| 1 |  |  | import functools | 
            
                                                                                                            
                            
            
                                    
            
            
                | 2 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 3 |  |  | from ... import problems | 
            
                                                                                                            
                            
            
                                    
            
            
                | 4 |  |  |  | 
            
                                                                                                            
                                                                
            
                                    
            
            
                | 5 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 6 |  |  | class SolowModel(problems.IVP): | 
            
                                                        
            
                                    
            
            
                | 7 |  |  |     """ | 
            
                                                        
            
                                    
            
            
                | 8 |  |  |     Class representing a generic Solow growth model. | 
            
                                                        
            
                                    
            
            
                | 9 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 10 |  |  |     Attributes | 
            
                                                        
            
                                    
            
            
                | 11 |  |  |     ---------- | 
            
                                                        
            
                                    
            
            
                | 12 |  |  |     equilibrium_capital : function | 
            
                                                        
            
                                    
            
            
                | 13 |  |  |         Equilibrium value for capital (per unit effective labor). | 
            
                                                        
            
                                    
            
            
                | 14 |  |  |     intensive_output : function | 
            
                                                        
            
                                    
            
            
                | 15 |  |  |         Output (per unit effective labor supply). | 
            
                                                        
            
                                    
            
            
                | 16 |  |  |     params : dict(str: float) | 
            
                                                        
            
                                    
            
            
                | 17 |  |  |         Dictionary of model parameters. | 
            
                                                        
            
                                    
            
            
                | 18 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 19 |  |  |     """ | 
            
                                                        
            
                                    
            
            
                | 20 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 21 |  |  |     def __init__(self, f, k_star, params): | 
            
                                                        
            
                                    
            
            
                | 22 |  |  |         """ | 
            
                                                        
            
                                    
            
            
                | 23 |  |  |         Initialize an instance of the SolowModel class. | 
            
                                                        
            
                                    
            
            
                | 24 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 25 |  |  |         Parameters | 
            
                                                        
            
                                    
            
            
                | 26 |  |  |         ---------- | 
            
                                                        
            
                                    
            
            
                | 27 |  |  |         f : function | 
            
                                                        
            
                                    
            
            
                | 28 |  |  |             Output (per unit effective labor supply). | 
            
                                                        
            
                                    
            
            
                | 29 |  |  |         k_star : function | 
            
                                                        
            
                                    
            
            
                | 30 |  |  |             Equilibrium value for capital (per unit effective labor). | 
            
                                                        
            
                                    
            
            
                | 31 |  |  |         params : dict(str: float) | 
            
                                                        
            
                                    
            
            
                | 32 |  |  |             Dictionary of model parameters. | 
            
                                                        
            
                                    
            
            
                | 33 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 34 |  |  |         """ | 
            
                                                        
            
                                    
            
            
                | 35 |  |  |         rhs = self._rhs_factory(f) | 
            
                                                        
            
                                    
            
            
                | 36 |  |  |         self._equilbrium_capital = k_star | 
            
                                                        
            
                                    
            
            
                | 37 |  |  |         self._intensive_output = f | 
            
                                                        
            
                                    
            
            
                | 38 |  |  |         super(SolowModel, self).__init__(self._initial_condition, 1, 1, params, rhs) | 
            
                                                        
            
                                    
            
            
                | 39 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 40 |  |  |     @property | 
            
                                                        
            
                                    
            
            
                | 41 |  |  |     def equilibrium_capital(self): | 
            
                                                        
            
                                    
            
            
                | 42 |  |  |         return self._equilbrium_capital | 
            
                                                        
            
                                    
            
            
                | 43 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 44 |  |  |     @property | 
            
                                                        
            
                                    
            
            
                | 45 |  |  |     def intensive_output(self): | 
            
                                                        
            
                                    
            
            
                | 46 |  |  |         return self._intensive_output | 
            
                                                        
            
                                    
            
            
                | 47 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 48 |  |  |     @staticmethod | 
            
                                                        
            
                                    
            
            
                | 49 |  |  |     def _initial_condition(t, k, k0, **params): | 
            
                                                        
            
                                    
            
            
                | 50 |  |  |         return [k - k0] | 
            
                                                        
            
                                    
            
            
                | 51 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 52 |  |  |     @classmethod | 
            
                                                        
            
                                    
            
            
                | 53 |  |  |     def _solow_model(cls, t, k, f, delta, g, n, s, **params): | 
            
                                                        
            
                                    
            
            
                | 54 |  |  |         return [s * f(k, **params) - (g + n + delta) * k] | 
            
                                                        
            
                                    
            
            
                | 55 |  |  |  | 
            
                                                        
            
                                    
            
            
                | 56 |  |  |     @classmethod | 
            
                                                        
            
                                    
            
            
                | 57 |  |  |     def _rhs_factory(cls, f): | 
            
                                                        
            
                                    
            
            
                | 58 |  |  |         return functools.partial(cls._solow_model, f=f) | 
            
                                                        
            
                                    
            
            
                | 59 |  |  |  |