How can marginal cost be expressed mathematicaly?
Marginal coet (MC) can be expressed as
A. , where is average cost and is cutput.
8. , where is fixed cost and is cutput.
C. MC= , where is total cost and is output.
D. , where TC is total cost and is cutput.
E. MC=TC-FC, where TC is total cost and FC is fixed cost.

For example, if the total cost of producing thee units of oufput is and the total cost of producing four units of cuput is , then the marginal cost of the fourth unit is . 7. (Enter ycur respoonse as an intiger)

Ask by Olson Dunn. in the United States

Mar 23,2025

Question

How can marginal cost be expressed mathematicaly?
Marginal coet (MC) can be expressed as
A. , where is average cost and is cutput.
8. , where is fixed cost and is cutput.
C. MC= , where is total cost and is output.
D. , where TC is total cost and is cutput.
E. MC=TC-FC, where TC is total cost and FC is fixed cost.

For example, if the total cost of producing thee units of oufput is and the total cost of producing four units of cuput is , then the marginal cost of the fourth unit is . 7. (Enter ycur respoonse as an intiger)

Ask by Olson Dunn. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

$$ \textbf{Step 1: Identify the correct formula} $$

Marginal cost (MC) is defined as the change in total cost when one additional unit of output is produced. Thus, the formula is given by

$$
MC = \frac{\Delta TC}{\Delta Q}
$$

where $$ \Delta TC $$ is the change in total cost and $$ \Delta Q $$ is the change in output. This corresponds to option C.

$$ \textbf{Step 2: Calculate the marginal cost for the fourth unit} $$

Given:
- Total cost for 3 units: $$ TC_3 = \$2783 $$
- Total cost for 4 units: $$ TC_4 = \$3239 $$

The change in total cost is

$$
\Delta TC = TC_4 - TC_3 = 3239 - 2783 = 456
$$

The change in quantity when moving from 3 to 4 units is

$$
\Delta Q = 4 - 3 = 1
$$

Thus, the marginal cost $$ MC $$ is

$$
MC = \frac{\Delta TC}{\Delta Q} = \frac{456}{1} = 456
$$

$$ \textbf{Conclusion:} $$
- The correct mathematical expression for marginal cost is $$ MC = \frac{\Delta TC}{\Delta Q} $$ (option C).
- The marginal cost of the fourth unit is $$ 456 $$ dollars.
Marginal cost (MC) is calculated as the change in total cost divided by the change in quantity. For the fourth unit, the marginal cost is \$456.

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