Question

If \(TC=\frac{Q^3}{3}+20\), what will be \(MC\)?

• A. \(3Q^2\)
• B. \(Q^2\)
• C. \(Q/3\)
• D. \(20\)

Hint:

To find marginal cost from total cost, differentiate total cost with respect to output: \(MC=\frac{dTC}{dQ}\).

Answer 1

The Correct Option is B

Concept: Marginal Cost is the additional cost of producing one more unit of output. Mathematically, it is obtained by differentiating Total Cost with respect to output \(Q\). \[ MC=\frac{d(TC)}{dQ} \]

Step 1: Write the given total cost function.
\[ TC=\frac{Q^3}{3}+20 \]

Step 2: Differentiate total cost with respect to \(Q\).
\[ MC=\frac{d}{dQ}\left(\frac{Q^3}{3}+20\right) \]

Step 3: Differentiate each term separately.
\[ \frac{d}{dQ}\left(\frac{Q^3}{3}\right)=\frac{1}{3}\cdot 3Q^2=Q^2 \] and \[ \frac{d}{dQ}(20)=0 \]

Step 4: Find marginal cost.
\[ MC=Q^2+0 \] \[ MC=Q^2 \] Therefore, the correct answer is option (B).