A consumer has Rs. 21 to spend on two goods X (Rs. 3 per unit) and Y (Rs. 4 per unit). His marginal utility schedules are given below. Using the Law of Equi-Marginal Utility, find the combination of X and Y that maximises his total utility.
| Units | MUx (utils) | MUy (utils) |
|---|---|---|
| 1 | 90 | 120 |
| 2 | 72 | 96 |
| 3 | 54 | 72 |
| 4 | 36 | 48 |
Dividing each MU by its own price:
| Units | MUx | MUx/Px (Px=3) | MUy | MUy/Py (Py=4) |
|---|---|---|---|---|
| 1 | 90 | 30 | 120 | 30 |
| 2 | 72 | 24 | 96 | 24 |
| 3 | 54 | 18 | 72 | 18 |
| 4 | 36 | 12 | 48 | 12 |
The two ratios are equal at every tier (30&30, 24&24, 18&18, 12&12), so the consumer buys matching pairs: 1 unit each costs (cumulative Rs. 7); 2 units each costs another Rs. 7 (cumulative Rs. 14); 3 units each costs another Rs. 7 (cumulative Rs. 21) — exactly exhausting the Rs. 21 income. Buying a 4th unit of each would need a further Rs. 7, taking cumulative spending to Rs. 28, which exceeds the income, so the consumer stops at 3 units of each, where MUx/Px = MUy/Py = 18 on the last units bought.
Equilibrium combination: 3 units of X and 3 units of Y, with MUx/Px = MUy/Py = 18 and total expenditure of Rs. 21 exactly equal to the given income.
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