Question

Exercise 1:

The following table shows the total utility or the marginal utility of three commodities, which are apples, grapes, and dates. If the price of apples is 10 riyals, the price of grapes is 2 riyals, the price of dates is 8 riyals, and you as a consumer have an income of 74 riyals, using the terms of the consumer's balance to achieve the greatest benefit, I find the following: -

1) Complete the table by calculating the missing data in the table.
2) Find the optimum quantity that each commodity should consume for the greatest utility.
3) Calculate the maximum total utility that you can obtain from your consumption of optimal quantities of the three commodities.

quantities	apple			grape			dates
Q	TU	MU	MU/P	TU	MU	MU/P	TU	MU	MU/P
1	42				14		46
2	82				12		80
3	118				10		104
4	148				8		120
5	170				6		130
6	182				4		136
7	182				2		140

Answer 1

	Apple			Grapes			Dates
Q	TU	MU	MU/P	TU	MU	MU/P	TU	MU	MU/P
1	42	42	4.2	14	14	7	46	46	5.75
2	82	40	4	26	12	6	80	34	4.25
3	118	36	3.6	36	10	5	104	24	3
4	148	30	3	44	8	4	120	16	2
5	170	22	2.2	50	6	3	130	10	1.25
6	182	12	1.2	54	4	2	136	6	0.75
7	182	0	0	56	2	1	140	4	0.5

MU=change in TU

MU/P = MU/price of the good

TU=cumulative of MU

The consumer maximizes his utility where the MU/P for all the goods is same

Income = 74

The consumer will purchase 4 units of Apple, 5 units of Grapes and 3 units of Dates = 4*10 + 5*2 + 3*8 = 74

Maximum Total utility = 148+50+104 = 302