Chapter 13 of Erik Haugom’s Essentials of Pricing Analytics deals with Monte Carlo simulations in pricing analytics. Interesting problem is presented in Exercise 11:

Interpretation: There is a 50% chance that the intercept of the price–response function is 250 and a 50% chance that it is 300. The slope takes a value of −10.0 with a 75% probability and −15.0 with a 25% probability. There is a 40% chance that the variable costs will be 2.25 USD/unit and a 60% chance that they will be 3.00 USD per unit. Finally, the fixed costs will be 0 USD with a probability of 20% and 300 USD with a probability of 80%. The objective function must now be based on a summary of many simulated trials of the profit. You shall now maximize (1) the average simulated profit from 1,000 trials and (2) the minimum profit level from all simulated trials.

1 Solution

I’ve made 1.000 trials per price level, and these are the results:

This plot shows the boxplot of profits for different price levels.

As in one of my previous posts that dealt with the topic of Monte Carlo Simulation, you can argue that there exists different optimum points based on the risk profile of the decision taker (i.e., the management). But, my recommendation would be to set the the price at 15. At that price, the profit does not go below zero, and though we are not reaching the maximum possible profit, we are so close to that point that increasing the price would only give us more risk than benefit. I’ve highlighted all feasible solutions, based on the criteria that minimum profit is strictly positive. Do note that from Price = 5 onwards, the spread of the results are greater. In case the management has conservative profile regarding risk sensitivity, the Price = 10 could be a good recommendation, since at that price the profits will range between approximately 500 and 1.500 USD (as opposed to 0 and almost 2k for active risk taker at Price 15).