Planes (price = $10) Trains (Price = $15) Automobiles (price = $5) Units Total u
ID: 1090980 • Letter: P
Question
Planes (price = $10)
Trains (Price = $15)
Automobiles (price = $5)
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
0
0
--
--
0
0
--
--
0
0
--
--
1
100
1
300
1
60
2
190
2
540
2
110
3
270
3
720
3
150
4
340
4
870
4
180
5
400
5
990
5
205
6
450
6
1080
6
225
7
490
7
1140
7
235
8
510
8
1170
8
240
Please answer the following questions. You must show all of your work where calculations are required:
a.Fill in the columns for MU and MU/P for each of the three goods to complete the table above (6pts)
b.What is the combination of planes, trains, and automobiles Kim should choose in order to maximize her total utility? How do you know this is the utility maximizing combination? Include a brief explanation of 25 words to receive full credit. (2pts)
c.Calculate Kim
Planes (price = $10)
Trains (Price = $15)
Automobiles (price = $5)
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
0
0
--
--
0
0
--
--
0
0
--
--
1
100
1
300
1
60
2
190
2
540
2
110
3
270
3
720
3
150
4
340
4
870
4
180
5
400
5
990
5
205
6
450
6
1080
6
225
7
490
7
1140
7
235
8
510
8
1170
8
240
Explanation / Answer
Marginal utility is defined as the increase in utility by buying one extra unit of the product. So here we need to find how much the utility has increased from the previous one. Subtracting successive utilities would give you the corresponding marginal utilities.
Marginal utility by the cost the of the product will give the marginal utility per dollar. The same has been summarised below
Planes (price = $10)
Trains (Price = $15)
Automobiles (price = $5)
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
0
0
--
--
0
0
--
--
0
0
--
--
1
100
1
300
1
60
2
190
2
540
2
110
3
270
3
720
3
150
4
340
4
870
4
180
5
400
5
990
5
205
6
450
6
1080
6
225
7
490
7
1140
7
235
8
510
8
1170
8
240
b) If i get 10 units of utility by spending $1 on product A and 5 units of utilities by spending on product B then obviously i would buy product A. In the similar fashion here too we to incorporate the notion of utility per dollar. Thus at our equilibrium point the money that we spend on each item should fetch the same marginal utility per dollar.
We also need to keep in mind the other constraint that we have is our income of $160. All the items bought should not cross $160.
So $10*A + $15*B + $5*C = $160
You can solve this by either bring one of the terms to the right hand side and then consider than the marginal utilities are same and the A,B and C have to be integers. Which would leave you with few choices and you have try out each of those combinations or you can use an online trial and error calculator.
Upon solving we get;
A = 5
B = 6
C = 4
i.e., Planes = 5; trains = 6; automobiles = 4.
c) Looking at the table we get the corresponding values of total utilities for each product at a given quantity so the total utility is $500 + $1080 + $180 = $1760
Planes (price = $10)
Trains (Price = $15)
Automobiles (price = $5)
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
Units
Total utility (TU)
Marg. Utility (MU)
MU per dollar
0
0
--
--
0
0
--
--
0
0
--
--
1
100
100 101
300
300 201
60
60 122
190
90 92
540
240 162
110
50 103
270
80 83
720
180 123
150
40 84
340
70 74
870
150 104
180
30 65
400
60 65
990
120 85
205
25 56
450
50 56
1080
90 66
225
20 47
490
40 47
1140
60 47
235
10 28
510
20 28
1170
30 28
240