Question

If TC = 2.5q³ − 13q² + 50_q + 12 derive the MC function and AC function.

Answer 1

Given:

TC= 2.5q³ – 13q² + 50_q + 12

Marginal cost function

MC = ${\displaystyle \frac{\text{d(TC)}}{\text{dQ}}}$

= ${\displaystyle \frac{\text{d}}{\text{dq}}}$ [2.5q³ – 13q² + 50q + 12]

2.5 (3q²) – 13 (2q) + 50 (1) + 0

MC = 7.5q – 26q + 50

Average cost AC = ${\displaystyle \frac{\text{TC}}{\text{q}}}$

= ${\displaystyle \frac{2.5{\text{q}}^3-13{\text{q}}^2+50q+12}{\text{q}}}$

= ${\displaystyle \frac{2.5{\text{q}}^3}{\text{q}}}$ - ${\displaystyle \frac{13{\text{q}}^2}{\text{q}}}$ + ${\displaystyle \frac{50\text{q}}{q}}$+ ${\displaystyle \frac{12}{\text{q}}}$