Question

Following is the total utility schedule of Mr. X:

Units of Commodity-X	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$T{U}_X$ Units	$20$	$37$	$51$	$61$	$66$	$66$	$64$

(i) Derive MU schedule
(ii) Find out the level of consumption at which Mr.X reaches the saturation point.
(iii) How many units should the consumer purchase to maximize satisfaction when the price of the commodity is Rs. $5$? Assume that utility is expressed in utils and $1$ util$=Rs.2$). Give reasons for your answer.

Answer 1

(i) MU Schedule:

Units TU MU

1 20 20

2 37 17

3 51 14

4 61 10

5 66 5

6 66 0

7 64 -2

(ii) Saturation point is struck when TU stops increasing even when consumption of the commodity is increased. In the present case, the saturation point is reached when 6 units of the commodity are consumed, as corresponding to the 6th unit, MU = 0

(iii) ) $P_X=Rs.5$ per unit, and ${MU}_M=2$.

We know, equilibrium is struck when: $\frac{{\text{MU}}_M}{{\text{P}}_X}$ $={MU}_M$

It happens when,

$\frac{{\text{MU}}_X}{5}$ $=2$

Or, when ${MU}_X=10$ Implying that the consumer purchases four units of the commodity-X to maximise satisfaction.