#!/usr/bin/env python
# coding: utf-8

# # Change in Consumer Surplus
# 
# **Randall Romero Aguilar, PhD**
# 
# This demo is based on the original Matlab demo accompanying the  <a href="https://mitpress.mit.edu/books/applied-computational-economics-and-finance">Computational Economics and Finance</a> 2001 textbook by Mario Miranda and Paul Fackler.
# 
# Original (Matlab) CompEcon file: **demqua50.m**
# 
# Running this file requires the Python version of CompEcon. This can be installed with pip by running
# 
#     !pip install compecon --upgrade
# 
# <i>Last updated: 2022-Oct-23</i>
# <hr>
# 
# 

# ## Initial tasks

# In[1]:


from compecon import qnwlege
import numpy as np
import matplotlib.pyplot as plt


# ## Define inverse demand curve

# In[2]:


f = lambda p: 0.15*p**(-1.25)
p, w = qnwlege(11, 0.3, 0.7)
change = w.dot(f(p))
change


# ## Make figure

# In[3]:


# Initiate figure
fig0, ax = plt.subplots()

# Set plotting parameters
n = 1001
qmin, qmax = 0, 1
pmin, pmax = 0, 1
p1, p2 = 0.7, 0.3

q1 = f(p1)
q2 = f(p2)

# Plot area under inverse demand curve
p = np.linspace(0,pmax, n)
q = f(p)

par = np.linspace(p2,p1, n)
ax.fill_betweenx(par, f(par), qmin, alpha=0.35, color='LightSkyBlue')

# Plot inverse demand curve
ax.plot(q,p)

# Annotate figure

ax.hlines([p1, p2], qmin, [q1, q2], linestyles=':', colors='gray')
ax.vlines([q1, q2], pmin, [p1, p2], linestyles=':', colors='gray')

ax.annotate('$p(q)$', [0.8,0.3], fontsize=14)

# To compute the change in consumer surplus `numerically'
[x,w] = qnwlege(15,p2,p1)
intn = w.T * f(x)

# To compute the change in consumer surplus `analytically'
F = lambda p: (0.15/(1-1.25))*p**(1-1.25)
inta = F(p1)-F(p2)

ax.set_aspect('equal')
ax.set(xlim=[qmin, qmax], xticks=[qmin,q1,q2,qmax], xticklabels=[r'$0$', r'$q_1$',r'$q_2$',r'$q$'],
       ylim=[pmin, pmax], yticks= [p1, p2, pmax], yticklabels=[r'$p_1$', r'$p_2$', r'$p$']);