def feasible(f_params, bvec_guess):
b_cnstr=np.zeros(bvec_guess.shape,dtype=bool)
nvec, A, alpha, delta, bq_distr, beta=f_params
K,K_cnstr=utils.get_K(bvec_guess)
L=utils.get_L(nvec)
r=utils.get_r(K,L,(A, alpha, delta))
w=utils.get_w(K,L,(A, alpha))
c_vec,c_cnstr=utils.get_cvec_ss(r, w, bvec_guess, nvec, bq_distr)
b_cnstr[0]=c_cnstr[0]
b_cnstr[-1]=c_cnstr[-1]
for k in range(1,len(c_cnstr)-1):
b_cnstr[k]=c_cnstr[k]
b_cnstr[k-1]=b_cnstr[k]
return b_cnstr, c_cnstr, K_cnstr
def get_SS(params, bvec_guess, SS_graphs):
start_time = time.clock()
beta, sigma, nvec, L, A, alpha, delta, SS_tol, bq_distr, chi = params
f_params = (nvec, A, alpha, delta, bq_distr, beta)
b1_cnstr, c1_cnstr, K1_cnstr = feasible(f_params, bvec_guess)
try:
if b1_cnstr.max() or c1_cnstr.max() or K1_cnstr.max():
raise cstError
else:
# errors=zero_func(bvec_guess,beta, sigma, nvec, L, A, alpha, delta)
b = opt.root(utils.EulerSys_ss, bvec_guess, args=(beta, sigma, nvec, A, alpha, delta, bq_distr,chi), tol=SS_tol)
except cstError:
print ('Did not pass the feasible test')
if b.success:
b_ss = b.x
# iterations=b.nit
K_ss, K_cnstr = utils.get_K(b_ss)
L=utils.get_L(nvec)
w_ss = utils.get_w(K_ss,L, (A, alpha))
r_ss = utils.get_r(K_ss, L, (A, alpha, delta))
Y_ss = utils.get_Y(K_ss, L, (A, alpha))
c_ss, c_cnstr = utils.get_cvec_ss(r_ss, w_ss, b_ss, nvec, bq_distr)
EulErr_ss = utils.EulerSys_ss(b_ss, beta, sigma, nvec, A, alpha, delta, bq_distr, chi)
C_ss=utils.get_C(c_ss)
RCerr_ss = Y_ss - C_ss - delta * K_ss
BQ_ss = b_ss[-1]
ss_time = time.clock() - start_time
ss_output={'b_ss': b_ss, 'c_ss': c_ss, 'w_ss': w_ss, 'r_ss': r_ss, 'K_ss': K_ss, 'Y_ss': Y_ss, 'C_ss': C_ss,
'EulErr_ss': EulErr_ss, 'RCerr_ss': RCerr_ss, 'BQ_ss': BQ_ss, 'ss_time': ss_time}
# print('\n Savings: \t\t\t {} \n Capital and Labor: \t\t {} \n Wage and Interest rate: \t {} \n Consumption: \t\t\t {}'.format(
