Perhaps the best way to understand marginal costs, average total costs, and their intersection is to imagine yourself as a business owner. You've invented a new product, the wingding, and a small audience is already interested in buying your new creation. Your business starts small. Your fixed costs are only your rent for your workshop. Your variable costs include your own labor and the materials used to make each wingding. Together, those two combine to make your total cost. You discover the average total cost by dividing your total cost by the number of wingdings you make. Let's say your total cost is $100, and you make 20 wingdings. Your average total cost is $5 per wingding.
Soon, you discover that those wingdings are really popular, and people are clamoring for more. You hire a couple friends to help you with production. Now you have to pay them for their labor and purchase more materials. Your total costs go up, but you're also making more wingdings, so your average total costs are actually going down. This is a good thing, but as your business expands, you also need to start thinking about marginal costs. Your marginal cost is what you will spend to make the very next wingding you produce.
Let's say that with the help of your friends, you are now producing 80 wingdings. Your total costs are $300, and your average total cost is $3.75 per wingding. To calculate your marginal cost, you determine the change in production—here, 60 wingdings—and your change in total cost—here, $200. Now divide the change in total cost by the change in production, and you have $3.34. That is your marginal cost, and it looks good. It's less than your average total cost.
Your business continues to grow as the demand for wingdings soars, and soon you have to hire more employees, rent a larger space, and purchase larger quantities of materials to make wingdings. But soon you realize something. Your marginal cost is starting to rise. It is a little more expensive to create your next wingding.
What's more, you've noticed that each additional employee adds fewer wingdings to the total production. After all, some of them are devoting more of their time to answering phones, replying to emails, and keeping the computer system going. You are starting to get a little nervous. Your average total cost per wingding has not yet risen, but you are keeping a close eye on the situation.
Then you hire one more employee, and you notice a change. Your average total cost starts rising. It is costing you a little bit more to make each wingding than it used to. You look back on your figures and see that there was one spot on your graphs when the marginal cost and the total average cost actually met. This was the lowest point for your average total cost, but your marginal cost was already rising, and it was threatening to push your average total cost up, too. When the two equaled, your production was just about right. When they both started rising, you realize that you have overreached, and you need to make a change if you want to maintain your level of profit.
We can think of this in yet another way. Your average total cost is like your average grade for a course. Your marginal cost is like your grade per assignment. If you mess up a few assignments and get lower scores, they will pull down your average grade. When you start to improve on assignments, they will eventually meet your average grade and start pulling it up.
That's what happens with marginal costs and average total costs, too. When marginal costs are low, they will pull down average total costs. When marginal costs rise, they will eventually meet up with average total costs and start start pulling them up.