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

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

$MU=\frac{dTU}{dQ}$

$=\frac{d}{dQ}(200Q-25Q^{2}+Q^{3})$   

 $=200-50Q+3Q^{2}$

Hence, 

$MU=200-50Q+3Q^{2}$

Table

Q Mu

1 153

2 112

3 77

4 48

5 25

6 8

7 -3

8 -8

Graph

The quantity is on the horizontal axis and the marginal utility on the vertical axis .

The marginal utility is convex to origin and downward sloping curve indicating that utility decreases at an increasing rate with each additional unit of consumption.