# b_ss, np.array([K_ss, L]), np.array([w_ss, r_ss]), c_ss))
#
# print('Euler errors: ', EulErr_ss)
# print('Resource Constraint error: ', RCerr_ss)
# print('Time needed: ', ss_time)
# print ('It took {iterations} iterations to get the solution.')
if SS_graphs:
cur_path = os.path.split(os.path.abspath(__file__))[0]
output_fldr = "images"
output_dir = os.path.join(cur_path, output_fldr)
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
age = np.arange(21, 101)
fig, ax = plt.subplots()
plt.plot(age, c_ss, marker='D', label='Consumption')
plt.plot(age, b_ss, marker='D', label='Savings')
minorLocator = MultipleLocator(1)
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Steady-state consumption and savings')
plt.xlabel('Age')
plt.ylabel('Consumption units')
plt.legend()
output_path = os.path.join(output_dir, 'ss_bc')
plt.savefig(output_path)
# plt.show()
plt.close()
return ss_output
def get_TPI(b1vec, c1_guess, ss_params, params):
t1=time.time()
# r_guess: guess of interest rate path from period 1 to T1
beta, sigma, S, l_ub, b, upsilon, chi, A, alpha, delta, tpi_max_iter, tpi_tol, xi_tpi, T1, T2 = params
r_ss, w_ss, c_ss, n_ss, b_ss, K_ss, L_ss = ss_params
abs_tpi = 1
tpi_iter = 0
rpath_old = np.zeros(T2 + S - 1)
rpath_old[:T1] = get_path(r_ss, r_ss, T1, 'quadratic')
rpath_old[T1:] = r_ss
while abs_tpi > tpi_tol and tpi_iter < tpi_max_iter:
tpi_iter += 1
wpath_old = utils.get_w(rpath_old, (A, alpha, delta))
bmat = np.zeros((S, T2 + S - 1))
bmat[:, 0] = b1vec
bmat[:, T2:] = numpy.matlib.repmat(b_ss, S - 1, 1).T
nmat = np.zeros((S, T2 + S - 1))
nmat[:, T2:] = numpy.matlib.repmat(n_ss, S - 1, 1).T
cmat = np.zeros((S, T2 + S - 1))
cmat[:, T2:] = numpy.matlib.repmat(c_ss, S-1, 1).T
# Solve the incomplete remaining lifetime decisions of agents alive
# in period t=1 but not born in period t=1
for p in range(S): # p is remaining periods of life
c1_args = (rpath_old[:p + 1], wpath_old[:p + 1], beta, sigma, l_ub, b, upsilon, p + 1, b1vec[S - p - 1], chi[S-p-1:])
result_c1 = opt.root(utils.get_b_last, c1_guess, args = (c1_args))
if result_c1.success:
c1 = result_c1.x
else:
raise ValueError("failed to find an appropriate initial consumption")
# Calculate aggregate supplies for capital and labor
cvec = utils.get_c(c1, rpath_old[:p + 1], beta, sigma, p + 1)
# print (np.shape(cvec))
nvec = utils.get_n(cvec, sigma, l_ub, b, upsilon, wpath_old[:p + 1], p + 1,chi[S-p-1:])
bvec = utils.get_b(cvec, nvec, rpath_old[:p + 1], wpath_old[:p + 1], p + 1, bs = b1vec[S - p - 1])[1:]
# Insert the vector lifetime solutions diagonally (twist donut)
DiagMaskbp = np.eye(p)
bp_path = DiagMaskbp * bvec
bmat[S - p:, 1:p + 1] += bp_path
DiagMasknp = np.eye(p + 1)
np_path = DiagMasknp * nvec
nmat[S - p - 1:, :p + 1] += np_path
DiagMasknp = np.eye(p + 1)
c_path = DiagMasknp * cvec
cmat[S - p - 1:, :p + 1] += c_path
# Solve for complete lifetime decisions of agents born in periods
# 1 to T2 and insert the vector lifetime solutions diagonally (twist
# donut) into the cpath, bpath, and EulErrPath matrices
for t in range(1, T2):
c1_args = (rpath_old[t: S + t], wpath_old[t: S + t], beta, sigma, l_ub, b, upsilon, S, 0.0, chi)
result_c1 = opt.root(utils.get_b_last, c1_guess, args = (c1_args))
if result_c1.success:
c1 = result_c1.x
else:
