Question

Robert consumes commodities X and Y. The price of commodity X is ₹ 2 and the price of commodity Y is ₹ 1. He has decided to spend ₹ 11 on these two commodities.

1. Using the following schedule, identify the combination of the two commodities X and Y that gives maximum satisfaction to Robert.     [4]
   

   Units	1	2	3	4	5	6
   MUX	16	14	12	10	8	6
   MUY	10	9	8	7	6	5

2. State the underlying law related to the schedule given above. Mention the equilibrium condition.     [2]

Answer 1

a.

Given:

Price of X (P_x) = ₹ 2

Price of Y (P_Y) = ₹ 1,

Budget = ₹ 11

Optimal Combination for Maximum Satisfaction Robert should allocate his ₹ 11 budget according to the Law of Equi-Marginal Utility, which states that utility is maximised when:

`(MU_X)/P_X = (MU_Y)/P_Y`

We Calculate the Marginal Utility per Rupee (MU/P) for each unit:

Units	MUX	MUX/PX (MUX/2)	MUY	MUY/PY (MUY/1)
1	16	8	10	10
2	14	7	9	9
3	12	6	8	8
4	10	5	7	7
5	8	4	6	6
6	6	3	5	5

Allocation of ₹ 11 for Maximum Satisfaction:

Buy 3 Units of X → Cost

= 3 × ₹ 2 

= ₹ 6

Buy 5 Units of Y → Cost

= 5 × ₹ 1

= ₹ 5

Total expenditure

= ₹ 6 + ₹ 5

= ₹ 11

At this combination:

`(MU_X)/P_X = (MU_Y)/P_Y = 6`

Thus, this combination provides maximum satisfaction.

b. 

Underlying Law and Equilibrium Condition

It's based on the Law of Equi-Marginal Utility, which says that a buyer is in equilibrium when the ratio of marginal utility to price is the same for all goods:

`(MU_X)/P_X = (MU_Y)/P_Y`

At equilibrium, the consumer distributes expenditure in such a way that the last rupee spent on each commodity gives equal marginal utility.