from compute_fp import compute_fixed_point
from scipy import interp
import mc_tools
def compute_asset_series(cp, T=500000):
"""
Simulates a time series of length T for assets, given optimal savings
behavior. Parameter cp is an instance of consumerProblem
"""
Pi, z_vals, R = cp.Pi, cp.z_vals, cp.R # Simplify names
v_init, c_init = initialize(cp)
c = compute_fixed_point(coleman_operator, cp, c_init)
cf = lambda a, i_z: interp(a, cp.asset_grid, c[:, i_z])
a = np.zeros(T+1)
z_seq = mc_tools.sample_path(Pi, sample_size=T)
for t in range(T):
i_z = z_seq[t]
a[t+1] = R * a[t] + z_vals[i_z] - cf(a[t], i_z)
return a
if __name__ == '__main__':
cp = consumerProblem(r=0.03, grid_max=4)
a = compute_asset_series(cp)
fig, ax = plt.subplots()
ax.hist(a, bins=20, alpha=0.5, normed=True)
ax.set_xlabel('assets')
ax.set_xlim(-0.05, 0.75)
plt.show()
from matplotlib import pyplot as plt
import numpy as np
from compute_fp import compute_fixed_point
from ifp import coleman_operator, consumerProblem, initialize
from solution_ifp_ex3 import compute_asset_series
M = 25
r_vals = np.linspace(0, 0.04, M)
fig, ax = plt.subplots()
for b in (1, 3):
asset_mean = []
for r_val in r_vals:
cp = consumerProblem(r=r_val, b=b)
mean = np.mean(compute_asset_series(cp, T=250000))
asset_mean.append(mean)
ax.plot(asset_mean, r_vals, label=r'$b = %d$' % b)
ax.set_yticks(np.arange(.0, 0.045, .01))
ax.set_xticks(np.arange(-3, 2, 1))
ax.set_xlabel('capital')
ax.set_ylabel('interest rate')
ax.grid(True)
ax.legend(loc='upper left')
fig.show()
from compute_fp import compute_fixed_point
from matplotlib import pyplot as plt
import numpy as np
from ifp import coleman_operator, consumerProblem, initialize
r_vals = np.linspace(0, 0.04, 4)
fig, ax = plt.subplots()
for r_val in r_vals:
cp = consumerProblem(r=r_val)
v_init, c_init = initialize(cp)
c = compute_fixed_point(coleman_operator, cp, c_init)
ax.plot(cp.asset_grid, c[:, 0], label=r'$r = %.3f$' % r_val)
ax.set_xlabel('asset level')
ax.set_ylabel('consumption (low income)')
ax.legend(loc='upper left')
plt.show()
