Question
In: Economics
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 |
$41 |
- What is Josie’s marginal benefit of the fourth unit of tomatoes? The second unit of potatoes?
- Calculate the total benefit is Josie consumes 3 unit of tomatoes and 1 unit of potato?
- If Josie consumes 2 unit of tomatoes and 4 units of potatoes, is this a utility maximizing combination?
- What is Josie’s optimal consumption of tomatoes and potatoes given her budget?
Solutions
Expert Solution
a.
MB of 4th unit of tomato: 4.
MB of 2nd unit of potato: 12
Explanation:
MB=change in TB/change in Q
MB of 4th unit of tomato =(28-24)/(4-1)
=4.
MB of 2nd unit of potato=(28-16)/(2-1)
=12.
b.
TB=TB from 3rd unit of tomato+ TB from 1 unit of potato.
=24+16
=40.
C.
No!
Explanation:
| QT | TBT | MBT | MBT/PT | QP | TBP | MBP | MBP/PP |
| 0 | 0 | 0 | 0 | ||||
| 1 | 10 | 10 | 5 | 1 | 16 | 16 | 4 |
| 2 | 18 | 8 | 4 | 2 | 28 | 12 | 3 |
| 3 | 24 | 6 | 3 | 3 | 36 | 8 | 2 |
| 4 | 28 | 4 | 2 | 4 | 40 | 4 | 1 |
| 5 | 30 | 2 | 1 | 5 | 41 | 1 | 0.25 |
MBT=change in TBT/change in QT
MBP=change in TBP/change in QP
utility is maximized when MBT/PT=MBP/PP
so, here MB per dollar for potato and tomato are not equal so it is not maximizing utility.
D.
4 tomato and 3 potato
Explanation:
utility is maximized when MBT/PT=MBP/PP
so, the first consumer will buy that product which has the highest MB per dollar. so first she will but 1 quantity of tomato and the next both have the same MB per dollar so she will buy one more unit of tomato and one unit of potato. now she spends a total 8$ 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 |
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