You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Frequency Table

Marginal util...

Question

Marginal utility schedule for $G o o d - X$ and $G o o d - Y$ is given in the following table.Assuming price of $X$ is $R s . 1$ , and price of $Y$ is $R s . 1$ and money income of the consumer is $R s . 13$ . Find the optimum combination of $G o o d - X$ and $G o o d - Y$ for maximising consumer's utility.
$Q$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$M U_{X} (U t i l s)$ $28$ $24$ $21$ $20$ $16$ $13$ $9$ $5$ $3$ $1$
$M U_{Y} (U t i l s)$ $32$ $29$ $27$ $23$ $20$ $18$ $17$ $16$ $12$ $9$

Open in App

Solution

At equilibrium, $\frac{M U_{X}}{M U_{Y}} = \frac{P_{X}}{P_{Y}} = M U_{M}$
$\frac{M U_{X}}{M U_{Y}} = 1 \Rightarrow M U_{X} = M U_{Y}$
The consumer gets maximum satisfaction when he purchases $5$ units of $X$ and $8$ units of $Y$ . Because at this combination, $M U_{X} = M U_{Y} = 16$ .

Suggest Corrections

Similar questions

Q. A consumer consumes goods

X

and

Y

. Given below is his marginal utility schedule for goods

X

and

Y

. Suppose, the price of

X

R s .2

Y

R s .1

and income

R s .12

. State the law of Equimarginal utility and explain how the consumer will attain equilibrium.

Units	1	2	3	4	5	6
$M U_{X}$	16	14	12	10	8	6
$M U_{Y}$	11	10	9	8	7	6

A consumer consumes only two goods X and Y whose prices are Rs. 2 and Rs. 1 per unit respectively. If the consumer chooses a combination of the two goods with marginal utility of X being 4 and that of Y being 4, is the consumer in equilibrium? Give reasons. Explain what a rational consumer would do in this situation. Use marginal utility analysis.

Q. A comsumer consumes only two goods

X

and

Y

whose prices are Rs. 2 and Rs. 1 per unit respectively. It the consumer chooses a combination of the two goods with marginal utility of

X

being

4

and that of

Y

also being

4

, is the consumer in equilibrium? Give reasons. Explain what will a rational consumer do in this situation. Use Marginal Utility Analysis.

A consumer consumes only two goods X and Y whose prices are Rs. 4 and Rs. 5 per unit respectively. If the consumer chooses a combination of the two goods with marginal utility of X equal to 5 and that of Y equal to 4, is the consumer in equilibrium? Give reasons. What will a rational consumer do in this situation? Use utility analysis.

Q. Suppose, price of commodity-Y (

P_{Y}

) is Rs.

10

per unit. Also, assume that marginal utility of money

(M U_{m})

8

(and constant). Using the following marginal utility schedule of the consumer, find out equilibrium level of consumption and total expenditure on commodity-Y

Units Consumed	$1$	$2$	$3$	$4$	$5$	$6$
Marginal Utility	$170$	$130$	$110$	$80$	$30$	$0$

Join BYJU'S Learning Program

$Q$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$M U_{X} (U t i l s)$	$28$	$24$	$21$	$20$	$16$	$13$	$9$	$5$	$3$	$1$
$M U_{Y} (U t i l s)$	$32$	$29$	$27$	$23$	$20$	$18$	$17$	$16$	$12$	$9$

At equilibrium, MUXMUY=PXPY=MUMMUXMUY=1⇒MUX=MUYThe consumer gets maximum satisfaction when he purchases 5 units of X and 8 units of Y. Because at this combination, MUX=MUY=16.

At equilibrium, $\frac{M U_{X}}{M U_{Y}} = \frac{P_{X}}{P_{Y}} = M U_{M}$
$\frac{M U_{X}}{M U_{Y}} = 1 \Rightarrow M U_{X} = M U_{Y}$
The consumer gets maximum satisfaction when he purchases $5$ units of $X$ and $8$ units of $Y$ . Because at this combination, $M U_{X} = M U_{Y} = 16$ .