Merge branch 'main' into anaconda=2024.02

Author: mmcky

lectures/BCG_complete_mkts.md

@@ -31,7 +31,6 @@ In addition to what's in Anaconda, this lecture will need the following librarie
 tags: [hide-output]
 ---
 !pip install --upgrade quantecon
-!pip install interpolation
 !conda install -y -c plotly plotly plotly-orca
 ```
 

lectures/BCG_incomplete_mkts.md

@@ -3,8 +3,10 @@ jupytext:
   text_representation:
     extension: .md
     format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.16.1
 kernelspec:
-  display_name: Python 3
+  display_name: Python 3 (ipykernel)
   language: python
   name: python3
 ---
@@ -26,12 +28,10 @@ kernelspec:
 
 In addition to what's in Anaconda, this lecture will need the following libraries:
 
-```{code-cell} ipython
----
-tags: [hide-output]
----
+```{code-cell} ipython3
+:tags: [hide-output]
+
 !pip install --upgrade quantecon
-!pip install interpolation
 !conda install -y -c plotly plotly plotly-orca
 ```
 
@@ -703,15 +703,14 @@ Parameters include:
 - $\beta$: Discount factor. Default value is 0.96.
 - bound: Bound for truncated normal distribution. Default value is 3.
 
-```{code-cell} ipython
+```{code-cell} ipython3
 import numpy as np
 from scipy.stats import truncnorm
 from scipy.integrate import quad
 from numba import njit
-from interpolation import interp
 ```
 
-```{code-cell} python3
+```{code-cell} ipython3
 class BCG_incomplete_markets:
 
     # init method or constructor
@@ -784,7 +783,7 @@ class BCG_incomplete_markets:
         rv = truncnorm(ta, tb, loc=𝜇, scale=𝜎)
         𝜖_range = np.linspace(ta, tb, 1000000)
         pdf_range = rv.pdf(𝜖_range)
-        self.g = njit(lambda 𝜖: interp(𝜖_range, pdf_range, 𝜖))
+        self.g = njit(lambda 𝜖: np.interp(𝜖, 𝜖_range, pdf_range))
 
 
     #*************************************************************
@@ -1206,14 +1205,14 @@ Below we show some examples computed with the class `BCG_incomplete markets`.
 In the first example, we set up an instance of the BCG incomplete
 markets model with default parameter values.
 
-```{code-cell} python3
-:tags: ["hide-output"]
+```{code-cell} ipython3
+:tags: [hide-output]
 
 mdl = BCG_incomplete_markets()
 kss,bss,Vss,qss,pss,c10ss,c11ss,c20ss,c21ss,𝜃1ss = mdl.solve_eq(print_crit=False)
 ```
 
-```{code-cell} python3
+```{code-cell} ipython3
 print(-kss+qss+pss*bss)
 print(Vss)
 print(𝜃1ss)
@@ -1229,7 +1228,7 @@ Thus, let’s see if the firm is actually maximizing its firm value given
 the equilibrium pricing function $q(k,b)$ for equity and
 $p(k,b)$ for  bonds.
 
-```{code-cell} python3
+```{code-cell} ipython3
 kgrid, bgrid, Vgrid, Qgrid, Pgrid = mdl.eq_valuation(c10ss, c11ss, c20ss, c21ss,N=30)
 
 print('Maximum valuation of the firm value in the (k,B) grid: {:.5f}'.format(Vgrid.max()))
@@ -1246,7 +1245,7 @@ Below we will plot the firm’s value as a function of $k,b$.
 We’ll also plot the equilibrium price functions $q(k,b)$ and
 $p(k,b)$.
 
-```{code-cell} python3
+```{code-cell} ipython3
 from IPython.display import Image
 import matplotlib.pyplot as plt
 from mpl_toolkits import mplot3d
@@ -1367,7 +1366,7 @@ $$
 
 The function also outputs agent 1’s bond holdings $\xi_1$.
 
-```{code-cell} python3
+```{code-cell} ipython3
 def off_eq_check(mdl,kss,bss,e=0.1):
     # Big K and big B
     k = kss
@@ -1603,7 +1602,7 @@ structure for the firm.
 We first check the case in which $b^{**} = b^* - e$ where
 $e = 0.1$:
 
-```{code-cell} python3
+```{code-cell} ipython3
 #====================== Experiment 1 ======================#
 Ve1,ke1,be1,pe1,qe1,c10e1,c11e1,c20e1,c21e1,𝜉1e1 = off_eq_check(mdl,
                                                                 kss,
@@ -1655,7 +1654,7 @@ Therefore, $(k^*,b^{*}-e)$ would not be an equilibrium.
 
 Next, we check for $b^{**} = b^* + e$.
 
