Revenue & Profit Posterior

rev_prof_post.py

def rev_posterior(samples=100, size=len(X)):
  for s in range(samples):
    idx = random.choice(range(size))
    m = trace.get_values('m')[idx]
    b = trace.get_values('b')[idx]
    rev = X * np.exp(m*X +b)
    plt.plot(X, rev)
  return 

# rev_posterior()  

import numpy as np
@np.vectorize
def cost(X):
  return 1.5*X + 50

def prof_posterior(samples=100, size=len(X)):
  prices = []
  profits = []
  for s in range(samples):
    idx = random.choice(range(size))
    m = trace.get_values('m')[idx]
    b = trace.get_values('b')[idx]
    demand = np.exp(m*X +b)
    rev = X * demand
    prof = rev - cost(demand)
    plt.plot(X, prof)
    
    best_price = X[np.argmax(prof)]
    best_prof = np.max(prof)
    prices.append(best_price)
    profits.append(best_prof)
  return prices,profits   

prices, profits = prof_posterior(samples=1000)

import seaborn as sns
sns.kdeplot(x=prices, y=profits, cmap='inferno', fill=True, thresh=0)