raise ValueError("failed to find an appropriate initial consumption")
# Calculate aggregate supplies for capital and labor
cvec = utils.get_c(c1, rpath_old[t : S + t], beta, sigma, S)
nvec = utils.get_n(cvec, sigma, l_ub, b, upsilon, wpath_old[t: S + t], S, chi)
bvec = utils.get_b(cvec, nvec, rpath_old[t: S + t], wpath_old[t: S + t], S)
# print ("nvec,cvec,bvec: {}".format(np.shape(nvec),np.shape(cvec),np.shape(bvec)))
DiagMaskbt = np.eye(S)
bt_path = DiagMaskbt * bvec
bmat[:, t: t + S] += bt_path
DiagMasknp = np.eye(S)
np_path = DiagMasknp * nvec
nmat[:, t: t + S] += np_path
DiagMasknp = np.eye(S)
c_path = DiagMasknp * cvec
cmat[:, t: t + S] += c_path
bmat[:, T2:] = np.matlib.repmat(b_ss, S - 1, 1).T
nmat[:, T2:] = np.matlib.repmat(n_ss, S - 1, 1).T
cmat[:, T2:] = np.matlib.repmat(c_ss, S - 1, 1).T
K = utils.get_K(bmat)[0]
L = utils.get_L(nmat)[0]
Y = utils.get_Y(K, L, (A, alpha))
C = utils.get_C(cmat)
rpath_new = utils.get_r(K, L, (A, alpha, delta))
# Calculate the implied capital stock from conjecture and the error
abs_tpi = ((rpath_old[:T2] - rpath_new[:T2]) ** 2).sum()
# Update guess
rpath_old[:T2] = xi_tpi * rpath_new[:T2] + (1 - xi_tpi) * rpath_old[:T2]
print('iteration:', tpi_iter, ' squared distance: ', abs_tpi)
b_last = abs(bmat[S - 1, :]).max()
b_err = abs(utils.get_b_errors(cmat[:, :T2 + S - 1], rpath_old[:T2 + S - 1], beta, sigma)).max()
n_err = abs(utils.get_n_errors(nmat[:, :T2 + S - 1], cmat[:, :T2 + S - 1], sigma, l_ub, b,
upsilon, wpath_old[:T2 + S - 1], chi[0] * np.ones(T2 + S - 1))).max()
cnt_err = abs(Y[:-1] - C[:-1] - K[1:] + (1 - delta) * K[:-1]).max()
t2=time.time()
t=t2-t1
print (f'It took {t} seconds to solve TPI.')
k_first = [k for k in K if abs(k - K_ss) < 0.0001][0]
T_1 = np.where(K == k_first)[0][0]
return rpath_old, wpath_old, K, L, bmat, nmat, cmat, b_last, b_err, n_err, cnt_err, T_1
def get_TPI(params, b1vec, graphs):
start_time = time.clock()
S, T, beta, sigma, nvec, L, A, alpha, delta, b_ss, K_ss, C_ss, BQ_ss, \
maxiter_TPI, mindist_TPI, xi, TPI_tol, bq_distr, chi = params
K1 = utils.get_K(b1vec)[0]
# K: s=1 ~ S, sum of b: s=2 ~ S+1
Kpath_old = np.zeros(T + S)
# print (f'K1: {K1}, K_ss: {K_ss}')
Kpath_old[:T] = np.linspace(K1, K_ss, T) # Until reaching steady state
Kpath_old[T:] = K_ss
r = utils.get_r(Kpath_old[0], utils.get_L(nvec), (A, alpha, delta))
BQ1 = (1 + r) * b1vec[-1]
BQpath_old = np.zeros(T + S)
BQpath_old[:T] = np.linspace(BQ1, BQ_ss, T) # Until reaching steady state
BQpath_old[T:] = BQ_ss
L = np.sum(nvec)
iter_TPI = int(0)
abs2 = 10.
Kpath_new = Kpath_old.copy()
r_params = (A, alpha, delta)
w_params = (A, alpha)
# cbe_params = (S, T, beta, sigma, nvec, b_ss, TPI_tol, A, alpha, delta, bq_distr, chi)
while (iter_TPI < maxiter_TPI) and (abs2 >= mindist_TPI):
iter_TPI += 1
# Kpath_init = xi * Kpath_new + (1 - xi) * Kpath_old
rpath = utils.get_r(Kpath_old, L, r_params)
wpath = utils.get_w(Kpath_old, L, w_params)
# cpath, bpath, EulErrPath = get_cbepath(cbe_params, rpath, wpath, b1vec)
# b: 2~S+1
bpath = np.append(b1vec.reshape(S, 1),
np.zeros((S, T + S - 2)),
axis=1)
cpath = np.zeros((S, T + S - 1))
EulErrPath = np.zeros((S, T + S - 1))
cpath[S - 1,
0] = ((1 + rpath[0]) * b1vec[S - 2] + wpath[0] * nvec[S - 1])
for p in range(1, S):
bvec_guess = np.diagonal(bpath[S - p:, :p])
