WHY DOES MARGINAL COST INTERSECT AVERAGE COST AND AVERAGE VARIABLE COST CURVES AT THE MINIMUM OF THE AVERAGE COST AND AVERAGE VARIABLE COST CURVES RESPECTIVELY?

Marginal cost is the additional cost of producing an additional unit of goods or services.

It is calculated as the change in total cost divided by a change in quantity 

It can also be calculated as the first derivative of the cost function.

On the other hand, the average cost is the cost per unit of producing goods. It is calculated as total costs divided by several quantities produced.

The average variable cost is the variable cost per-unit of production. It is calculated by dividing the total cost by the number of quantities produced

The question is this:

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

The marginal cost always intersects the average cost curve at the minimum of the average cost curve because the average cost will keep falling as long as the marginal cost is lesser than the average cost.

When the marginal cost equals the average cost, the average cost curve will stop falling and instead remain constant, so that it can no longer fall further

This indicates that when marginal cost equals average cost, the average cost curve will be at its minimum point of falling.

If the marginal cost is increased above the average cost, however, the average cost will begin to rise and average cost will begin to slope upward.

From the foregoing, we can deduce that:

1. As long as marginal cost is lower than average cost, average cost will continue to decline.

2. The average cost will be at its lowest point as soon as marginal cost equals average cost because any increase in marginal cost above average cost will only result in an increase in the cost per unit.

Therefore, the quantity with the lowest per-unit cost is the quantity where marginal cost equals average cost or where average cost curve intersects marginal cost curve.

Why does marginal cost always intersect the average variable cost curve at the its minimum point.

The reason marginal cost intersects average variable cost at its minimum is very similar to the reason why marginal cost intersects average cost at its minimum.

The average variable cost will keep falling as long as the average variable cost is greater than marginal cost.

When average variable cost equals marginal cost, then the average variable cost will be at its minimum so that any attempt to raise the average variable cost above marginal cost will only raise the variable cost.

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