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
def plot1(Epsilon, DiscFac, PopGrowth, YearsPerGeneration, Initialk):
'''Inputs:
Epsilon: Elasticity of output with respect to capital/labour ratio
DiscFac: One period discount factor
YearPerGeneration: No. of years per generation
PopGrowth: Gross growth rate of population in one period'''
#
kMax = 0.1
# Define some parameters
Beta = DiscFac**YearsPerGeneration
xi = PopGrowth**YearsPerGeneration
Q = (1-Epsilon)*(Beta/(1+Beta))/xi
kBar = Q**(1/(1-Epsilon))
# Create an agent that will solve the consumption problem
PFagent = PerfForesightConsumerType(**init_perfect_foresight)
PFagent.cycles = 1 # let the agent live the cycle of periods just once
PFagent.T_cycle = 2 # Number of periods in the cycle
PFagent.assign_parameters(PermGroFac = [0.000001]) # Income only in the first period
PFagent.LivPrb = [1.]
PFagent.DiscFac = Beta
# Hark seems to have trouble with log-utility
# so pass rho = 1 + something small.
PFagent.CRRA = 1.001
PFagent.solve()
# Plot the OLG capital accumulation curve and 45 deg line
plt.figure(figsize=(9,6))
kt_range = np.linspace(0, kMax, 300)
# Analitical solution plot
ktp1 = Q*kt_range**Epsilon
plt.plot(kt_range, ktp1, 'b-', label='Capital accumulation curve')
plt.plot(kt_range, kt_range, 'k-', label='45 Degree line')
# Plot the path
kt_ar = Initialk
ktp1_ar = 0.
for i in range(3):
# Compute Next Period's capital using HARK
wage = (1-Epsilon)*kt_ar**Epsilon
c = PFagent.solution[0].cFunc(wage)
a = wage - c
k1 = a/xi
plt.arrow(kt_ar, ktp1_ar, 0., k1-ktp1_ar,
length_includes_head=True,
lw=0.01,
width=0.0005,
color='black',
edgecolor=None)
plt.arrow(kt_ar, k1, k1-kt_ar , 0.,
length_includes_head=True,
lw=0.01,
width=0.0005,
color='black',
edgecolor=None)
# Update arrow
kt_ar = k1
ktp1_ar = kt_ar
# Plot kbar and initial k
plt.plot(kBar, kBar, 'ro', label=r'$\bar{k}$')
plt.plot(Initialk, 0.0005, 'co', label = '$k_0$')
plt.legend()
plt.xlim(0 ,kMax)
plt.ylim(0, kMax)
plt.xlabel('$k_t$')
plt.ylabel('$k_{t+1}$')
plt.show()
return None
def FisherPlot3(M1, R, Beta, CRRA, 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 = 1 # One single non-terminal period
PFexample.PermGroFac = [0] # No income in the second period
PFexample.LivPrb = [1.] # No chance of dying before the second period
# Set interest rate and bank balances from input.
PFexample.Rfree = R
PFexample.CRRA = CRRA
PFexample.DiscFac = Beta
# 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!'
)
return
# 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, M1, 10, endpoint=True)
C2_bc = (M1 - C1_bc) * R
plt.plot(C1_bc, C2_bc, 'k-', label='Budget Constraint')
# Plot the optimal consumption bundle
C1 = PFexample.solution[0].cFunc(M1)
C2 = PFexample.solution[1].cFunc((M1 - C1) * R)
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)) + 0.1, 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