beg_wealth = bpath[S - p - 1, 0]
#beg_wealth, nvec, beta, sigma, wpath, rpath, BQpath, chi, bq_distr
args_sol = (beg_wealth, nvec[-p:], beta, sigma, wpath[:p],
rpath[:p], BQpath_old[:p], chi[-p:], bq_distr[-p:])
b_sol = opt.root(utils.EulerSys_tpi, bvec_guess, args=(args_sol)).x
#rpath, wpath, bvec, nvec, bq, bq_distr
cp, c_cnstr_p = utils.get_cvec_tpi(rpath[:p], wpath[:p],
np.append(beg_wealth,
b_sol), nvec[-p:],
BQpath_old[:p], bq_distr[-p:])
# rpath, wpath, bvec, nvec, bq, bq_distr
b_err_p = utils.EulerSys_tpi(b_sol, beg_wealth, nvec[-p:], beta,
sigma, wpath[:p], rpath[:p],
BQpath_old[:p], chi[-p:],
bq_distr[-p:])
# Insert the vector lifetime solutions diagonally (twist donut)
bp_path = np.eye(p) * b_sol
cp_path = np.eye(p) * cp
ep_path = np.eye(p) * b_err_p
bpath[S - p:, 1:p + 1] += bp_path
cpath[S - p:, 1:p + 1] += cp_path
EulErrPath[S - p:, 1:p + 1] += ep_path
for t in range(1, T):
bvec_guess_t = np.diagonal(bpath[:, t - 1:S + t - 1])
args_bt = (0, nvec, beta, sigma, wpath[t - 1:S + t - 1],
rpath[t - 1:S + t - 1], BQpath_old[t - 1:S + t - 1],
chi, bq_distr)
bt = opt.root(utils.EulerSys_tpi, bvec_guess_t, args=(args_bt)).x
# print (f'bt.shape: {bt.shape}, ')
#np.append(nvec,[0.2])
# rpath, wpath, bvec, nvec, bq, bq_distr
ct, c_cnstr_t = utils.get_cvec_tpi(rpath[t - 1:S + t - 1],
wpath[t - 1:S + t - 1],
np.append([0], bt), nvec,
BQpath_old[t - 1:S + t - 1],
bq_distr)
b_err_t = utils.EulerSys_tpi(bt, 0, nvec, beta, sigma,
wpath[t - 1:S + t - 1],
rpath[t - 1:S + t - 1],
BQpath_old[t - 1:S + t - 1], chi,
bq_distr)
# DiagMask = np.eye(S)
bt_path = np.eye(p + 1) * bt
# print(f'bt: {bt.shape}, btpath:{bt_path.shape}, t:{t}, bpath:{bpath.shape}')
ct_path = np.eye(p + 1) * ct
et_path = np.eye(p + 1) * b_err_t
bpath[:, t:S + t] += bt_path
cpath[:, t:S + t] += ct_path
EulErrPath[:, t:S + t] += et_path
Kpath_new = np.zeros(T + S)
Kpath_new[:T], Kpath_cnstr = utils.get_K(bpath[:, :T])
Kpath_new[T:] = K_ss * np.ones(S)
Kpath_cnstr = np.append(Kpath_cnstr, np.zeros(S, dtype=bool))
Kpath_new[Kpath_cnstr] = 0.1
BQpath_new = np.zeros(T + S)
# print (f'Here: bpath {bpath[S, :T].shape}')
#, BQ:{BQpath_new.shape}, rpath:{rpath[:T].shape}
BQpath_new[:T] = (1 + rpath[:T]) * bpath[-1, :T]
BQpath_new[T:] = BQ_ss * np.ones(S)
abs2 = (((Kpath_old[:T] - Kpath_new[:T]) / Kpath_old[:T] * 100) ** 2).sum() + \
(((BQpath_old[:T] - BQpath_new[:T]) / BQpath_old[:T] * 100) ** 2).sum()
Kpath_old[:T] = xi * Kpath_new[:T] + (1 - xi) * Kpath_old[:T]
BQpath_old[:T] = xi * BQpath_new[:T] + (1 - xi) * BQpath_old[:T]
print('iter: ', iter_TPI, ', squared pct deviation sum: ', abs2,
',max Eul err: ',
np.absolute(EulErrPath).max())
BQ_path = BQpath_old
Kpath = Kpath_old
Ypath = utils.get_Y(Kpath, L, (A, alpha))
Cpath = np.zeros(Kpath.shape)
Cpath[:T - 1] = utils.get_C(cpath[:, :T - 1])
Cpath[T - 1:] = C_ss * np.ones(S + 1)
RCerrPath = (Ypath[:-1] - Cpath[:-1] - Kpath[1:] +
(1 - delta) * Kpath[:-1])
tpi_time = time.clock() - start_time
tpi_output = {
'bpath': bpath,
'cpath': cpath,
'wpath': wpath,
'rpath': rpath,
'Kpath': Kpath_new,
'Ypath': Ypath,
'Cpath': Cpath,
'EulErrPath': EulErrPath,
'RCerrPath': RCerrPath,
'tpi_time': tpi_time,
'BQ_path': BQ_path
}
# Print TPI computation time
print(f'It took {tpi_time} seconds to run.')
