model = DDPmodel(f, g, delta).solve()
## Analysis
# Plot Optimal Policy
demo.figure('Optimal Investment', 'Wealth', 'Investment')
plt.plot(S, X[model.policy] * S)
# Plot Optimal Policy
demo.figure('Optimal Consumption', 'Wealth', 'Consumption')
plt.plot(S, S - X[model.policy] * S)
# Plot Value Function
demo.figure('Optimal Value Function', 'Wealth', 'Value')
plt.plot(S, model.value)
# Simulate Model
nyrs = 20
t = np.arange(0, nyrs + 1)
st, xt = model.simulate(smin, nyrs)
# Plot State Path
demo.figure('Optimal State Path', 'Year', 'Wealth')
plt.plot(t, S[st])
# Compute Steady State Distribution and Mean
pi = model.markov()
avgstock = np.dot(S, pi)
print('Steady-state Wealth {:8.2f}, {:8.2f}'.format(*avgstock))
plt.show()
header = '{:^8s} {:^8s} {:^8s} {:^8s}'.format('Age','Lo', 'Med', 'Hi')
print('Optimal Policy')
print(header)
print(*('{:^8d} {:^8s} {:^8s} {:^8s}\n'.format(s, *X[x]) for s, x in zip(s1, xtemp)))
# Plot Value Function
demo.figure('Optimal Replacement Value', 'Age', 'Optimal Value (thousands)')
plt.plot(s1, model.value.reshape((n1,n2)) / 1000)
plt.legend(['Low','Med','Hi'])
# Compute Steady-State distribution
pi = model.markov().reshape((n1, n2))
# Display Steady-State distribution
print(' Invariant Distribution ')
print(header)
print(*('{:^8d} {:8.3f} {:8.3f} {:8.3f}\n'.format(s, *x) for s, x in zip(s1, pi)))
# Compute Steady-State Mean Cow Age and Productivity
pi = pi.flatten()
avgage = np.dot(pi.T, S1)
avgpri = np.dot(pi.T, S2)
print('Steady-state Age = {:8.2f}'.format(avgage))
print('Steady-state Productivity = {:8.2f}'.format(avgpri))
# Display Optimal Policy
xtemp = model.policy.reshape((n1, n2))
header = '{:^8s} {:^8s} {:^8s} {:^8s}'.format('Age', 'Lo', 'Med', 'Hi')
print('Optimal Policy')
print(header)
print(*('{:^8d} {:^8s} {:^8s} {:^8s}\n'.format(s, *X[x])
for s, x in zip(s1, xtemp)))
# Plot Value Function
demo.figure('Optimal Replacement Value', 'Age', 'Optimal Value (thousands)')
plt.plot(s1, model.value.reshape((n1, n2)) / 1000)
plt.legend(['Low', 'Med', 'Hi'])
# Compute Steady-State distribution
pi = model.markov().reshape((n1, n2))
# Display Steady-State distribution
print(' Invariant Distribution ')
print(header)
print(*('{:^8d} {:8.3f} {:8.3f} {:8.3f}\n'.format(s, *x)
for s, x in zip(s1, pi)))
# Compute Steady-State Mean Cow Age and Productivity
pi = pi.flatten()
avgage = np.dot(pi.T, S1)
avgpri = np.dot(pi.T, S2)
print('Steady-state Age = {:8.2f}'.format(avgage))
print('Steady-state Productivity = {:8.2f}'.format(avgpri))
plt.show()
## Analysis
# Plot Optimal Policy
demo.figure('Optimal Investment', 'Wealth', 'Investment')
plt.plot(S, X[model.policy] * S)
# Plot Optimal Policy
demo.figure('Optimal Consumption', 'Wealth', 'Consumption')
plt.plot(S, S - X[model.policy] * S)
# Plot Value Function
demo.figure('Optimal Value Function', 'Wealth', 'Value')
plt.plot(S, model.value)
# Simulate Model
nyrs = 20
t = np.arange(0, nyrs + 1)
st, xt = model.simulate(smin, nyrs)
# Plot State Path
demo.figure('Optimal State Path', 'Year', 'Wealth')
plt.plot(t, S[st])
# Compute Steady State Distribution and Mean
pi = model.markov()
avgstock = np.dot(S, pi)
print('Steady-state Wealth {:8.2f}, {:8.2f}'.format(*avgstock))
plt.show()