e=e,
w=w)
# Deterministic Steady-State
kstar = ((1 - delta * gamma) / (delta * beta))**(
1 / (beta - 1)) # determistic steady-state capital investment
sstar = gamma * kstar + kstar**beta # deterministic steady-state wealth
# Check Model Derivatives
# dpcheck(model,sstar,kstar)
## SOLUTION
# Solve Bellman Equation
growth.solve()
resid, s, v, k = growth.solution()
# Plot Optimal Policy
demo.figure('Optimal Investment Policy', 'Wealth', 'Investment')
plt.plot(s, k.T)
# Plot Value Function
demo.figure('Value Function', 'Wealth', 'Value')
plt.plot(s, v.T)
# Plot Shadow Price Function
demo.figure('Shadow Price Function', 'Wealth', 'Shadow Price')
plt.plot(s, growth.Value(s, order=1).T)
# Plot Residual
demo.figure('Bellman Equation Residual', 'Wealth', 'Residual')
model = DPmodel(basis, reward, transition, bounds,
i=['Low price', 'Average price', 'High Price'],
x=['Current production'],
discount=delta, q=q)
# Check Model Derivatives
# dpcheck(model,sstar,sstar)
## SOLUTION
# Solve Bellman Equation
model.solve()
resid, s, v, x = model.solution()
"""
# Plot Optimal Policy
figure
plot(s,x)
legend('Low Price','Average Price','High Price')
legend('Location','Best')
legend('boxoff')
title('Optimal Production Policy')
xlabel('Lagged Production')
reward,
transition,
bounds,
i=['Low price', 'Average price', 'High Price'],
x=['Current production'],
discount=delta,
q=q)
# Check Model Derivatives
# dpcheck(model,sstar,sstar)
## SOLUTION
# Solve Bellman Equation
model.solve()
resid, s, v, x = model.solution()
"""
# Plot Optimal Policy
figure
plot(s,x)
legend('Low Price','Average Price','High Price')
legend('Location','Best')
legend('boxoff')
title('Optimal Production Policy')
xlabel('Lagged Production')
ylabel('Production')
qstar = sstar - (delta * alpha - 1) / (delta * beta) # steady-state action
# Print Steady-States
print('Steady States')
print('\tStock = %5.2f' % sstar)
print('\tHarvest = %5.2f' % qstar)
# Check Model Derivatives
# dpcheck(model,sstar,qstar)
## SOLUTION
# Solve Bellman Equation
model.solve()
resid, s, v, q = model.solution()
# Plot Optimal Policy
demo.figure('Optimal Harvest Policy', 'Stock', 'Harvest')
plt.plot(s, q.T)
# Plot Value Function
demo.figure('Value Function', 'Stock', 'Value')
plt.plot(s, v.T)
# Plot Shadow Price Function
demo.figure('Shadow Price Function', 'Stock', 'Shadow Price')
plt.plot(s, model.Value(s, 1).T)
# Plot Residual
demo.figure('Bellman Equation Residual','Stock', 'Residual')
sstar = (alpha**2 - 1 / delta**2) / (2 * beta) # steady-state stock
qstar = sstar - (delta * alpha - 1) / (delta * beta) # steady-state action
# Print Steady-States
print('Steady States')
print('\tStock = %5.2f' % sstar)
print('\tHarvest = %5.2f' % qstar)
# Check Model Derivatives
# dpcheck(model,sstar,qstar)
## SOLUTION
# Solve Bellman Equation
model.solve()
resid, s, v, q = model.solution()
# Plot Optimal Policy
demo.figure('Optimal Harvest Policy', 'Stock', 'Harvest')
plt.plot(s, q.T)
# Plot Value Function
demo.figure('Value Function', 'Stock', 'Value')
plt.plot(s, v.T)
# Plot Shadow Price Function
demo.figure('Shadow Price Function', 'Stock', 'Shadow Price')
plt.plot(s, model.Value(s, 1).T)
# Plot Residual
demo.figure('Bellman Equation Residual', 'Stock', 'Residual')
x=['investment'], discount=delta, e=e, w=w)
# Deterministic Steady-State
kstar = ((1 - delta * gamma) / (delta * beta)) ** (1 / (beta - 1)) # determistic steady-state capital investment
sstar = gamma * kstar + kstar ** beta # deterministic steady-state wealth
# Check Model Derivatives
# dpcheck(model,sstar,kstar)
## SOLUTION
# Solve Bellman Equation
growth.solve()
resid, s, v, k = growth.solution()
# Plot Optimal Policy
demo.figure('Optimal Investment Policy', 'Wealth', 'Investment')
plt.plot(s, k.T)
# Plot Value Function
demo.figure('Value Function', 'Wealth', 'Value')
plt.plot(s, v.T)
# Plot Shadow Price Function
demo.figure('Shadow Price Function', 'Wealth', 'Shadow Price')
plt.plot(s, growth.Value(s, order=1).T)