if graphs:
'''
----------------------------------------------------------------
cur_path = string, path name of current directory
output_fldr = string, folder in current path to save files
output_dir = string, total path of images folder
output_path = string, path of file name of figure to be saved
tvec = (T+S-2,) vector, time period vector
tgridTm1 = (T-1,) vector, time period vector to T-1
tgridT = (T,) vector, time period vector to T-1
sgrid = (S,) vector, all ages from 1 to S
sgrid2 = (S-1,) vector, all ages from 2 to S
tmatb = (2, 18) matrix, time periods for all savings
decisions ages (S-1) and time periods (T)
smatb = (2, 18) matrix, ages for all savings decision ages
(S-1) and time periods (T)
tmatc = (3, 17) matrix, time periods for all consumption
decisions ages (S) and time periods (T-1)
smatc = (3, 17) matrix, ages for all consumption decisions
ages (S) and time periods (T-1)
----------------------------------------------------------------
'''
# Create directory if images directory does not already exist
cur_path = os.path.split(os.path.abspath(__file__))[0]
output_fldr = "images"
output_dir = os.path.join(cur_path, output_fldr)
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
# Plot time path of aggregate capital stock
tvec = np.linspace(1, T + 5, T + 5)
minorLocator = MultipleLocator(1)
fig, ax = plt.subplots()
plt.plot(tvec, Kpath[:T + 5], marker='D')
# for the minor ticks, use no labels; default NullFormatter
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Time path for aggregate capital stock K')
plt.xlabel(r'Period $t$')
plt.ylabel(r'Aggregate capital $K_{t}$')
output_path = os.path.join(output_dir, "Kpath")
plt.savefig(output_path)
# plt.show()
# Plot time path of aggregate capital stock
tvec = np.linspace(1, T + 5, T + 5)
minorLocator = MultipleLocator(1)
fig, ax = plt.subplots()
plt.plot(tvec, BQ_path[:T + 5], marker='D')
# for the minor ticks, use no labels; default NullFormatter
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Time path for bequest BQ')
plt.xlabel(r'Period $t$')
plt.ylabel(r'Bequest $BQ$')
output_path = os.path.join(output_dir, "BQpath")
plt.savefig(output_path)
# plt.show()
# Plot time path of aggregate output (GDP)
fig, ax = plt.subplots()
plt.plot(tvec, Ypath[:T + 5], marker='D')
# for the minor ticks, use no labels; default NullFormatter
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Time path for aggregate output (GDP) Y')
plt.xlabel(r'Period $t$')
plt.ylabel(r'Aggregate output $Y_{t}$')
output_path = os.path.join(output_dir, "Ypath")
plt.savefig(output_path)
# plt.show()
# Plot time path of aggregate consumption
fig, ax = plt.subplots()
plt.plot(tvec, Cpath[:T + 5], marker='D')
# for the minor ticks, use no labels; default NullFormatter
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Time path for aggregate consumption C')
plt.xlabel(r'Period $t$')
plt.ylabel(r'Aggregate consumption $C_{t}$')
output_path = os.path.join(output_dir, "C_aggr_path")
plt.savefig(output_path)
# plt.show()
# Plot time path of real wage
fig, ax = plt.subplots()
plt.plot(tvec, wpath[:T + 5], marker='D')
# for the minor ticks, use no labels; default NullFormatter
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Time path for real wage w')
plt.xlabel(r'Period $t$')
