A consumer has an income of Rs. 20 to spend on two goods X and Y, priced at Rs. 2 and Rs. 3 per unit respectively. His marginal utility schedules for the two goods are given below. Using the Law of Equi-Marginal Utility, find the utility-maximising combination of X and Y.
| Units | MUx (utils) | MUy (utils) |
|---|---|---|
| 1 | 48 | 72 |
| 2 | 40 | 60 |
| 3 | 32 | 48 |
| 4 | 24 | 36 |
Divide each good's marginal utility by its price to get marginal utility PER RUPEE spent:
| Units | MUx | MUx/Px (Px=2) | MUy | MUy/Py (Py=3) |
|---|---|---|---|---|
| 1 | 48 | 24 | 72 | 24 |
| 2 | 40 | 20 | 60 | 20 |
| 3 | 32 | 16 | 48 | 16 |
| 4 | 24 | 12 | 36 | 12 |
A rational consumer spends each successive rupee on whichever good currently offers the higher marginal utility per rupee. Here, at every tier the two ratios are exactly EQUAL (24 & 24, then 20 & 20, then 16 & 16, then 12 & 12), so the consumer is indifferent between the two goods at each stage and buys one unit of each together: buying the 1st unit of X (Rs. 2) and 1st unit of Y (Rs. 3) costs Rs. 5 (cumulative Rs. 5); the 2nd units cost another Rs. 5 (cumulative Rs. 10); the 3rd units another Rs. 5 (cumulative Rs. 15); the 4th units another Rs. 5 (cumulative Rs. 20). At this point the ENTIRE income of Rs. 20 is spent, and the ratio MUx/Px = MUy/Py = 12 holds on the last (4th) unit of each good purchased — both conditions for equilibrium (equal ratios AND full expenditure of income) are satisfied simultaneously.
Equilibrium combination: 4 units of X and 4 units of Y, with MUx/Px = MUy/Py = 12 and total expenditure of Rs. 20 exactly matching the given income.
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