Remove unused imports

Author: Smit-create

lectures/BCG_complete_mkts.md

@@ -802,44 +802,44 @@ It consists of 4 functions that do the following things:
     - First, create a grid for capital.
     - Then for each value of capital stock in the grid, compute the left side of the planner's
       first-order necessary condition for  $k$, that is,
-      
+
       $$
       \beta \alpha A K^{\alpha -1} \int \left( \frac{w_1(\epsilon) + A K^\alpha e^\epsilon}{w_0 - K } \right)^{-\gamma} e^\epsilon g(\epsilon) d \epsilon  - 1 =0
       $$
-      
+
     - Find $k$ that solves this equation.
 * `q` computes Arrow security prices as a function of the productivity shock $\epsilon$ and capital $K$:
-  
+
   $$
   q(\epsilon;K) = \beta \left( \frac{u'\left( w_1(\epsilon) + A K^\alpha e^\epsilon\right)} {u'(w_0 - K )} \right)
   $$
-  
+
 * `V` solves for the firm value given capital $k$:
-  
+
   $$
   V = - k + \int A k^\alpha e^\epsilon q(\epsilon; K) d \epsilon
   $$
-  
+
 * `opt_c` computes optimal consumptions $c^i_0$, and $c^i(\epsilon)$:
     - The function first computes weight $\eta$ using the
       budget constraint for agent 1:
-      
+
       $$
       w_0^1 + \theta_0^1 V + \int w_1^1(\epsilon) q(\epsilon) d \epsilon
       = c_0^1 + \int c_1^1(\epsilon) q(\epsilon) d \epsilon
       = \eta \left( C_0 + \int C_1(\epsilon) q(\epsilon) d \epsilon \right)
       $$
       where
-      
+
       $$
       \begin{aligned}
       C_0 & = w_0 - K \cr
       C_1(\epsilon) & = w_1(\epsilon) + A K^\alpha e^\epsilon \cr
       \end{aligned}
       $$
-      
+
     - It computes consumption for each agent as
-    
+
       $$
       \begin{aligned}
       c_0^1 & = \eta C_0 \cr
@@ -848,7 +848,7 @@ It consists of 4 functions that do the following things:
       c_1^2 (\epsilon) & = (1 - \eta) C_1(\epsilon)
       \end{aligned}
       $$
-  
+
 
 The list of parameters includes:
 
@@ -868,7 +868,6 @@ The list of parameters includes:
   Gauss-Hermite quadrature: default value is 10
 
 ```{code-cell} ipython
-import pandas as pd
 import numpy as np
 import matplotlib.pyplot as plt
 from scipy.stats import norm
@@ -1205,4 +1204,3 @@ Image(fig.to_image(format="png"))
 # fig.show() will provide interactive plot when running
 # notebook locally
 ```
-

