Simulation of a profit problem

You work for a company that manufactures industrial equipment. The sales price of each piece of equipment is $100,000. You also know that there is a strong negative correlation between the inflation_rate and sales volume. This relationship is captured by the covariance matrix cov_matrix, which is available in the console for you.

The function profit_next_year_mc() performs a Monte Carlo simulation returning expected profit (in thousands of dollars), given the mean inflation rate and mean sales volume as arguments. You'll also need to pass n, the number of time the simulation should be run. The function has been loaded for you, and the definition is below.

def profit_next_year_mc(mean_inflation, mean_volume, n):
  profits = []
  for i in range(n):
    # Generate inputs by sampling from the multivariate normal distribution
    rate_sales_volume = st.multivariate_normal.rvs(mean=[mean_inflation,mean_volume], cov=cov_matrix,size=1000)
    # Deterministic calculation of company profit
    price = 100 * (100 + rate_sales_volume[:,0])/100
    volume = rate_sales_volume[:,1]
    loan_and_cost = 50 * volume + 45 * (100 + 3 * rate_sales_volume[:,0]) * (volume/100)
    profit = (np.mean(price * volume - loan_and_cost))
    profits.append(profit)
  return profits

The following packages have been imported for you: pandas as pd, numpy as np, scipy.stats as st, matplotlib.pyplot as plt, and seaborn as sns.

This exercise is part of the course

Monte Carlo Simulations in Python

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Exercise instructions

Perform a Monte Carlo simulation by running profit_next_year_mc() 500 times using a mean_inflation of 2 and a mean_volume of 500.
Visualize the simulation results using a displot.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Run a Monte Carlo simulation 500 times using a mean_inflation of 2 and a mean_volume of 500
profits = profit_next_year_mc(____)

# Create a displot of the results
____
plt.show()

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