i_ε] - p * policy_m2[i_m1, i_m2, i_x, i_θ, i_ε]
return V_new, policy_m1, policy_m2, policy_x, policy_c
qe.tic()
V = compute_fixed_point(bellman_operator_discrete,
V_guess,
max_iter=1,
error_tol=0.1)
V2 = compute_fixed_point(bellman_operator_discrete,
V,
max_iter=100,
error_tol=0.01)
qe.toc()
V_next, g_m1, g_m2, g_x, g_c = bellman_operator_policies(V2)
#%% Asset policy functions across shocks
def plot_policy(policy, policy_name, m0=0, x0=0, save=False, folder=folder):
fig, ax = plt.subplots()
ax.plot(m_grid,
np.array(policy[:, m0, x0, 1, 1]),
label=policy_name + r'($\theta=1, \varepsilon=1)$')
ax.plot(m_grid,
np.array(policy[:, m0, x0, 0, 1]),
label=policy_name + r'($\theta=0, \varepsilon=1)$')
ax.plot(m_grid,
np.array(policy[:, m0, x0, 1, 0]),
g[i] = np.argmax(X[i, :])
if np.max(Vj - Vi) >= epsilon:
Vi = np.copy(Vj)
Vj = np.empty([nk, 1])
s += 1
else:
convergence = True
# Policy functions:
gk = np.empty(nk)
gc = np.empty(nk)
for i in range(nk):
gk[i] = k[int(g[i])]
gc[i] = k[i]**(1 - theta) + (1 - delta) * k[i] - gk[i]
T = qe.toc()
# Plotting:
plt.plot(k, Vj, label='V(k)')
plt.xlabel('k')
plt.ylabel('V(k)')
plt.show()
print("Convergence of the value functions took " + str(s) +
" iterations, in " + str(T) + " seconds.")
#%% (b) Monotonicity of the optimal decision rule
#------------------------------------------------------------------------------
# Value function iteration:
qe.tic()
epsilon = 0.01