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.
