Question

Derive the MU function from the following TU function: 𝑇𝑈 = 200𝑄 − 25𝑄 2 + 𝑄 3 From this MU function, draw up a table up to the level of Q where MU becomes negative. i.e (Q = 1, 2, etc). Graph these figures

Answer 1

Answer

$Given TU= 200Q-25Q^{2}+Q^{3}$

We have to know that;

$At Q=1, TU= 200-25+1=176$

$At Q=2, TU=200\times2-25\times4+2^3=308$

$At Q=3, TU=200\times3-25\times3+3^3=402$

$At Q=4, TU=200\times4-25\times4^2+4^3=464$

$At Q=20, TU=200\times20-25\times20^2+20^3=2000$

When MU becomes negative TU lowers thus decreasing the level of Q.

$So MU_{n}=TU_{n}-TU_{n-1}$

$Therefore the marginal function will be ; MU=\frac{2TU}{2Q}=200-50Q+3Q^2$ $at Q=1, MU=176-0=176$

$at Q=2, MU=308-176=132$

$at Q=3, MU=402-308=94$

$at Q=4, MU=464-402=62$

So graph of MU: