def postSolve(self):
'''
This method adds consumption at m=0 to the list of stable arm points,
then constructs the consumption function as a cubic interpolation over
those points. Should be run after the backshooting routine is complete.
Parameters
----------
none
Returns
-------
none
'''
# Add bottom point to the stable arm points
self.solution[0].mNrm_list.insert(0, 0.0)
self.solution[0].cNrm_list.insert(0, 0.0)
self.solution[0].MPC_list.insert(0, self.MPCmax)
# Construct an interpolation of the consumption function from the stable arm points
self.solution[0].cFunc = CubicInterp(self.solution[0].mNrm_list,
self.solution[0].cNrm_list,
self.solution[0].MPC_list,
self.PFMPC * (self.h - 1.0),
self.PFMPC)
self.solution[0].cFunc_U = lambda m: self.PFMPC * m
def makevFunc(self, solution):
'''
Make the beginning-of-period value function (unconditional on the shock).
Parameters
----------
solution : ConsumerSolution
The solution to this single period problem, which must include the
consumption function.
Returns
-------
vFuncNow : ValueFunc
A representation of the value function for this period, defined over
normalized market resources m: v = vFuncNow(m).
'''
# Compute expected value and marginal value on a grid of market resources,
# accounting for all of the discrete preference shocks
PrefShkCount = self.PrefShkVals.size
mNrm_temp = self.mNrmMinNow + self.aXtraGrid
vNrmNow = np.zeros_like(mNrm_temp)
vPnow = np.zeros_like(mNrm_temp)
for j in range(PrefShkCount):
this_shock = self.PrefShkVals[j]
this_prob = self.PrefShkPrbs[j]
cNrmNow = solution.cFunc(mNrm_temp,
this_shock * np.ones_like(mNrm_temp))
aNrmNow = mNrm_temp - cNrmNow
vNrmNow += this_prob * (this_shock * self.u(cNrmNow) +
self.EndOfPrdvFunc(aNrmNow))
vPnow += this_prob * this_shock * self.uP(cNrmNow)
# Construct the beginning-of-period value function
vNvrs = self.uinv(vNrmNow) # value transformed through inverse utility
vNvrsP = vPnow * self.uinvP(vNrmNow)
mNrm_temp = np.insert(mNrm_temp, 0, self.mNrmMinNow)
vNvrs = np.insert(vNvrs, 0, 0.0)
vNvrsP = np.insert(vNvrsP, 0,
self.MPCmaxEff**(-self.CRRA / (1.0 - self.CRRA)))
MPCminNvrs = self.MPCminNow**(-self.CRRA / (1.0 - self.CRRA))
vNvrsFuncNow = CubicInterp(mNrm_temp, vNvrs, vNvrsP,
MPCminNvrs * self.hNrmNow, MPCminNvrs)
vFuncNow = ValueFunc(vNvrsFuncNow, self.CRRA)
return vFuncNow