def _cFuncLinear(aXtraGrid, mNrmMinNow, mNrmNow, cNrmNow, MPCminNow, hNrmNow):
mNrmGrid = mNrmMinNow + aXtraGrid
mNrmCnst = np.array([mNrmMinNow, mNrmMinNow + 1])
cNrmCnst = np.array([0.0, 1.0])
cFuncNowCnst = linear_interp_fast(mNrmGrid.flatten(), mNrmCnst, cNrmCnst)
cFuncNowUnc = linear_interp_fast(mNrmGrid.flatten(), mNrmNow, cNrmNow,
MPCminNow * hNrmNow, MPCminNow)
cNrmNow = np.where(cFuncNowCnst <= cFuncNowUnc, cFuncNowCnst, cFuncNowUnc)
return cNrmNow, mNrmGrid
def _solveConsIndShockLinearNumba(
mNrmMinNext,
mNrmNext,
CRRA,
mNrmUnc,
cNrmUnc,
DiscFacEff,
Rfree,
PermGroFac,
PermShkVals_temp,
ShkPrbs_temp,
aNrmNow,
BoroCnstNat,
cFuncInterceptNext,
cFuncSlopeNext,
):
"""
Calculate end-of-period marginal value of assets at each point in aNrmNow.
Does so by taking a weighted sum of next period marginal values across
income shocks (in a preconstructed grid self.mNrmNext).
"""
mNrmCnst = np.array([mNrmMinNext, mNrmMinNext + 1])
cNrmCnst = np.array([0.0, 1.0])
cFuncNextCnst = linear_interp_fast(mNrmNext.flatten(), mNrmCnst, cNrmCnst)
cFuncNextUnc = linear_interp_fast(
mNrmNext.flatten(), mNrmUnc, cNrmUnc, cFuncInterceptNext, cFuncSlopeNext
)
cFuncNext = np.minimum(cFuncNextCnst, cFuncNextUnc)
vPfuncNext = utilityP(cFuncNext, CRRA).reshape(mNrmNext.shape)
EndOfPrdvP = (
DiscFacEff
* Rfree
* PermGroFac ** (-CRRA)
* np.sum(PermShkVals_temp ** (-CRRA) * vPfuncNext * ShkPrbs_temp, axis=0)
)
# Finds interpolation points (c,m) for the consumption function.
cNrmNow = utilityP_inv(EndOfPrdvP, CRRA)
mNrmNow = cNrmNow + aNrmNow
# Limiting consumption is zero as m approaches mNrmMin
cNrm = _np_insert(cNrmNow, 0, 0.0, axis=-1)
mNrm = _np_insert(mNrmNow, 0, BoroCnstNat, axis=-1)
return (cNrm, mNrm, EndOfPrdvP)
def _find_mNrmStELinear(
m, PermGroFac, Rfree, Ex_IncNext, mNrmMin, mNrm, cNrm, MPC, MPCmin, hNrm
):
# Make a linear function of all combinations of c and m that yield mNext = mNow
mZeroChange = (1.0 - PermGroFac / Rfree) * m + (PermGroFac / Rfree) * Ex_IncNext
mNrmCnst = np.array([mNrmMin, mNrmMin + 1])
cNrmCnst = np.array([0.0, 1.0])
cFuncNowCnst = linear_interp_fast(np.array([m]), mNrmCnst, cNrmCnst)
cFuncNowUnc = linear_interp_fast(np.array([m]), mNrm, cNrm, MPCmin * hNrm, MPCmin)
cNrmNow = np.where(cFuncNowCnst <= cFuncNowUnc, cFuncNowCnst, cFuncNowUnc)
# Find the steady state level of market resources
res = cNrmNow[0] - mZeroChange
# A zero of this is SS market resources
return res
