Oranges Total Utility Mangoes Total Utility 1 100 1 50 2 190 2 95 3 270 3 135 4 340 4 170 5 400 5 200 6 450 6 225 7 490 7 245 8 520 8 260 The table above sh...
Question 1 Report
| Oranges | Total Utility | Mangoes | Total Utility |
| 1 | 100 | 1 | 50 |
| 2 | 190 | 2 | 95 |
| 3 | 270 | 3 | 135 |
| 4 | 340 | 4 | 170 |
| 5 | 400 | 5 | 200 |
| 6 | 450 | 6 | 225 |
| 7 | 490 | 7 | 245 |
| 8 | 520 | 8 | 260 |
The table above shows Mr. Y's schedule of total utility for oranges and mangoes. The prices of oranges and mangoes are at $1.00 each. Mr. Y has $10 00 to spend on the goods.
Use the information contained in thetable to answer the questions that follow
(a) Calculate the marginal utility for all the levels of consumption for the goods.
(b) At equilibrium, how many (i) oranges (ii) mangoes, will the consumer buy?
(c) (i)State the law of diminishing marginal utility. (ii) State the marginal condition for utility maximization.
Answer Details
(a) Marginal utility \( MU_n = TU_n - TU_{n-1} \) for each good.
| Unit | Oranges TU | Oranges MU | Mangoes TU | Mangoes MU |
|---|---|---|---|---|
| 1 | 100 | 100 | 50 | 50 |
| 2 | 190 | 90 | 95 | 45 |
| 3 | 270 | 80 | 135 | 40 |
| 4 | 340 | 70 | 170 | 35 |
| 5 | 400 | 60 | 200 | 30 |
| 6 | 450 | 50 | 225 | 25 |
| 7 | 490 | 40 | 245 | 20 |
| 8 | 520 | 30 | 260 | 15 |
(b) Equilibrium. With both prices equal to \$1.00, the equi-marginal condition \( \dfrac{MU_o}{P_o} = \dfrac{MU_m}{P_m} \) reduces to \( MU_o = MU_m \), and the consumer must spend the whole \$10 (so \( Q_o + Q_m = 10 \) units at \$1 each).
The marginal utilities are equal at \( MU = 40 \): the 7th orange gives 40 and the 3rd mango gives 40. This uses \( 7 + 3 = 10 \) units, exactly the \$10 budget.
- (i) Oranges bought: 7.
- (ii) Mangoes bought: 3.
(c)(i) Law of diminishing marginal utility: as a consumer consumes more units of a good, the additional (marginal) utility derived from each successive unit falls, other things being equal. Both columns above show MU declining.
(c)(ii) Marginal condition for utility maximisation: the consumer maximises satisfaction when the marginal utility per naira (or dollar) spent is the same for every good, \( \dfrac{MU_o}{P_o} = \dfrac{MU_m}{P_m} \), while the entire income is spent. This is the equi-marginal principle.
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