lectures/BCG_incomplete_mkts.md

@@ -581,47 +581,47 @@ Here goes:
    $|\theta^1_h - \theta^1_l|$ is large:
     * Compute agent 1’s valuation of the equity claim with a
       fixed-point iteration:
-      
+
       $q_1 = \beta \int \frac{u^\prime(c^1_1(\epsilon))}{u^\prime(c^1_0)} d^e(k,b;\epsilon) g(\epsilon) \ d\epsilon$
-      
+
       where
-      
+
       $c^1_1(\epsilon) = w^1_1(\epsilon) + \theta^1 d^e(k,b;\epsilon)$
-      
+
       and
-      
+
       $c^1_0 = w^1_0 + \theta^1_0V - q_1\theta^1$
     * Compute agent 2’s valuation of the bond claim with a
       fixed-point iteration:
-      
+
       $p = \beta \int \frac{u^\prime(c^2_1(\epsilon))}{u^\prime(c^2_0)} d^b(k,b;\epsilon) g(\epsilon) \ d\epsilon$
-      
+
       where
-      
+
       $c^2_1(\epsilon) = w^2_1(\epsilon) + \theta^2 d^e(k,b;\epsilon) + b$
-      
+
       and
-      
+
       $c^2_0 = w^2_0 + \theta^2_0 V - q_1 \theta^2 - pb$
     * Compute agent 2’s valuation of the equity claim with a
       fixed-point iteration:
-      
+
       $q_2 = \beta \int \frac{u^\prime(c^2_1(\epsilon))}{u^\prime(c^2_0)} d^e(k,b;\epsilon) g(\epsilon) \ d\epsilon$
-      
+
       where
-      
+
       $c^2_1(\epsilon) = w^2_1(\epsilon) + \theta^2 d^e(k,b;\epsilon) + b$
-      
+
       and
-      
+
       $c^2_0 = w^2_0 + \theta^2_0 V - q_2 \theta^2 - pb$
     * If $q_1 > q_2$, Set $\theta_l = \theta^1$;
       otherwise, set $\theta_h = \theta^1$.
     * Repeat steps 6Aa through 6Ad until
       $|\theta^1_h - \theta^1_l|$ is small.
 1. Set bond price as $p$ and equity price as  $q = \max(q_1,q_2)$.
 1. Compute optimal choices of consumption:
-   
+
    $$
    \begin{aligned}
    c^1_0 &= w^1_0 + \theta^1_0V - q\theta^1 \\
@@ -630,29 +630,29 @@ Here goes:
    c^2_1(\epsilon) &= w^2_1(\epsilon) + \theta^2 d^e(k,b;\epsilon) + b
    \end{aligned}
    $$
-   
+
 1. (Here we confess to abusing notation again, but now in a different
    way. In step 7, we interpret frozen $c^i$s as Big
    $C^i$. We do this to solve the firm’s problem.) Fixing the
    values of $c^i_0$ and $c^i_1(\epsilon)$, compute optimal
    choices of capital $k$ and debt level $b$ using the
    firm’s first order necessary conditions.
 1. Compute deviations from the firm’s FONC for capital $k$ as:
-   
+
    $kfoc = \beta \alpha A k^{\alpha - 1} \left( \int \frac{u^\prime(c^2_1(\epsilon))}{u^\prime(c^2_0)}  e^\epsilon g(\epsilon) \ d\epsilon \right) - 1$
     - If $kfoc > 0$, Set $k_l = k$; otherwise, set
       $k_h = k$.
     - Repeat steps 4 through 7A until $|k_h-k_l|$ is small.
 1. Compute deviations from the firm’s FONC for debt level $b$  as:
-   
+
    $bfoc = \beta \left[ \int_{\epsilon^*}^\infty \left( \frac{u^\prime(c^1_1(\epsilon))}{u^\prime(c^1_0)} \right) g(\epsilon) \ d\epsilon -  \int_{\epsilon^*}^\infty \left( \frac{u^\prime(c^2_1(\epsilon))}{u^\prime(c^2_0)} \right)  g(\epsilon) \ d\epsilon \right]$
     - If $bfoc > 0$, Set $b_h = b$; otherwise, set
       $b_l = b$.
     - Repeat steps 3 through 7B until $|b_h-b_l|$ is small.
 1. Given prices $q$ and $p$ from step 6, and the firm
    choices of $k$ and $b$ from step 7, compute the synthetic
    firm value:
-   
+
    $V_x = -k + q + pb$
     - If $V_x > V$, then set $V_l = V$; otherwise, set
       $V_h = V$.
@@ -705,12 +705,9 @@ Parameters include:
 - bound: Bound for truncated normal distribution. Default value is 3.
 
 ```{code-cell} ipython
-import pandas as pd
 import numpy as np
-from scipy.stats import norm
 from scipy.stats import truncnorm
 from scipy.integrate import quad
-from scipy.optimize import bisect
 from numba import njit
 from interpolation import interp
 ```
@@ -1943,4 +1940,3 @@ Agents of type 2 value bonds more highly (they want more hedging).
 
 Taken together with our earlier plot of equity holdings, these graphs confirm our earlier conjecture that while both type
 of agents hold equities, only agents of type 2 holds bonds.
-

lectures/additive_functionals.md

@@ -75,7 +75,6 @@ Let's start with some imports:
 
 ```{code-cell} ipython3
 import numpy as np
-import scipy as sp
 import scipy.linalg as la
 import quantecon as qe
 import matplotlib.pyplot as plt

lectures/amss.md

@@ -41,11 +41,8 @@ Let's start with following imports:
 ```{code-cell} ipython
 import numpy as np
 import matplotlib.pyplot as plt
-from scipy.optimize import root
-from interpolation.splines import eval_linear, UCGrid, nodes
-from quantecon import optimize, MarkovChain
-from numba import njit, prange, float64
-from numba.experimental import jitclass
+from interpolation.splines import UCGrid, nodes
+from quantecon import MarkovChain
 
 %matplotlib inline
 ```
@@ -1033,4 +1030,3 @@ problem, there exists another realization $\tilde s^t$ with
 the same history up until the previous period, i.e., $\tilde s^{t-1}=
 s^{t-1}$, but where the multiplier on constraint {eq}`AMSS_46` takes  a positive value, so
 $\gamma_t(\tilde s^t)>0$.
-

lectures/arellano.md

@@ -78,10 +78,8 @@ Let's start with some imports:
 import matplotlib.pyplot as plt
 import numpy as np
 import quantecon as qe
-import random
 
-from numba import njit, int64, float64, prange
-from numba.experimental import jitclass
+from numba import njit, prange
 %matplotlib inline
 ```