Josie has a fixed budget of $20, and she spends it all on two goods, tomatoes...

Josie has a fixed budget of $20, and she spends it all on two goods, tomatoes and potatoes. The price of tomatoes is $2 per unit, and the price of potatoes is $4 per unit. The table below shows the total benefit, measured in dollars, Martha receives from the consumption of each good.

Quantity of Tomatoes	Total Benefit from Tomatoes	Quantity of Potatoes	Total Benefit from Potatoes
0	$0	0	$0
1	$10	1	$16
2	$18	2	$28
3	$24	3	$36
4	$28	4	$40
5	$30	5	$41

What is Josie’s marginal benefit of the fourth unit of tomatoes? The second unit of potatoes?
Calculate the total benefit is Josie consumes 3 unit of tomatoes and 1 unit of potato?
If Josie consumes 2 unit of tomatoes and 4 units of potatoes, is this a utility maximizing combination?
What is Josie’s optimal consumption of tomatoes and potatoes given her budget?

Solutions

Expert Solution

MB of 4th unit of tomato: 4.

MB of 2nd unit of potato: 12

Explanation:

MB=change in TB/change in Q

MB of 4th unit of tomato =(28-24)/(4-1)

=4.

MB of 2nd unit of potato=(28-16)/(2-1)

=12.

TB=TB from 3rd unit of tomato+ TB from 1 unit of potato.

=24+16

=40.

No!

Explanation:

QT	TBT	MBT	MBT/PT	QP	TBP	MBP	MBP/PP
0	0			0	0
1	10	10	5	1	16	16	4
2	18	8	4	2	28	12	3
3	24	6	3	3	36	8	2
4	28	4	2	4	40	4	1
5	30	2	1	5	41	1	0.25

MBT=change in TBT/change in QT

MBP=change in TBP/change in QP

utility is maximized when MBT/PT=MBP/PP

so, here MB per dollar for potato and tomato are not equal so it is not maximizing utility.

4 tomato and 3 potato

Explanation:

utility is maximized when MBT/PT=MBP/PP

so, the first consumer will buy that product which has the highest MB per dollar. so first she will but 1 quantity of tomato and the next both have the same MB per dollar so she will buy one more unit of tomato and one unit of potato. now she spends a total 8$ on both good and she has now left 12$. so further she will buy more quantity. she will buy 1 more unit of both product and now she has left $6. and she will buy one more unit of both products. and so total she will buy 4, units of tomato and 3 units of potato.

QT	TBT	MBT	MBT/PT	QP	TBP	MBP	MBP/PP
0	0			0	0
1	10	10	5	1	16	16	4
2	18	8	4	2	28	12	3
3	24	6	3	3	36	8	2
4	28	4	2	4	40	4	1
5	30	2	1	5	41	1	0.25

Rahul Sunny answered 1 month ago

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