from numba import float64

from numba.experimental import jitclass

opt_growth_data = [

('α', float64), # Production parameter

class OptimalGrowthModel:

def __init__(self,

α=0.4,

β=0.96,

α=0.4,

β=0.96,

μ=0,

s=0.1,

grid_max=4,

# Store shocks (with a seed, so results are reproducible)

np.random.seed(seed)

self.shocks = np.exp(μ + s * np.random.randn(shock_size))

def f(self, k):

"The production function"

return k**self.α

def u(self, c):

"The utility function"

def u_prime_inv(self, c):

"Inverse of u'"

return 1/c

from numba import float64

from numba.experimental import jitclass

opt_growth_data = [

('α', float64), # Production parameter

class OptimalGrowthModel_CRRA:

def __init__(self,

α=0.4,

β=0.96,

α=0.4,

β=0.96,

μ=0,

s=0.1,

γ=1.5,

γ=1.5,

grid_max=4,

grid_size=120,

shock_size=250,

# Store shocks (with a seed, so results are reproducible)

np.random.seed(seed)

self.shocks = np.exp(μ + s * np.random.randn(shock_size))

def f(self, k):

"The production function."

def u_prime_inv(c):

return c**(-1 / self.γ)

import matplotlib.pyplot as plt

plt.rcParams["figure.figsize"] = (11, 5) #set default figure size

import numpy as np

import quantecon as qe

from quantecon.markov import DiscreteDP

from numba import jit

```

plt.show()

```

import matplotlib.pyplot as plt

plt.rcParams["figure.figsize"] = (11, 5) #set default figure size

import numpy as np

import quantecon as qe

from interpolation import interp

from quantecon.optimize import brentq

from numba import njit, float64

from numba.experimental import jitclass

from numba import njit

```

## The Euler Equation

---

tags: [hide-output]

---

!pip install quantecon

!pip install interpolation

```

import matplotlib.pyplot as plt

plt.rcParams["figure.figsize"] = (11, 5) #set default figure size

import numpy as np

import quantecon as qe

from interpolation import interp

from numba import njit, float64

from numba.experimental import jitclass

from quantecon.optimize import brentq

from numba import njit

```

## Key Idea

This is due to the lack of a numerical root-finding step.

We can now solve the optimal growth model at given parameters extremely fast.

plt.rcParams["figure.figsize"] = (11, 5) #set default figure size

import numpy as np

import sympy as sym

from sympy import init_printing, latex

from sympy import init_printing

from matplotlib import cm

from mpl_toolkits.mplot3d import Axes3D

```