-```{code-cell} python3
+```{code-cell} ipython3
 #====================== Experiment 2 ======================#
 Ve2,ke2,be2,pe2,qe2,c10e2,c11e2,c20e2,c21e2,𝜉1e2 = off_eq_check(mdl,
                                                                 kss,
@@ -1708,7 +1707,7 @@ want to hold corporate debt.
 
 For example,  $\xi^1 > 0$:
 
-```{code-cell} python3
+```{code-cell} ipython3
 print('Bond holdings of agent 1: {:.3f}'.format(𝜉1e2))
 ```
 
@@ -1726,7 +1725,7 @@ It is also interesting to look at the equilibrium price functions
 $q(k,b)$ and $p(k,b)$ faced by firms in our rational
 expectations equilibrium.
 
-```{code-cell} python3
+```{code-cell} ipython3
 # Equity Valuation
 fig = go.Figure(data=[go.Scatter3d(x=[kss],
                                    y=[bss],
@@ -1756,7 +1755,7 @@ Image(fig.to_image(format="png"))
 # code locally
 ```
 
-```{code-cell} python3
+```{code-cell} ipython3
 # Bond Valuation
 fig = go.Figure(data=[go.Scatter3d(x=[kss],
                                    y=[bss],
@@ -1815,8 +1814,8 @@ $$
 The function `valuations_by_agent` is used in calculating these
 valuations.
 
-```{code-cell} python3
-:tags: ["hide-output"]
+```{code-cell} ipython3
+:tags: [hide-output]
 
 # Lists for storage
 wlist = []
@@ -1864,7 +1863,7 @@ for i in range(10):
     p2list.append(P2)
 ```
 
-```{code-cell} python3
+```{code-cell} ipython3
 # Plot
 fig, ax = plt.subplots(3,2,figsize=(12,12))
 ax[0,0].plot(wlist,klist)
@@ -1909,7 +1908,7 @@ Now let’s see how the two types of agents value bonds and equities,
 keeping in mind that the type that values the asset highest determines
 the equilibrium price (and thus the pertinent set of Big $C$’s).
 
-```{code-cell} python3
+```{code-cell} ipython3
 # Comparing the prices
 fig, ax = plt.subplots(1,3,figsize=(16,6))
 

lectures/_static/lecture_specific/opt_tax_recur/recursive_allocation.py

@@ -131,17 +131,17 @@ def simulate(self, b0, s0, T, sHist=None):
         # Time 1 onward
         for t in range(1, T):
             s, x = sHist[t], xHist[t-1]
-            cHist[t] = interp(self.x_grid, self.c1[:, s], x)
-            nHist[t] = interp(self.x_grid, self.n1[:, s], x)
+            cHist[t] = np.interp(x, self.x_grid, self.c1[:, s])
+            nHist[t] = np.interp(x, self.x_grid, self.n1[:, s])
 
             τHist[t] = self.τ(cHist[t], nHist[t])
 
             Bhist[t] = x / Uc(cHist[t], 1-nHist[t])
 
             c, n = np.empty((2, self.S))
             for sprime in range(self.S):
-                c[sprime] = interp(x_grid, self.c1[:, sprime], x)
-                n[sprime] = interp(x_grid, self.n1[:, sprime], x)
+                c[sprime] = np.interp(x, x_grid, self.c1[:, sprime])
+                n[sprime] = np.interp(x, x_grid, self.n1[:, sprime])
             Euc = π[sHist[t-1]] @ Uc(c, 1-n)
             RHist[t-1] = Uc(cHist[t-1], 1-nHist[t-1]) / (self.pref.β * Euc)
 
@@ -150,7 +150,7 @@ def simulate(self, b0, s0, T, sHist=None):
 
             if t < T-1:
                 sprime = sHist[t+1]
-                xHist[t] = interp(self.x_grid, self.xprime1[:, s, sprime], x)
+                xHist[t] = np.interp(x, self.x_grid, self.xprime1[:, s, sprime])
 
         return [cHist, nHist, Bhist, τHist, gHist, yHist, xHist, RHist]
 
@@ -209,7 +209,7 @@ def obj_V(z_sub, x, s, V, pref, π, g, x_grid, b0=None):
     # prepare Vprime vector
     Vprime = np.empty(S)
     for sprime in range(S):
-        Vprime[sprime] = interp(x_grid, V[:, sprime], xprime[sprime])
+        Vprime[sprime] = np.interp(xprime[sprime], x_grid, V[:, sprime])
 
     # compute the objective value
     obj = U(c, l) + β * π[s] @ Vprime

lectures/coase.md

@@ -3,8 +3,10 @@ jupytext:
   text_representation:
     extension: .md
     format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.16.1
 kernelspec:
-  display_name: Python 3
+  display_name: Python 3 (ipykernel)
   language: python
   name: python3
 ---
@@ -24,15 +26,6 @@ kernelspec:
 :depth: 2
 ```
 
