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import functools |
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import numpy as np |
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from ... import problems |
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class RamseyCassKoopmansModel(problems.TwoPointBVP): |
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""" |
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Class representing a generic Solow growth model. |
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Attributes |
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---------- |
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equilibrium_capital : function |
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Equilibrium value for capital (per unit effective labor). |
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equilibrium_consumption : function |
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Equilibrium value for consumption (per unit effective labor). |
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intensive_output : function |
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Output (per unit effective labor supply). |
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marginal_product_capital : function |
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Marginal product of capital (i.e., first derivative of intensive output). |
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params : dict(str: float) |
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Dictionary of model parameters. |
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pratt_arrow_risk_aversion : function |
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Pratt-Arrow relative risk aversion function. |
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""" |
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def __init__(self, ARA, f, k_star, mpk, params): |
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""" |
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Initialize an instance of the RamseyCassKoopmans class. |
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Parameters |
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---------- |
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ARA : function |
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Pratt-Arrow absolute risk aversion function. |
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f : function |
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Output (per unit effective labor supply). |
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k_star : function |
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Equilibrium (i.e., steady-state) value for capital stock (per unit |
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effective labor supply). |
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mpk : function |
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Marginal product of capital (per unit effective labor supply). |
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params : dict(str: float) |
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Dictionary of model parameters |
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""" |
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self._equilibrium_capital = k_star |
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self._intensive_output = f |
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self._marginal_product_capital = mpk |
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self._pratt_arrow_risk_aversion = ARA |
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# construct the terminal condition |
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c_star = self._c_star_factory(k_star) |
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terminal_condition = self._terminal_condition_factory(c_star) |
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self._equilibrium_consumption = c_star |
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# construct the RHS of the system of ODEs |
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rhs = self._rhs_factory(ARA, f, mpk) |
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super(RamseyCassKoopmansModel, self).__init__(self._initial_condition, |
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terminal_condition, 1, 2, |
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params, rhs) |
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@property |
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def equilibrium_capital(self): |
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return self._equilibrium_capital |
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@property |
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def equilibrium_consumption(self): |
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return self._equilibrium_consumption |
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@property |
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def intensive_output(self): |
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return self._intensive_output |
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@property |
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def marginal_product_capital(self): |
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return self._marginal_product_capital |
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@property |
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def pratt_arrow_risk_aversion(self): |
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return self._pratt_arrow_risk_aversion |
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@staticmethod |
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def _actual_investment(k_tilde, c_tilde, f, **params): |
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return f(k_tilde, **params) - c_tilde |
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@staticmethod |
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def _breakeven_investment(k_tilde, delta, g, n, **params): |
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return (g + n + delta) * k_tilde |
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@classmethod |
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def _c_tilde_dot(cls, t, k_tilde, c_tilde, ARA, mpk, A0, delta, g, rho, **params): |
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A = cls._technology(t, A0, g) |
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return ((mpk(k_tilde, **params) - delta - rho) / (A * ARA(t, A * c_tilde, **params))) - g * c_tilde |
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@staticmethod |
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def _initial_condition(t, k_tilde, c_tilde, A0, K0, N0, **params): |
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return [k_tilde - (K0 / (A0 * N0))] |
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@staticmethod |
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def _technology(t, A0, g): |
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return A0 * np.exp(g * t) |
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@classmethod |
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def _k_dot(cls, t, k_tilde, c_tilde, f, delta, g, n, **params): |
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k_dot = (cls._actual_investment(k_tilde, c_tilde, f, **params) - |
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cls._breakeven_investment(k_tilde, delta, g, n)) |
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return k_dot |
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@classmethod |
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def _ramsey_model(cls, t, k_tilde, c_tilde, ARA, f, mpk, A0, delta, g, n, rho, **params): |
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out = [cls._k_dot(t, k_tilde, c_tilde, f, delta, g, n, **params), |
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cls._c_tilde_dot(t, k_tilde, c_tilde, ARA, mpk, A0, delta, g, rho, **params)] |
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return out |
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@classmethod |
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def _rhs_factory(cls, ARA, f, mpk): |
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return functools.partial(cls._ramsey_model, ARA=ARA, f=f, mpk=mpk) |
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@staticmethod |
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def _terminal_condition(t, k_tilde, c_tilde, c_star, **params): |
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return [c_tilde - c_star(**params)] |
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@classmethod |
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def _terminal_condition_factory(cls, c_star): |
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return functools.partial(cls._terminal_condition, c_star=c_star) |
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def _c_star(self, k_star, **params): |
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k_tilde = k_star(**params) |
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c_star = (self.intensive_output(k_tilde, **params) - |
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self._breakeven_investment(k_tilde, **params)) |
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return c_star |
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def _c_star_factory(self, k_star): |
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return functools.partial(self._c_star, k_star=k_star) |
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davidrpugh /
pyCollocation
