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

# # <font color="880000"> A Competitive Market </font>
# 
# Last edited: 2019-08-17
# 
# A Python class for a simple one good market where agents are price takers.
# 
# The market consists of the following objects:
# 
# A linear demand curve:
# 
# > (1) $ P_d = WTP_{max} - d*Q_d   $
# 
# A linear supply curve:
# 
# > (2) $ P_s = OC_{min} + s*Q_s  $
# 
# $P_d$ is the price paid by the consumer. $P_s$ is the price received by the producer. $Q_d$ is the quantity the consumer wishes to purchase at their price. $Q_s$ is the quantity the producer wishes to supply at their price. $WTP_{max}$ is the maximum willingness-to-pay of any consumer—the y-intercept of the demand curve. $OC_{min}$ is the minimum opportunity cost of any producer—the y-intercept of the supply curve. s is the slope of the supply curve. d is the slope of the demand curve.
# 
# The class provides methods to compute competitive equilibrium price and quantity, supply and demand curves, consumer surplus and producer surplus, and total surplus.
# 
# Here is the implementation:

# In[13]:


class market:

    def __init__(self, WTPmax, OCmin, d, s):
        """
        Set up market parameters. 𝑊𝑇𝑃𝑚𝑎𝑥 is the maximum willingness-to-pay 
        of any consumer—the y-intercept of the demand curve. 𝑂𝐶𝑚𝑖𝑛 is the 
        minimum opportunity cost of any producer—the y-intercept of the 
        supply curve. s is the slope of the supply curve. d is the slope 
        of the demand curve...
        """
        
        self.WTPmax, self.OCmin, self.d, self.s = WTPmax, OCmin, d, s
        
        if WTPmax < OCmin:
            raise ValueError('Insufficient demand.')

    def equilibrium_quantity(self):
        "Compute equilibrium quantity"
        return  (self.WTPmax - self.OCmin)/(self.d + self.s)


    def equilibrium_price(self):
        "Return equilibrium price"
        return  self.WTPmax - self.d * self.equilibrium_quantity()


    def consumer_surplus(self):
        "Compute consumer surplus"
        return (self.WTPmax - self.equilibrium_price())*self.equilibrium_quantity()/2

    def producer_surplus(self):
        "Compute producer surplus"
        return (self.equilibrium_price() - self.OCmin) * self.equilibrium_quantity() /2

    def total_surplus(self):
        "Compute total surplus"
        return self.producer_surplus() + self.consumer_surplus()
    
    def demand_curve(self,x):
        "Compute demand curve"
        return self.WTPmax - self.d*x
        
    def supply_curve(self,x):
        "Compute supply curve"
        return self.OCmin + self.s*x


# In[16]:


import numpy as np
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')

# Baseline WTPmax, OCmin, d, s
baseline_params = 10,0,1,1
m = market(*baseline_params)

q_max = m.equilibrium_quantity() * 2
q_grid = np.linspace(0.0, q_max, 100)
pd = m.demand_curve(q_grid)
ps = m.supply_curve(q_grid)

fig, ax = plt.subplots()
ax.plot(q_grid, pd, lw=2, alpha=0.6, label='demand')
ax.plot(q_grid, ps, lw=2, alpha=0.6, label='supply')
ax.set_xlabel('quantity', fontsize=14)
ax.set_xlim(0, q_max)
ax.set_ylabel('price', fontsize=14)
ax.legend(loc='lower right', frameon=False, fontsize=14)
ax.set(title='Market Supply, Demand, and Equilibrium')
plt.show()


# In[14]:


import numpy as np
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')

# Baseline WTPmax, OCmin, d, s
baseline_params = 10,0,1,1
m = market(*baseline_params)

print(m.producer_surplus(), "= producer surplus")
print(m.consumer_surplus(), "= consumer surplus")
print(m.total_surplus(), "= total surplus")
print(m.equilibrium_quantity(), "= equilibrium quantity")
print(m.equilibrium_price(), "= equilibrium price")


# ----
# 
# &nbsp;
# 
# ## <font color="880000"> A Competitive Market </font>
# 
# <img src="https://tinyurl.com/20190119a-delong" width="300" style="float:right" />
# 
# ### <font color="000088">Catch Our Breath—Further Notes:</font>
# 
# <br clear="all" />
# 
# ----
# 
# * Weblog Support <https://github.com/braddelong/LS2019/blob/master/2019-08-10_market.ipynb>
# * nbViewer <https://nbviewer.jupyter.org/github/braddelong/LS2019/blob/master/2019-08-10_market.ipynb>
# 
# &nbsp;
# 
# ----