Answer to Question #185331 in Macroeconomics for HASAN ALI KHAN

Question

Q) Given TC = 120 + 50Q – 10Q² + Q³

Find

a.      The equations of the TVC, AVC, and MC functions.

b.     The level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-shaped.

c.      Find the AVC and MC for the level of output at which the AVC curve is minimum.

Answer 1

a) $TVC=50Q-10Q^2+Q^3$

$AVC=\frac{TVC} {Q} = 50 - 10Q + Q^2$

$MC = TC' = 50 - 20Q + 3Q^2$

b) for minimum AVC: $AVC' = 0; AVC' = -10 +2Q; Q= 5$

for minimum MC: $MC' = 0; MC' = -20 + 6Q; Q = \frac{10}{3}$

to prove that MC and AVC are U-shaped $AVC''> 0, MC''>0$

$AVC'' = 2>0; MC''= 6$

c) AVC is minimum when $Q = 5$. At this level of output $AVC = MC = 25$