Meera's Fruit Budget: Equalising Marginal Utility per Rupee
Meera has ₹120 a week to spend on apples and guavas, and she spends it all. Apples cost ₹20 each and guavas ₹10 each. Her marginal utility (MU) from successive units, in utils, is: apples 100, 80, 60, 40, 20, 10; guavas 50, 40, 30, 20, 10, 0. Last week she bought 5 apples and 2 guavas because she likes apples more. She said she did not compare MU per rupee and would not save money or buy fractional fruit. A friend tells her that buying more apples than guavas must maximise satisfaction because apples cost twice as much. Meera asks whether her bundle is utility-maximising and what she should do if the price of apples doubles to ₹40, with income and the guava price unchanged.
1. Test whether Meera's current bundle of 5 apples and 2 guavas is in consumer equilibrium. Show MU per rupee and total utility, and state the direction of adjustment.
Read the worked answer
Budget check: 5 × ₹20 + 2 × ₹10 = ₹100 + ₹20 = ₹120, so the bundle is affordable.
MU per rupee:
| Unit | MU apples | MU/P apples (P = 20) | MU guavas | MU/P guavas (P = 10) |
|---|---|---|---|---|
| 1 | 100 | 5.0 | 50 | 5.0 |
| 2 | 80 | 4.0 | 40 | 4.0 |
| 3 | 60 | 3.0 | 30 | 3.0 |
| 4 | 40 | 2.0 | 20 | 2.0 |
| 5 | 20 | 1.0 | 10 | 1.0 |
At the current bundle, the 5th apple gives 1 util per rupee, while the 2nd guava gives 4 utils per rupee. Since MU_g/P_g > MU_a/P_a, Meera gets more satisfaction per rupee from guavas than from the last apple. Total utility = (100 + 80 + 60 + 40 + 20) + (50 + 40) = 300 + 90 = 390 utils.
She should shift spending from apples to guavas. For example, dropping one apple frees ₹20, which buys 2 guavas, giving 4 apples and 4 guavas. At that bundle, MU/P for the 4th apple = 40/20 = 2 and for the 4th guava = 20/10 = 2. Total utility rises to 280 + 140 = 420 utils. So the current bundle is not utility-maximising.
2. Find Meera's equilibrium bundle and verify that it uses the whole budget. Explain why the rule is equality of MU per rupee, not equality of MU.
Read the worked answer
The equilibrium bundle is 4 apples and 4 guavas.
Check the budget: 4 × ₹20 + 4 × ₹10 = ₹80 + ₹40 = ₹120. The whole income is spent.
Check the marginal condition: MU_a/P_a = 40/20 = 2 and MU_g/P_g = 20/10 = 2. The ratios are equal, so there is no gain from moving ₹1 from one fruit to the other.
Total utility = (100 + 80 + 60 + 40) + (50 + 40 + 30 + 20) = 280 + 140 = 420 utils. This is higher than nearby affordable bundles: 5 apples + 2 guavas gives 390; 3 apples + 6 guavas gives 240 + 150 = 390; 6 apples + 0 guavas gives 310. So 4 + 4 is the best affordable bundle under the given schedules.
The correct rule is equality of MU per rupee, not equality of MU. If Meera equalised MU, she might choose 5 apples (MU = 20) and 4 guavas (MU = 20), but that costs ₹100 + ₹40 = ₹140, which exceeds her ₹120 budget. The per-rupee comparison accounts for both satisfaction and price, so it is the relevant condition for a consumer with a fixed budget.
3. If the price of apples doubles to ₹40 while income stays ₹120 and guavas stay at ₹10, predict the direction of change in Meera's apple consumption. Use the MU per rupee rule and explain the substitution and income effects. Check whether 2 apples and 4 guavas satisfy the rule.
Read the worked answer
At ₹40 per apple, each apple's MU per rupee is halved: 2.5, 2.0, 1.5, 1.0, 0.5 for the first five units. Guava's MU per rupee is unchanged: 5, 4, 3, 2, 1, 0.
At the old equilibrium of 4 apples + 4 guavas, the 4th apple now gives 40/40 = 1 util per rupee, while the 4th guava gives 20/10 = 2. Apples have become less attractive per rupee, so Meera will buy fewer apples and more guavas. This is the substitution effect: apples are now relatively more expensive in utility terms.
There is also an income effect: with ₹120, her real purchasing power over apples has fallen because apples cost twice as much. For a normal good, this reinforces the fall in apple quantity.
Check the candidate bundle 2 apples + 4 guavas: 2 × ₹40 + 4 × ₹10 = ₹80 + ₹40 = ₹120. MU/P for the 2nd apple = 80/40 = 2; MU/P for the 4th guava = 20/10 = 2. The rule is satisfied. Total utility is 180 + 140 = 320. So the predicted direction is a fall in apple consumption, specifically from 4 to 2 apples if the schedules stay unchanged.