Graphs of MC, AVC and ATC

In the previous video, we began our study of ABC Watch Factory, and we tried to understand the economics of the business based on some data that we had already collected on our costs and how much output we can produce based on how many labor units we had.

Then from that, we calculated things like the marginal product of labor, the marginal cost, the average variable cost, the average fixed cost, and the average total cost. What we're going to do in this video is take this information, especially total output and all of these things that we just calculated, and we're going to graph it so that we can better appreciate how these various calculations and the curves that we can get from the calculations are interrelated.

So let me scroll over a little bit so we have some space, and then let me set up a little coordinate plane here. On our vertical axis, this is our cost, and then down here in our horizontal axis, this is our output.

First, let's just hand graph it. I encourage you to go through the exercise yourself. It's one thing to watch me do it, but when you actually graph something, you digest the numbers that much better. So let's start with marginal cost, and I'm going to do it in this blue-green color.

So let's see, when our total output is 25, our marginal cost is $267. So when our output is 25, $267 would be right about there. We're just trying to visualize what's going on.

Then, when our total output is 45, our marginal cost is $150. So 45 is here, and then $150 is right about there. Next, when our total output is 58, our marginal cost is $231. So 58 is right about there, and then it's going to be $231, so it's about right there.

When our total output is 65, our marginal cost is $429. So 65 is right over there, and then $429 will get us right about there. We see our marginal cost is going up a lot now. It might be a little bit lower than that, so it's going to be right over there.

Last but not least, when our total output is 70, our marginal cost is $600. So at 70, we get to $600, and I'm eyeballing it now. It's not exact graph paper, but this gives you a sense of what the marginal cost curve looks like.

Here, we've kind of graphed it based on where we are in terms of output, so that's our marginal cost curve. I'll just label that marginal cost. Now let's see how that relates to the curves for average variable cost and average total cost.

So, average variable cost I'll do in this orange color. At an output of 25, our average variable cost is $240. So, at 25, we are going to be at $240, which is right about there. Then, when we are at 45 units, our average variable cost is $200, it's at 45 units, and our average variable cost is right over there.

At 58 units, it's $207. So, 58 units it is $207, so it's going to be right about there. At 65 units, it's $230. It should be about right there. Then, at 70 units, we're at $257. So 70 units, $257 looks something like this.

Now, before I actually draw in this curve and connect the dots, let's just think about how the average variable cost relates to the marginal cost. When the marginal cost is less than the average variable cost, well, that means that as we do more, as we produce more and more, our average variable costs should go down.

We see that happening in this early stage. I won't go into all the details of what's happening exactly right over there, but in that early stage, as we see that while our marginal cost is less than our average variable costs, our average variable cost is trending down.

That makes sense; every incremental unit is getting a little bit cheaper to produce, which brings down the average. But as soon as the marginal cost curve crosses the average variable cost, every incremental unit is now more than the average. Well, that should bring up the average.

The average variable cost should start sloping up. It's good to realize this as a rule of thumb. More importantly, it's essential to understand where the marginal cost curve and the average variable cost curve intersect. That's going to be the point at which the average variable cost goes from trending down to trending up. If you view it as this very wide U shape, that would be the bottom of the U.

We could do the same thing with average total costs. Now they're going to cross a little bit later because the average total costs are higher since they're factoring in the fixed costs as well. But you can imagine that while your marginal costs are lower than your average total cost, every incremental unit is going to bring down the average total cost.

As soon as the marginal cost crosses the average total cost, it's going to start bringing up the average. We can see that by trying to graph average total cost, and I'll do that in this yellow color. So at 25 units, we're at $440. That makes sense because we have all that fixed cost that we're spreading along among not that many units.

At 45 units, we're at $311. At 58 units, we're at $293, which is right about there. At 65 units, we're at $308, and at 70 units, we're at $329. So maybe something like this.

This is our average total cost. Just as you could imagine, while your marginal costs for every incremental unit cost less than your average total cost, it'll bring down your average total costs until the point that they cross.

Now after these two curves cross, every incremental unit is bringing up the average cost; it's costing more than the average. Once again, where these two curves intersect, if you view the average total cost curve as this big wide U, it would represent the bottom of the U.

The last thing that we didn't graph, and this is maybe the most intuitive, is the average fixed cost. This is just going to ask them to total down. At 25 units, we're at $225. At 45 units, we're at $200. At 58 units, we're at $186.

At 65 units, we're at $177, and then at 70 units, we're at $171. You can see that just gets lower and lower and lower as you produce more and more output because you're able to spread those fixed costs among more and more output.

The big takeaways here are not just to understand the rule of thumb that where the marginal cost curve intersects the average variable cost or the average total cost, you could view it as the minimum point of the average total cost or the average variable cost curves. But it's essential to understand why that is happening.