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Profit Generating Functions [Bayesian Inference
Posted on June 13, 2013 @ 04:51:00 PM by Paul Meagher

In this blog, I want to get under the hood of what causes a profit distribution (which I have discussed in my last three blogs).

One cause of a Profit Distribution Function (PDF) is one or more Profit Generating Functions (PGF).

A profit generating function simulates expected profits based upon a set of parameters that are fed into it.

An example would be a line-of-business that involves shearing sheep for the wool fiber they produce. If you are at the beginning of the sheep shearing season, and are trying to estimate your profits for the end of the upcoming sheep shearing season, you would need to estimate how much money you might make per kg of wool fiber, how much wool fiber each sheep might produce (affected by heat, rain, nutrition, genetics), how many sheep you will have to shear at the future date, the fixed costs of raising your sheep, and the variable costs of raising each sheep. Each of these factors will have a range of uncertainty associated with them. The uncertainty associated with the price per kg and amount of wool in kgs per sheep are illustrated below in the tree diagram below.

The full calculation of how much you will make at the end of a season is a function of the values that each of these parameters might reasonable attain over the forecast period. A profit generating function will sample from each pool of uncertainty according to the distributional characteristics of that parameter and then use some arithmetic to generate a single possible profit value. When the profit generating function is re-run many times, it will generate a large number of possible values that can be graphed and this graph would look like your estimated profit distribution, or something that approximates it.

When estimating the probability to assign to each profit interval for Google (see Google 2013 Profit Distribution), we could constrain our estimates based upon the profit generating functions we believed were critical to generating the actual amount of profit they might attain. The profit generating function for adwords might include the estimated average cost per click and the volume of clicks over a given period (among other factors). Or, we could ignore the profit generating function and estimate our values on something less concrete but still significant - the level of goodwill that will exist towards Google over the forecast period (e.g., big brother privacy concerns creating negative sentiment), or social network rivals taking more of the advertising budget of companies, or search engine rivals like Yahoo gaining more market share, etc... As a Bayesian you are free to base your subjective estimates upon whatever factors you feel are the most critical to determining the actual profit of Google. In certain cases, you might want to rely more upon what your profit generating functions might be telling you. It could be argued that it is always a good idea to construct a profit generating functions for a company just so you understand in concrete terms how the company makes money. Then you can choose to ignore it in your profit forcasts, or not, or base you estimate on a blend of profit generating functions modified by subjective Bayesian factors.

What I am here calling a Profit Generating Function, is somewhat akin to what I have referred to as a Business Model in the past. If you want some ideas for how profit generating functions could be implemented, I would encourage you to examine my blog entitled A Complete and Profitable Business Model. Perhaps in a future blog I will try my hand at implementing a profit generating function that samples from several pools of uncertainty to deliver a forecast profit, and which will generate a profit distribution when re-run many times.

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