Transcript To Volume Index

Now let’s have a little side bar on what I’ve been talking about with a volume index, and I’ve been saying that you can think of it as just quantity. Well, often times that works well enough if you’re thinking about things like the number of plates that are coming out to a table at a restaurant, or the number of cars that are rolling off a lot, and that all makes sense as a kind of quantity measure, but what it hides is there’s a little bit of heterogeneity that’s hiding about there. Not every plate that goes out is going to have the same dish in it, unless it’s a special kind of restaurant. Not every car that’s produced is going to be identical to the one before, there’s always going to be some kinds of variations. That’s why thinking of it as an index is the exact, correct way of doing it. Indexes are ways of combining unlike things into a single measure. If you want some examples of indexes, there’s the Consumer Price Index, which is a way of combining prices on a whole bunch of different items, putting them together and telling you how much stuff costs. Gross Domestic Product is actually an index itself because what it does is it combines a whole lot of unlike produced goods and services, combines them together to say, here’s how much we actually made. So Index Theory is a way of combining unlike items. So in a sense, quantity isn’t quite right, but it’s still a quantity measure.

Now, besides having this problem of combining together unlike items, you frequently have a choice of what index to use and there are many possible measures of combining output into a single item. For example, you could have as your choices for measuring the output of something like an electrical plant, or the electricity you’re providing to an individual facility, you can go ahead and measure output in terms of something like KWh, (Kilowatt hours), and that’s great because it measures what your actually collecting over the course of a month. You could also measure it in terms of Kilowatts, (KW), which is the peak load that they have going around right there, and each one of these two actually helps you in forecasting certain kinds of costs. KWh would be great for forecasting fuel costs, KW would be great for the fixed costs that’s associated with your facilities. So you’ll actually have the option of having many different kinds of indexes available to you and you’ll have to pick and choose which one seems best, which has commonly developed new indexes in order to make it so that your cost functions are a little bit more accurate than before and you’re going to find out that choosing the right index brings you a long ways towards making it so that your cost estimates are better, and I’ll show you how that works.

Let’s go ahead and give you two cost indexes right here. So, we’ll call this volume index 0, (graph on left) and here’s volume index 1 over here, (graph on the right). Both of them will be measuring the exact same month or week that were going to have at a manufacturing plant, so these costs are all going to be the same, but each of these output costs is going to be different because the output levels are going to be measured a little bit differently. Volume index 0, when we’re measuring total costs, has a kind of a weak relationship, (draws loosely spaced individual tick marks), between the volume index, (x), and the total cost, (y), that you’re actually observing. So you can see kind of a spread that’s about the graph and you can say that on average the total cost is going to be like that, (have a positive and upward slope to the right, in between the many individual tick-marks), but you can say that at any particular output level, like this, (draws vertical dashed line in middle of the volume index 0 graph), you have a significant amount of uncertainty, (draws solid vertical line next to dashed line with bulge to the right, on the average slope drawn previously between the tick marks), about what you actually should be forecasting at the cost, at that particular volume index level. We can have another volume index over here, (starts drawing tick marks on volume index 1), but there’s a much tighter relationship between the volume index and total cost, (the tick marks are much more tightly grouped around its average slope). So we can choose again, (draws vertical dashed line in middle of volume index 1), an analogues level of the volume index, and well have much less uncertainty, (draws solid line with much smaller bulge near average slope), about what to specify as our guess about costs. And so we have two volume indexes, this one, (volume index 1), has less uncertainty when you’re trying to forecast what your total cost is, and this has more, (points to volume index 0). This is what I mean in that your choice of volume index is one of the most critical choices you’re going to make when trying to make your future cost estimates.

Now, I’m not stating this as merely an abstract problem, these kinds of choices evolve all the time. To give you an example, I used to do a little bit of work in trying to cost or price insurance. I don’t mean that I used to be an insurance agent, I meant that I used to do a little bit of transportation research. And so, insurance companies may look and see if they’re going to go into a specific zip code, and they go ahead and try and figure out what it’s going to cost to try and service the clients in this particular zip code. Now, they have a choice of volume indexes that are there. The first volume index that comes to mind is the number of people insured because, as the number of people insured goes up, the cost to insure those people goes up and also it works out to be that the revenue from insuring those people goes up. And so that would go ahead and give you kind of a noise measure, because the number of people that your insuring alone doesn’t go ahead and give you all the best information possible about what it’s going to cost to insure them - people get into accidents and, people get into accidents because they drive. And so, although the industry did go ahead and start off with the number of people (jumbled garble @ 5.52), moved over to another measure, something that was a little more precise, and the first measure they moved into was something they called, vehicle miles traveled. You can still see this used in a lot of transportation sources, because the more you drive the more likely you’ll get into an accident because each mile provides you with an additional amount of risk. Now it’s true, city miles are going to be a little bit different than country miles, as far as the risk goes, but if you’re dealing with one geographic area, or various areas of similar type, you know that as people in the district drive more miles there going to have a greater cost associated with them. So there’s an improvement that was made there on this other volume index another one. Now further improvements can be made on vehicle miles traveled by switching to yet another volume index, something along the lines of say “garbled” (6.37). Now that means that you have greater costs associated with having a lot of people in the car because the cost of an accident isn’t in the cost of the vehicle that you originally measured, but the people that are inside the vehicle, because medical expenses will usually outweigh anything that has to do with damage to the vehicle, so people are more expensive than the cars that are there. So again, whenever your working on your cost estimates keep in mind what you’re using for your volume indexes right there, keep an eye out for a measure which is better than the one you’re using. A lot of old measures have hung around for a long time and they outlive their proper use, and a simple refinement of a new measure, that is actually testable because you can see how well correlated these things are, can make it so that your cost estimates are a lot more precise and you’re a lot less likely to be wrong. It’s just one of those hints I can give you as your entering your job; you are going to make some cost estimates, and its best to start thinking about these very systemic ways of improving the cost estimates that your making.

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