plt.ylabel(r'Real wage $w_{t}$')
output_path = os.path.join(output_dir, "wpath")
plt.savefig(output_path)
# plt.show()
# Plot time path of real interest rate
fig, ax = plt.subplots()
plt.plot(tvec, rpath[:T + 5], marker='D')
# for the minor ticks, use no labels; default NullFormatter
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Time path for real interest rate r')
plt.xlabel(r'Period $t$')
plt.ylabel(r'Real interest rate $r_{t}$')
output_path = os.path.join(output_dir, "rpath")
plt.savefig(output_path)
# plt.show()
# Plot time path of real wage
fig, ax = plt.subplots()
plt.plot(tvec, bpath[24, :T + 5], marker='D')
# for the minor ticks, use no labels; default NullFormatter
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Time path for savings by 25-year-olds $b_{25}$')
plt.xlabel(r'Period $t$')
plt.ylabel(r'$b_{25}$')
output_path = os.path.join(output_dir, "b25path")
plt.savefig(output_path)
# plt.show()
return tpi_output
def get_SS(params, bvec_guess, SS_graphs):
start_time = time.clock()
beta, sigma, nvec, A, alpha, delta, SS_tol, fert_rates, mort_rates, imm_rates, omega_SS, gn_SS, g_y = params
b = opt.root(utils.EulerSys_ss,
bvec_guess,
args=(beta, sigma, nvec, A, alpha, delta, gn_SS, g_y,
omega_SS, mort_rates, imm_rates),
tol=SS_tol)
if b.success:
b_ss = b.x
# iterations=b.nit
K_ss = utils.get_K(b_ss, omega_SS, gn_SS, imm_rates)
L = utils.get_L(nvec, omega_SS)
w_ss = utils.get_w(K_ss, L, alpha, A)
r_ss = utils.get_r(K_ss, L, alpha, delta, A)
Y_ss = utils.get_Y(K_ss, L, (A, alpha))
c_ss, c_cnstr = utils.get_cvec_ss(r_ss, w_ss, b_ss, nvec, gn_SS, g_y,
omega_SS, mort_rates)
EulErr_ss = utils.EulerSys_ss(b_ss, beta, sigma, nvec, A, alpha, delta,
gn_SS, g_y, omega_SS, mort_rates, imm_rates)
C_ss = utils.get_C(c_ss, omega_SS)
RCerr_ss = Y_ss - C_ss - (
(1 + gn_SS) * np.exp(g_y) - 1 + delta) * K_ss + np.exp(g_y) * (
imm_rates * omega_SS * np.append(b_ss, [0]))
BQ_ss = utils.get_BQ(b_ss, r_ss, gn_SS, omega_SS, mort_rates)
ss_time = time.clock() - start_time
ss_output = {
'b_ss': b_ss,
'c_ss': c_ss,
'w_ss': w_ss,
'r_ss': r_ss,
'K_ss': K_ss,
'Y_ss': Y_ss,
'C_ss': C_ss,
'EulErr_ss': EulErr_ss,
'RCerr_ss': RCerr_ss,
'BQ_ss': BQ_ss,
'ss_time': ss_time
}
# print('\n Savings: \t\t\t {} \n Capital and Labor: \t\t {} \n Wage and Interest rate: \t {} \n Consumption: \t\t\t {}'.format(
# b_ss, np.array([K_ss, L]), np.array([w_ss, r_ss]), c_ss))
#
# print('Euler errors: ', EulErr_ss)
# print('Resource Constraint error: ', RCerr_ss)
# print('Time needed: ', ss_time)
# print ('It took {iterations} iterations to get the solution.')
if SS_graphs:
cur_path = os.path.split(os.path.abspath(__file__))[0]
output_fldr = "images_ss_tpi"
output_dir = os.path.join(cur_path, output_fldr)
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
age = np.arange(21, 101)
fig, ax = plt.subplots()
plt.plot(age, c_ss, marker='D', label='Consumption')
plt.plot(age, np.append([0], b_ss), marker='D', label='Savings')
minorLocator = MultipleLocator(1)
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
plt.title('Steady-state consumption and savings')
plt.xlabel('Age')
plt.ylabel('Consumption units')
plt.legend()
output_path = os.path.join(output_dir, 'ss_bc')
plt.savefig(output_path)
# plt.show()
plt.close()
return ss_output