Question

Derive

the MU function from the following TU function:

𝑇𝑈 = 200𝑄 − 25𝑄2 + 𝑄3

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. (10 marks)

Answer 1

$$Solution$$

Considering the above $TU$ function, marginal utility will be obtained by differentiating $TU$ as will be shown below.

$MU=\frac{\delta\ x}{\delta\ y}=200-50q+3q^2$

Below are the calculations obtained from the $MU$ function after replacing $1,2,3,4,5,6, and\ 7$ in the $MU$ function

$1. \ 200 –50 + 3 = 153\\ 2. \ 200 –100 + 12 = 112 \\ 3 .\ 200 –150 + 27 = 77 \\ 4.\ 200 –200 + 48= 48 \\ 5. \ 200 –250 + 75 = 25 \\ 6. \ 200 –300 + 108 = 8 \\ 7. \ 200 –350 + 147 = –3 \\$

Then the following graph will be obtained from the table above.