def __init__(self, Rfree=1.001, CRRA=2):
PFaux = PerfForesightConsumerType(
) # set up a consumer type and use default parameteres
PFaux.cycles = 0 # Make this type have an infinite horizon
PFaux.DiscFac = 1 / Rfree
PFaux.Rfree = Rfree
PFaux.LivPrb = [1.0]
PFaux.PermGroFac = [1.0]
PFaux.CRRA = CRRA
PFaux.solve() # solve the consumer's problem
PFaux.unpackcFunc() # unpack the consumption function
self.cFunc = PFaux.solution[0].cFunc
PatR_array = Pat_array/Rfree_array
# +
# Set the time preference factor to match the interest factor so that $(R \beta) = 1$
Paramod['DiscFac'] = 1/Rfree
# +
# Plot average deviation from true consumption function
PFagent = PerfForesightConsumerType(**Paramod) # construct a consumer with our previous parameters
plt.figure(figsize=(9,6)) #set the figure size
mean_dev = np.zeros(30)
for i in range(len(Rfree_array)):
PFagent.Rfree = Rfree_array[i]
# Now we just copy the lines of code from above that we want
PFagent.solve()
cHARK = PFagent.solution[0].cFunc(m_range)
wealthHmn = PFagent.solution[0].hNrm
wealthTot = wealthHmn+m_range
rfree=Rfree-1
discRte=(1/DiscFac)-1
cApprox = wealthTot*(rfree - (1/CRRA)*(rfree-discRte))
deviation = np.mean(np.abs(cApprox/cHARK))
mean_dev[i] = deviation
plt.plot(Rfree_array,mean_dev)
plt.xlabel('Return Factor') # x axis label
plt.ylabel(' Average deviation along consumption function') # y axis label
def FisherPlot(Y1, Y2, B1, R, c1Max, c2Max):
# Basic setup of perfect foresight consumer
# We first create an instance of the class
# PerfForesightConsumerType, with its standard parameters.
PFexample = PerfForesightConsumerType()
PFexample.cycles = 1 # let the agent live the cycle of periods just once
PFexample.T_cycle = 2 # Number of periods in the cycle
PFexample.PermGroFac = [1.] # No automatic growth in income across periods
PFexample.LivPrb = [1.] # No chance of dying before the second period
PFexample.aNrmInitStd = 0.
PFexample.AgentCount = 1
CRRA = PFexample.CRRA
Beta = PFexample.DiscFac
# Set interest rate and bank balances from input.
PFexample.Rfree = R
PFexample.aNrmInitMean = B1
# Solve the model: this generates the optimal consumption function.
# Try-except blocks "try" to execute the code in the try block. If an
# error occurs, the except block is executed and the application does
# not halt
try:
PFexample.solve()
except:
print(
'Those parameter values violate a condition required for solution!'
)
# Create the figure
c1Min = 0.
c2Min = 0.
plt.figure(figsize=(8, 8))
plt.xlabel('Period 1 Consumption $C_1$')
plt.ylabel('Period 2 Consumption $C_2$')
plt.ylim([c2Min, c2Max])
plt.xlim([c1Min, c1Max])
# Plot the budget constraint
C1_bc = np.linspace(c1Min, B1 + Y1 + Y2 / R, 10, endpoint=True)
C2_bc = (Y1 + B1 - C1_bc) * R + Y2
plt.plot(C1_bc, C2_bc, 'k-', label='Budget Constraint')
# Plot the optimal consumption bundle
C1 = PFexample.solution[0].cFunc(B1 + Y1 + Y2 / R)
C2 = PFexample.solution[1].cFunc((Y1 + B1 - C1) * R + Y2)
plt.plot(C1, C2, 'ro', label='Optimal Consumption')
# Plot the indifference curve
V = C1**(1 - CRRA) / (1 - CRRA) + Beta * C2**(1 - CRRA) / (
1 - CRRA) # Get max utility
C1_V = np.linspace(((1 - CRRA) * V)**(1 / (1 - CRRA)) + 0.5, c1Max, 1000)
C2_V = (((1 - CRRA) * V - C1_V**(1 - CRRA)) / Beta)**(1 / (1 - CRRA))
plt.plot(C1_V, C2_V, 'b-', label='Indiferrence Curve')
# Add a legend and display the plot
plt.legend()
plt.show()
return None