The world is going to give you [is] data. And so, for whatever volume index you are using to measure your output you are going to end up with a series of dots, and that means in order to figure out what your cost functions are going to be you have to provide yourself with a statistical measure to get there. What I’m going to be measuring right here is going to be your average total cost so that’s the last function we are dealing with things that costs can take on.

Anyway, the world will go ahead and give you data, which means that in order to analyze this you are going to need some fairly high level statistics. Now I know enough of you have taken some statistical classes that you have seen some regression analysis. But for the most part you have to be more sophisticated than what you’ve had in your classes. Commonly, you want to use some things referred to your regression [video cutout] that costs are not always as low as they can possibly be. You’re making the assumption that whenever anyone makes a mistake; it’s always going to be a mistake that is going to increase cost in some way. And so, what you’re looking at here is not trying to put a line through the mass of dots that’s right here, but you’re trying to put a little line that is under most of the mass of dots. [video cutout] Instead of your common regression having as your error term in something that is symmetric, where it’s equally likely to be positive as negative but doing something which is more likely to be positive than negative, making it show through that your mistakes are always going to be things that are going to cost you a little bit more.

So, given that you should be a little bit afraid about doing the high level stats, here’s where you get to remember that rule, don’t try to do it yourself, hire somebody else to do it, and it ends up being a little bit cheaper in the long run. So, lets get you to a couple of the characteristics that you find of your average cost functions on the Y. The first one is, you will usually see some kind of range [that] the average cost function is going to decline. And so, this is typically because there is a bunch of fixed costs that you’re slowly, slowly, slowly weathering away, making the average fixed costs lower and lower and lower, but it will reach some kind of minimum. Now after that, you tend to see a kind of scallop shape that comes through on the bottom. That’s “scallop” or “scallop” – I’m talking about the little bivalves that are kind of tasty to eat. That scallop shapes take place because there’s a certain lumpiness to the inputs you are adding to production function. So it could be, you’re adding a shift and then adding another shift – you don’t add a fraction of a shift, you add a whole shift. It could be that you’re adding a piece of machinery, it could be [that] you’re adding a production line, but you’re adding these things in [video cutout] you can’t go ahead and add, you know, 3.78 of a car if you have some old car that is there.

And so the scallop shape tends to evolve because of the lumpiness of the things that you’re using to produce your output. Now I’ve drawn this right here as if the average cost doesn’t vary too much after you’ve gone through this period where you have worn away all those fixed costs that are there. [video cutout] …Referred to as firms that have constant margin cost. Or you may think of them as constant cost industries. So they’re things where if you have an observation of what it costs on average to produce a unit of the good at a relatively small scale, you can say [video cutout] its relatively high scale. Plenty of industries go ahead and work this way, they’re things where it’s easy to replicate or you’re just going ahead and taking what you have done before and duplicating again. So craftwork-type industries work relatively well on this. You can actually get this to go for construction type elements, and so roofers, cost of providing a roof is the same, whether you’re doing ten roofs or five roofs or 100 roofs, it’s just approximately the same because the equipment you can use is going to be just about the same after you get past a certain scale.

Now the other alternatives you have available to you are things that have your average cost increasing as your volume increases, which are known as increasing cost industries. And those that have your average cost continuing to decrease as the volume index increases, and you can guess these are the increasing cost industries. Now, with the increasing cost industries, typically this doesn’t mean that they’re doing just a worse and worse and worse job, it just means that as you get larger it becomes harder and harder and harder to coordinate all the factors that are flying around. Typical examples of this would be any time you’re dealing with wild coordination problems. I think the best example I have is a concrete delivery, because you do have to coordinate an awful lot mixing along with your orders, getting things on time during certain time frames, and that’s relatively hard to do after you’ve passed a certain [video cutout] …more expensive, worse than trying to schedule taxes or something along those lines.

Decreasing cost industries are things where you can actually use different kinds of techniques, as you get larger in order to make things more and more and more efficient. An example of this has to do with basic things, you know, as simple as cutting cheese. In your own house you know that if you have a block of cheese you can a cutting board, you can get a knife, and you can slice it up – it’s a relatively easy thing to do. If you’ve ever been to Tillamook Cheese Factory, you know that there’s special equipment, as you watch the line, to turn the cheese 45 degrees, another one to slice it, another one to weigh out the proper portions, another way of grabbing all the other things that are spare, that are there in a stack, so there’s a lot more tools that are available to you as you increase the scale that make it cheaper per ounce of cheese.

And so again the assumption is going to be that we’re making some wild assumptions about cost that make our math easier. Real life has costs, which are much different shape than what we are going to be assuming here, in order to actually get at these shades and figure out what is going on, you in general will need to handle and hire a general statistician to help you out. And so that’s the last little warning about the difference between out theoretical assumptions and what we’re actually going to find out a lot of, so here’s another brief…