Why does the marginal cost curve always intersect with the average total cost curve at its lowest point?

The marginal cost curve always intersects the average total cost curve at its lowest point because the marginal cost of making the next unit of output will always affect the average total cost. As a result, so long as marginal cost is less than average total cost, average total cost will fall. Eventually, the marginal cost of producing another unit will be greater than the average total cost, and then the average total cost curve will start to rise.

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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.

Last Updated by eNotes Editorial on December 23, 2020
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The marginal cost curve and the average total cost curve are both graphical representations of the changing cost of producing a product in business. The marginal cost measures the difference in cost of producing individual pieces or products, while the average total cost is just an overall average of how much each part cost.

As the marginal cost approaches the average total cost curve, the average total cost is decreasing, because it is still producing pieces at a value less than the average total cost. However, there comes a point when average total cost is equal to marginal cost, which is where the graphs meet. At this point, marginal cost will become larger than average total cost, meaning each new product will increase the overall average cost of parts produced. At this point the average total cost will continue to increase as well.

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The short answer of this is that when the marginal cost is equal to the average total cost, the average total cost will begin increasing. When producing a product, the marginal cost of each piece is the additional cost of each subsequent piece, whereas the average total cost is the total cost divided by the number of pieces produced. When the cost to produce the next piece is equal to average total cost you have reached an equilibrium. However, when your marginal cost is higher than the average total cost, each new piece produced will increased the overall average, as a basic principle of math. Because of this, after the two lines have intersected, the Average Total Cost Curve will inflect and begin to turn upward, while the Marginal Cost Curve will continue to rise as well.

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Marginal cost is the cost incurred in producing one more unit, and it is solely affected by variable costs. Marginal cost can be calculated by getting the change in total cost when one unit is produced or added. The cost is also affected by the principle of variable proportions given that it is derived from variable costs. Its curve will drop briefly at the start before rising sharply.

The marginal cost curve cuts the average total cost curve from below and at its lowest point. This situation occurs because when the marginal cost curve is below the average total cost curve, it drops the average total cost. During the marginal cost curve’s upturn, the average total cost curve also rises, but not as sharply as the marginal cost curve. Thus, the marginal cost curve eventually cuts the average total cost curve, and both continue rising at different rates.

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The reason for this is that the marginal cost is part of the average total cost.  Therefore, a change in the marginal cost of making the next unit of output will affect the average total cost.

We know that the marginal cost (MC) curve is upward sloping when it intersects with the average total cost (ATC) curve.  So now let us think about why the MC curve must intersect with the ATC curve at the ATC's minimum.

When the MC is less than the ATC, each new unit of output lowers the the ATC.  This is mathematically necessary.  If you have an average and you add another number that is lower than the average to it and then you take the new average, it has to go down because the number that was added to it was lower.   This means that for as long as MC is less than ATC, ATC will go down with each extra unit made.

At some point, MC rises to the point that it equals ATC and the curves intersect.  Now let's look at what happens from there.  MC keeps rising.  It is now greater than ATC.  This means that ATC has to go up because every new unit produced increases ATC.

When we put this all together, it means that ATC decreases as MC rises to intersect with it.  After they intersect, they both rise.  This happens because MC is part of ATC.

 

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