-In addition to what's in Anaconda, this lecture will need the following libraries:
-
-```{code-cell} ipython
----
-tags: [hide-output]
----
-!pip install interpolation
-```
-
 ## Overview
 
 In 1937, Ronald Coase wrote a brilliant essay on the nature of the firm {cite}`coase1937nature`.
@@ -57,12 +50,10 @@ Couldn't the associated within-firm planning be done more efficiently by the mar
 
 We'll use the following imports:
 
-```{code-cell} ipython
+```{code-cell} ipython3
 import numpy as np
 import matplotlib.pyplot as plt
-%matplotlib inline
 from scipy.optimize import fminbound
-from interpolation import interp
 ```
 
 ### Why Firms Exist
@@ -447,7 +438,7 @@ At each iterate, we will use continuous piecewise linear interpolation of functi
 
 To begin, here's a class to store primitives and a grid:
 
-```{code-cell} python3
+```{code-cell} ipython3
 class ProductionChain:
 
     def __init__(self,
@@ -464,7 +455,7 @@ Now let's implement and iterate with $T$ until convergence.
 Recalling that our initial condition must lie in $\mathcal P$, we set
 $p_0 = c$
 
-```{code-cell} python3
+```{code-cell} ipython3
 def compute_prices(pc, tol=1e-5, max_iter=5000):
     """
     Compute prices by iterating with T
@@ -481,7 +472,7 @@ def compute_prices(pc, tol=1e-5, max_iter=5000):
 
     while error > tol and i < max_iter:
         for j, s in enumerate(grid):
-            Tp = lambda t: delta * interp(grid, p, t) + c(s - t)
+            Tp = lambda t: delta * np.interp(t, grid, p) + c(s - t)
             new_p[j] = Tp(fminbound(Tp, 0, s))
         error = np.max(np.abs(p - new_p))
         p = new_p
@@ -492,14 +483,14 @@ def compute_prices(pc, tol=1e-5, max_iter=5000):
     else:
         print(f"Warning: iteration hit upper bound {max_iter}")
 
-    p_func = lambda x: interp(grid, p, x)
+    p_func = lambda x: np.interp(x, grid, p)
     return p_func
 ```
 
 The next function computes optimal choice of upstream boundary and range of
 task implemented for a firm face price function p_function and with downstream boundary $s$.
 
-```{code-cell} python3
+```{code-cell} ipython3
 def optimal_choices(pc, p_function, s):
     """
     Takes p_func as the true function, minimizes on [0,s]
@@ -524,7 +515,7 @@ their respective upstream boundary, treating the previous firm's upstream bounda
 
 In doing so, we start with firm 1, who has downstream boundary $s=1$.
 
-```{code-cell} python3
+```{code-cell} ipython3
 def compute_stages(pc, p_function):
     s = 1.0
     transaction_stages = [s]
@@ -539,7 +530,7 @@ Let's try this at the default parameters.
 The next figure shows the equilibrium price function, as well as the
 boundaries of firms as vertical lines
 
-```{code-cell} python3
+```{code-cell} ipython3
 pc = ProductionChain()
 p_star = compute_prices(pc)
 
@@ -558,7 +549,7 @@ plt.show()
 Here's the function $\ell^*$, which shows how large a firm with
 downstream boundary $s$ chooses to be
 
-```{code-cell} python3
+```{code-cell} ipython3
 ell_star = np.empty(pc.n)
 for i, s in enumerate(pc.grid):
     t, e = optimal_choices(pc, p_star, s)
@@ -590,9 +581,9 @@ Check your intuition by computing the number of firms at delta in (1.01, 1.05, 1
 ```{solution-start}  coa_ex1
 :class: dropdown
 ```
-Here is one solution 
+Here is one solution
 
-```{code-cell} python3
+```{code-cell} ipython3
 for delta in (1.01, 1.05, 1.1):
 
    pc = ProductionChain(delta=delta)
@@ -601,6 +592,7 @@ for delta in (1.01, 1.05, 1.1):
    num_firms = len(transaction_stages)
    print(f"When delta={delta} there are {num_firms} firms")
 ```
+
 ```{solution-end}
 ```
 
@@ -636,7 +628,7 @@ associated with diminishing returns to management --- which induce convexity ---
 
 Here's one way to compute and graph value added across firms
 
-```{code-cell} python3
+```{code-cell} ipython3
 pc = ProductionChain()
 p_star = compute_prices(pc)
 stages = compute_stages(pc, p_star)
@@ -654,4 +646,4 @@ plt.show()
 ```
 
 ```{solution-end}
-```
+```