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Add numerical guards for CES with heterogeneous epsilon #1096

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Add numerical guards for CES with heterogeneous epsilon #1096

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70 changes: 46 additions & 24 deletions ogcore/firm.py
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Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,10 @@
------------------------------------------------------------------------
"""

# Floor for quantities raised to potentially negative powers in CES.
# Prevents 0^(negative) → inf/NaN when epsilon != 1.
_FLOOR = 1e-12

"""
------------------------------------------------------------------------
Functions
Expand Down Expand Up @@ -60,18 +64,21 @@ def get_Y(K, K_g, L, p, method, m=-1):
* (L ** (1 - gamma - gamma_g))
)
else:
K_f = np.maximum(K, _FLOOR)
K_g_f = np.maximum(K_g, _FLOOR)
L_f = np.maximum(L, _FLOOR)
Y = Z * (
(
(gamma ** (1 / epsilon))
* (K ** ((epsilon - 1) / epsilon))
* (K_f ** ((epsilon - 1) / epsilon))
)
+ (
(gamma_g ** (1 / epsilon))
* (K_g ** ((epsilon - 1) / epsilon))
* (K_g_f ** ((epsilon - 1) / epsilon))
)
+ (
((1 - gamma - gamma_g) ** (1 / epsilon))
* (L ** ((epsilon - 1) / epsilon))
* (L_f ** ((epsilon - 1) / epsilon))
)
) ** (epsilon / (epsilon - 1))
else:
Expand All @@ -85,15 +92,18 @@ def get_Y(K, K_g, L, p, method, m=-1):
gamma = p.gamma
epsilon = p.epsilon
Z = p.Z[-1, :]
K_f = np.maximum(K, _FLOOR)
K_g_f = np.maximum(K_g, _FLOOR)
L_f = np.maximum(L, _FLOOR)
Y = Z * (
((gamma ** (1 / epsilon)) * (K ** ((epsilon - 1) / epsilon)))
((gamma ** (1 / epsilon)) * (K_f ** ((epsilon - 1) / epsilon)))
+ (
(gamma_g ** (1 / epsilon))
* (K_g ** ((epsilon - 1) / epsilon))
* (K_g_f ** ((epsilon - 1) / epsilon))
)
+ (
((1 - gamma - gamma_g) ** (1 / epsilon))
* (L ** ((epsilon - 1) / epsilon))
* (L_f ** ((epsilon - 1) / epsilon))
)
) ** (epsilon / (epsilon - 1))
Y2 = Z * (K**gamma) * (K_g**gamma_g) * (L ** (1 - gamma - gamma_g))
Expand All @@ -117,18 +127,21 @@ def get_Y(K, K_g, L, p, method, m=-1):
* (L ** (1 - gamma - gamma_g))
)
else:
K_f = np.maximum(K, _FLOOR)
K_g_f = np.maximum(K_g, _FLOOR)
L_f = np.maximum(L, _FLOOR)
Y = Z * (
(
(gamma ** (1 / epsilon))
* (K ** ((epsilon - 1) / epsilon))
* (K_f ** ((epsilon - 1) / epsilon))
)
+ (
(gamma_g ** (1 / epsilon))
* (K_g ** ((epsilon - 1) / epsilon))
* (K_g_f ** ((epsilon - 1) / epsilon))
)
+ (
((1 - gamma - gamma_g) ** (1 / epsilon))
* (L ** ((epsilon - 1) / epsilon))
* (L_f ** ((epsilon - 1) / epsilon))
)
) ** (epsilon / (epsilon - 1))
else:
Expand All @@ -141,15 +154,18 @@ def get_Y(K, K_g, L, p, method, m=-1):
gamma = p.gamma
epsilon = p.epsilon
Z = p.Z[: p.T, :]
K_f = np.maximum(K, _FLOOR)
K_g_f = np.maximum(K_g, _FLOOR)
L_f = np.maximum(L, _FLOOR)
Y = Z * (
((gamma ** (1 / epsilon)) * (K ** ((epsilon - 1) / epsilon)))
((gamma ** (1 / epsilon)) * (K_f ** ((epsilon - 1) / epsilon)))
+ (
(gamma_g ** (1 / epsilon))
* (K_g ** ((epsilon - 1) / epsilon))
* (K_g_f ** ((epsilon - 1) / epsilon))
)
+ (
((1 - gamma - gamma_g) ** (1 / epsilon))
* (L ** ((epsilon - 1) / epsilon))
* (L_f ** ((epsilon - 1) / epsilon))
)
) ** (epsilon / (epsilon - 1))
Y2 = Z * (K**gamma) * (K_g**gamma_g) * (L ** (1 - gamma - gamma_g))
Expand Down Expand Up @@ -273,9 +289,10 @@ def get_KLratio_KLonly(r, p, method, m=-1):
# General CES case
cost_of_capital = get_cost_of_capital(r, p, method, m)
bracket = cost_of_capital * (Z * (gamma ** (1 / epsilon))) ** -1
denom = (bracket ** (epsilon - 1)) - (gamma ** (1 / epsilon))
denom = np.maximum(denom, _FLOOR)
KLratio = (
((1 - gamma) ** (1 / epsilon))
/ ((bracket ** (epsilon - 1)) - (gamma ** (1 / epsilon)))
((1 - gamma) ** (1 / epsilon)) / denom
) ** (epsilon / (epsilon - 1))

return KLratio
Expand Down Expand Up @@ -337,12 +354,13 @@ def get_MPx(Y, x, share, p, method, m=-1):
Z = p.Z[: p.T, m].reshape(p.T, 1)
Y = Y[: p.T].reshape(p.T, 1)
x = x[: p.T].reshape(p.T, 1)
if np.any(x) == 0:
if np.any(x == 0):
MPx = np.zeros_like(Y)
else:
MPx = Z ** ((p.epsilon[m] - 1) / p.epsilon[m]) * ((share * Y) / x) ** (
1 / p.epsilon[m]
)
x_f = np.maximum(x, _FLOOR)
MPx = Z ** ((p.epsilon[m] - 1) / p.epsilon[m]) * (
(share * Y) / x_f
) ** (1 / p.epsilon[m])

return MPx

Expand Down Expand Up @@ -656,13 +674,17 @@ def solve_L(Y, K, K_g, p, method, m=-1):
if epsilon == 1.0:
L = (Y / (Z * K**gamma * K_g**gamma_g)) ** (1 / (1 - gamma - gamma_g))
else:
Y_f = np.maximum(Y, _FLOOR)
K_f = np.maximum(K, _FLOOR)
K_g_f = np.maximum(K_g, _FLOOR)
numer = (
(Y_f / Z) ** ((epsilon - 1) / epsilon)
- gamma ** (1 / epsilon) * K_f ** ((epsilon - 1) / epsilon)
- gamma_g ** (1 / epsilon) * K_g_f ** ((epsilon - 1) / epsilon)
)
numer = np.maximum(numer, _FLOOR)
L = (
(
(Y / Z) ** ((epsilon - 1) / epsilon)
- gamma ** (1 / epsilon) * K ** ((epsilon - 1) / epsilon)
- gamma_g ** (1 / epsilon) * K_g ** ((epsilon - 1) / epsilon)
)
/ ((1 - gamma - gamma_g) ** (1 / epsilon))
numer / ((1 - gamma - gamma_g) ** (1 / epsilon))
) ** (epsilon / (epsilon - 1))

return L
Expand Down
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