Oranges Total Utility Mangoes Total Utility 1 100 1 50 2 190 2 95 3
| 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.
Explanation
(a)
| Oranges | Total Utility | Marginal Utility | Mangoes | Total Utility | Marginal Utility |
| 1 | 100 | 100-0 = 100 | 1 | 50 | 50 - 0 = 50 |
| 2 | 190 | 190 - 100 = 90 | 2 | 95 | 95 - 50 = 45 |
| 3 | 270 | 270 - 190 = 80 | 3 | 135 | 135 - 95 = 40 |
| 4 | 340 | 340 - 270 = 70 | 4 | 170 | 170 - 135 = 35 |
| 5 | 400 | 400 - 340 = 60 | 5 | 200 | 200 - 170 = 30 |
| 6 | 450 | 450 - 400 = 50 | 6 | 225 | 225 - 200 = 25 |
| 7 | 490 | 490 - 450 = 40 | 7 | 245 | 245 - 225 = 20 |
| 8 | 520 | 520 - 490 = 30 | 8 | 260 | 260 - 245 = 15 |
MUn = TUn -Tu or MU = \(\frac{\DeltaTU}{\DeltaQ}\
(b)(i) 7 oranges, (ii) 3 mangoes
(c) (i) As a consumer consumes successive units of a commodity, a point is eventually reached where consumption of an additional unit yields less satisfaction.
(ii) \(\frac{MUo}{Po}\) = \(\frac{MUm}{Pm}\)
Where O = Oranges
m = Mangoes
mu = Marginal Utility
P = Price
OR \(\frac{Muo}{Mum}\) = \(\frac{Po}{Pm}\) OR Muo = Po ffor single good.