpha_h)*H_h[t-1]
    
    # calculate the change in government debt from rUK operations
    H_g[t] = H_g[t-1] + T_i[t] + T_s[t] - G - G_t - i[t]



In [2]:

    
fig = plt.figure(figsize=(14, 10))

consumption_plot = fig.add_subplot(341, xlim=(0, N), ylim=(0, np.max([np.max(Y),np.max(Y)])*1.1))
consumption_plot.plot(range(N), C, lw=3)
consumption_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('consumption')

gov_plot = fig.add_subplot(342, xlim=(0, N), ylim=(0, np.max((Y))*1.1))
gov_plot.plot(range(N), np.repeat(G,N), lw=3)
gov_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('government spending')

#ca_plot = fig.add_subplot(343, xlim=(0, N), ylim=(np.min([np.min(CA_UK),np.min(CA_S)])*1.1, np.max([np.max(CA_UK),np.max(CA_S)])*1.1))
#ca_plot.plot(range(N), CA_UK, lw=3)
#ca_plot.grid()
## label axes
#plt.xlabel('time')
#plt.ylabel('trade balance')

income_plot = fig.add_subplot(344, xlim=(0, N), ylim=(0, np.max(Y)*1.1))
income_plot.plot(range(N), Y, lw=3)
income_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('income')

tax_plot = fig.add_subplot(345, xlim=(0, N), ylim=(0, np.max(T_i+T_s)*1.1))
tax_plot.plot(range(N), T_i+T_s, lw=3)
tax_plot.plot(range(N), T_i, lw=3)
tax_plot.plot(range(N), T_s, lw=3)
tax_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('tax revenue')

tax_gdp_plot = fig.add_subplot(346, xlim=(0, N), ylim=(0, 1))
tax_gdp_plot.plot(range(N), (T_i+T_s)/Y, lw=3)
tax_gdp_plot.plot(range(N), T_i/Y, lw=3)
tax_gdp_plot.plot(range(N), T_s/Y, lw=3)
tax_gdp_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('tax revenue (% GDP)')

deficit_plot = fig.add_subplot(347, xlim=(0, N), ylim=(-100,100))
deficit_plot.plot(range(N), T_i+T_s-np.repeat(G,N)-np.repeat(G_t,N)-i, lw=3)
deficit_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('government budget')

debt_plot = fig.add_subplot(348, xlim=(0, N), ylim=(np.min(H_g)*1.1,0))
debt_plot.plot(range(N), H_g, lw=3)
debt_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('government debt')

gov_balance_gdp_plot = fig.add_subplot(3,4,9, xlim=(0, N), ylim=(-1, 1))
gov_balance_gdp_plot.plot(range(N-1), (T_i[1:]+T_s[1:]-np.repeat(G,N-1)-np.repeat(G_t,N-1)-i[t])/Y[1:], lw=3)
gov_balance_gdp_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('government balance (% GDP)')

private_balance_gdp_plot = fig.add_subplot(3,4,10, xlim=(0, N), ylim=(-1,1))
private_balance_gdp_plot.plot(range(N-1), np.diff(H_h)/Y[1:], lw=3)
private_balance_gdp_plot.grid()
# label axes
plt.xlabel('time')
plt.ylabel('private balance (% GDP)')

# space subplots neatly
plt.tight_layout()









    



-c:41: RuntimeWarning: invalid value encountered in divide
-c:42: RuntimeWarning: invalid value encountered in divide
-c:43: RuntimeWarning: invalid value encountered in divide



In [57]:

    
i









    Out[57]:





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