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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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Kale Emmerich eNotes educator | Certified Educator

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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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Tim Mbiti eNotes educator | Certified Educator

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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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