import numpy as np
from scipy.optimize import minimize_scalar
 
# Define profit function
def profit(p):
    return p * (2/(3*p)) - 0.1 * (2/(3*p))
 
# Find the maximum of the profit function using the bisection method
result = minimize_scalar(lambda p: -profit(p), bounds=(0.01, 10), method='bounded')
 
# Optimal price p*
optimal_price = result.x
 
# Quantity x* at the optimal price
x_star = 2 / (3 * optimal_price)
 
# Calculate revenue and cost at the optimal price
revenue = optimal_price * x_star
cost = 0.1 * x_star
 
# Calculate net utility received by the EU and money received by the ISP
net_utility = 0.4 * revenue
money_received_ISP = 0.6 * revenue
 
# Print the results
print("Price that maximizes profit (p*):", optimal_price)
print("Quantity created and delivered (x*):", x_star)
print("Maximum profit of the CP:", -result.fun)  # Minimization result is negative of profit
print("Net utility received by the EU:", net_utility)
print("Money received by the ISP:", money_received_ISP)
 

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