An Example: Modeling with WorldModeler vs Spreadsheets

The easiest way to understand the differences between building a model in WorldModeler vs. using a conventional spreadsheet is to follow a short example. We'll walk through building a simple financial model, where we try to find the price that maximizes the total contribution margin of a particular product. We'll do it first using a spreadsheet, and then again in WorldModeler.

To focus on the tools, rather than the mathematics, the problem we have chosen is particularly simple, and our treatment of it simplifies it even further. Yet, as we see below, even in this most trivial example, as soon as we wish to explore the space we are modeling with spreadsheets we are faced with what we shall refer to as an extensional explosion.

The example we will use is a problem faced by many businesses who must determine the correct price for a product. If the price is too high, too few people will purchase the product. If the price is too low, margin is sacrificed. Businesses seek an optimal price that takes fullest advantage of the large margins that come from high prices, while not raising prices so high that sales volume drops to a point where the total revenue suffers.

Contribution Margin

Businesses receive money when they sell their goods and services. However, to make and deliver these goods and services, they also incur a given unit of cost for each unit of good or service they sell. This cost is called the Variable Cost of the product. For example, to sell a CD, a recording company incurs a small amount of cost to press the CD, print the artwork for the cover, and ship it to the store (note that variable cost does not include the outlays the company had to make to record the CD in the first place. This cost does not change as the number of CDs sold goes up or down, and is referred to as fixed cost).

The contribution margin (CM) per sale is the difference between the price the business charges for the product being sold and the product's variable cost. That is:

CM  =  Price  -  Variable Cost

For simplicity, let's assume that every unit is sold at the same price and has the same variable cost. Therefore, at any given price, we make the same contribution margin on each sale. Since we'll assume variable cost doesn't change at all, the higher the price, the higher the contribution margin from each individual sale. Our objective is to maximize the total contribution margin by finding the optimal balance between:

• The number of units sold (or the sales volume), and
• the contribution margin made on each sale.

These two quantities generally oppose one another; to raise the volume, we must lower the price. However, lowering the price decreases the contribution margin per sale. On the other hand, if we wish to make a bigger margin per sale by raising the price, we will drive down volume and sell fewer items.

Sales Volume

As we have seen, a key piece of information we need to determine the total margin we make on a product is the number of people who will buy that product at a given price. Typically, the desire for our product and the ability to pay for it will not be constant throughout our market. Different groups (or market segments may desire it more than others, and be more willing and/or able to pay higher prices for it. Alternatively, some segments may be so large that lowering our price to sell to a larger proportion of that segment (or achieving a higher penetration) may turn out to be more profitable.

In our example, let's assume that the market we are trying to sell our product to is as follows:

• There are 5 market segments, each defined by an age group.
• Each segment has a "cutoff price", beyond which members of that segment will find the product too expensive and will not purchase it.
• Each segment has a fixed penetration percentage; that is, a percentage of individuals who will purchase the product (provided it is below the cutoff price).

To make this concrete, let us suppose that the segments, their size, cutoff price, and their penetration percentage are given in the table below:

The Total Contribution Marign Model

The total contribution margin from each segment can be determined from the above table, simply by multiplying the contribution margin per sale by the number of sales we make into each segment. However, this depends on price since if the price at which the product is offered is greater than the cutoff price for that segment, both the revenue and variable cost from that segment (and therefore that segment's contribution margin) will be 0. In other words, the contribution margin CM_S from any segment S is given by:

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