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

# # Weekly exercise 4: Optimal choice in the bungle good market
# 
# In this exercise I ask you to apply the machinery of bungled goods
# we have created in video 08 for answering some economic questions.
# Make sure you use the code written in that video which is stored
# in the notebook *08_bundles_ex2*.

# In[ ]:


# copy the working code of the bungle_good class into this cell and run it


# ## Optimal choice of bundle goods
# 
# Consider a consumer with a utility function over the individual goods
# given by
# 
# $$
# u(x_1,\dots,x_7)=\log(x_1+1)+\big((x_2)^{0.4}+0.5(x_3)^{0.4}\big)^{2.5}-0.5\log(x_4+1)-0.2(x_5*x_6)^{0.2}+2\log(x_7+1).
# $$
# 
# Find the optimal set of bundle goods to be consumed by comparing
# different combinations of the available bundles shown below.
# 
# There are only three bundle goods on the market, so we
# can afford a brute force optimization algorithm implemented as a
# triple nested loop, with each level corresponding to one bundle good
# and looping from 0 to some reasonable number (think which number
# would be reasonable).
# 
# Compute the optimal choice for budgets of 100, 200 and 300 price units.
# 
# Use the starter code below.  Each occurrence of **@@@** has to be replaced with appropriate code.

# In[ ]:


# Available bundle goods
a = bundle_good([2,0,1,3,1,1,0],10.50)
b = bundle_good([0,5,0,4,2,2,2],15.36)
c = bundle_good([1,0,1,2,0,5,4],12.72)
market = [a,b,c]

import math

# utility function
def u(x):
    '''Returns the utility of a bundle'''
    return @@@

# optimization routine
def optim(budget,util,market):
    '''Returns the optimal combination of goods at the market, given the budget'''
    nn = @@@ #heuristic for the maximum quantity to check
    # loop over all combination of three bundles to find max utility
    m = -float('inf') #initialize with negative infinity
    for i in range(nn):
        for j in range(nn):
            for k in range(nn):
                bnd = @@@  # combination of so many of each of the three bundled goods
                u = util(@@@)
                if bnd.price <= budget and m<u:
                    # found new maximum which is within the budget
                    m = @@@  # remember the new max utility
                    x = @@@  # remember the combination of bundle goods where max is attained
    return x #return the optimal combination of goods

def report(budget,util,x,market):
    '''Makes nice readable output'''
    @@@

# main program
for budget in [@@@]:
    x=optim(budget,u,market)
    report(budget,u,x,market)


# ## Sales tax
# 
# Imagine the newly introduced sales tax raised all prices by 15%.
# Recompute the optimal choices in previous question.
# 
# Do the optimal choices change, and how?

# In[ ]:


# Write your code here


# ## Sale for one good
# 
# Imagine the sale for bundle good **c** lowers its price by 20%. Recompute
# the optimal choices in previous question.
# 
# Do the optimal choices change, and how?

# In[ ]:


# Write your code here