def post_solve(self):
self.solution_fast = deepcopy(self.solution)
if self.cycles == 0:
cycles = 1
else:
cycles = self.cycles
self.solution[-1] = self.solution_terminal_cs
for i in range(cycles):
for j in range(self.T_cycle):
solution = self.solution[i * self.T_cycle + j]
# Define the borrowing constraint (limiting consumption function)
cFuncNowCnst = LinearInterp(
np.array([solution.mNrmMin, solution.mNrmMin + 1]),
np.array([0.0, 1.0]),
)
"""
Constructs a basic solution for this period, including the consumption
function and marginal value function.
"""
if self.CubicBool:
# Makes a cubic spline interpolation of the unconstrained consumption
# function for this period.
cFuncNowUnc = CubicInterp(
solution.mNrm,
solution.cNrm,
solution.MPC,
solution.cFuncLimitIntercept,
solution.cFuncLimitSlope,
)
else:
# Makes a linear interpolation to represent the (unconstrained) consumption function.
# Construct the unconstrained consumption function
cFuncNowUnc = LinearInterp(
solution.mNrm,
solution.cNrm,
solution.cFuncLimitIntercept,
solution.cFuncLimitSlope,
)
# Combine the constrained and unconstrained functions into the true consumption function
cFuncNow = LowerEnvelope(cFuncNowUnc, cFuncNowCnst)
# Make the marginal value function and the marginal marginal value function
vPfuncNow = MargValueFuncCRRA(cFuncNow, self.CRRA)
# Pack up the solution and return it
consumer_solution = ConsumerSolution(
cFunc=cFuncNow,
vPfunc=vPfuncNow,
mNrmMin=solution.mNrmMin,
hNrm=solution.hNrm,
MPCmin=solution.MPCmin,
MPCmax=solution.MPCmax,
)
if self.vFuncBool:
vNvrsFuncNow = CubicInterp(
solution.mNrmGrid,
solution.vNvrs,
solution.vNvrsP,
solution.MPCminNvrs * solution.hNrm,
solution.MPCminNvrs,
)
vFuncNow = ValueFuncCRRA(vNvrsFuncNow, self.CRRA)
consumer_solution.vFunc = vFuncNow
if self.CubicBool or self.vFuncBool:
_searchFunc = (
_find_mNrmStECubic if self.CubicBool else _find_mNrmStELinear
)
# Add mNrmStE to the solution and return it
consumer_solution.mNrmStE = _add_mNrmStEIndNumba(
self.PermGroFac[j],
self.Rfree,
solution.Ex_IncNext,
solution.mNrmMin,
solution.mNrm,
solution.cNrm,
solution.MPC,
solution.MPCmin,
solution.hNrm,
_searchFunc,
)
self.solution[i * self.T_cycle + j] = consumer_solution
def makeSolution(self,cNrm,mNrm):
'''
Construct an object representing the solution to this period's problem.
Parameters
----------
cNrm : np.array
Array of normalized consumption values for interpolation. Each row
corresponds to a Markov state for this period.
mNrm : np.array
Array of normalized market resource values for interpolation. Each
row corresponds to a Markov state for this period.
Returns
-------
solution : ConsumerSolution
The solution to the single period consumption-saving problem. Includes
a consumption function cFunc (using cubic or linear splines), a marg-
inal value function vPfunc, a minimum acceptable level of normalized
market resources mNrmMin, normalized human wealth hNrm, and bounding
MPCs MPCmin and MPCmax. It might also have a value function vFunc
and marginal marginal value function vPPfunc. All of these attributes
are lists or arrays, with elements corresponding to the current
Markov state. E.g. solution.cFunc[0] is the consumption function
when in the i=0 Markov state this period.
'''
solution = ConsumerSolution() # An empty solution to which we'll add state-conditional solutions
# Calculate the MPC at each market resource gridpoint in each state (if desired)
if self.CubicBool:
dcda = self.EndOfPrdvPP/self.uPP(np.array(self.cNrmNow))
MPC = dcda/(dcda+1.0)
self.MPC_temp = np.hstack((np.reshape(self.MPCmaxNow,(self.StateCount,1)),MPC))
interpfunc = self.makeCubiccFunc
else:
interpfunc = self.makeLinearcFunc
# Loop through each current period state and add its solution to the overall solution
for i in range(self.StateCount):
# Set current-period-conditional human wealth and MPC bounds
self.hNrmNow_j = self.hNrmNow[i]
self.MPCminNow_j = self.MPCminNow[i]
if self.CubicBool:
self.MPC_temp_j = self.MPC_temp[i,:]
# Construct the consumption function by combining the constrained and unconstrained portions
self.cFuncNowCnst = LinearInterp([self.mNrmMin_list[i], self.mNrmMin_list[i]+1.0],
[0.0,1.0])
cFuncNowUnc = interpfunc(mNrm[i,:],cNrm[i,:])
cFuncNow = LowerEnvelope(cFuncNowUnc,self.cFuncNowCnst)
# Make the marginal value function and pack up the current-state-conditional solution
vPfuncNow = MargValueFunc(cFuncNow,self.CRRA)
solution_cond = ConsumerSolution(cFunc=cFuncNow, vPfunc=vPfuncNow,
mNrmMin=self.mNrmMinNow)
if self.CubicBool: # Add the state-conditional marginal marginal value function (if desired)
solution_cond = self.addvPPfunc(solution_cond)
# Add the current-state-conditional solution to the overall period solution
solution.appendSolution(solution_cond)
# Add the lower bounds of market resources, MPC limits, human resources,
# and the value functions to the overall solution
solution.mNrmMin = self.mNrmMin_list
solution = self.addMPCandHumanWealth(solution)
if self.vFuncBool:
vFuncNow = self.makevFunc(solution)
solution.vFunc = vFuncNow
# Return the overall solution to this period
return solution