Columns 1 through 4 in the accompanying table show the marginal utility, measure
ID: 1112466 • Letter: C
Question
Columns 1 through 4 in the accompanying table show the marginal utility, measured in utils, that Sean would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Sean gets from saving. Assume that the price of good A is $18.00, the price of good B is $6.00, the price of good C is $4.00 and the price of good D is $12.00. Sean's income is $142.00.
Column 1
Column 2
Column 3
Column 4
Column 5
Units of
Good A
MU
Units of
Good B
MU
Units of
Good C
MU
Units of
Good D
MU
Number of Dollars Saved
MU
1
72
1
24
1
15
1
36
1
5.00
2
54
2
15
2
12
2
30
2
4.00
3
45
3
12
3
8
3
24
3
3.00
4
36
4
9
4
7
4
18
4
2.00
5
27
5
7
5
5
5
13
5
1.00
6
18
6
5
6
4
6
7
6
0.50
7
15
7
2
7
3.5
7
4
7
0.25
8
12
8
1
8
3
8
2
8
0.13
a. What quantities of A, B, C, and D will Sean purchase in maximizing his utility?
b. How many dollars will Sean choose to save? $ ___________
c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.
Other Side
Using the figure below, answer the following three questions:
Explain why the point of tangency of the budget line with an indifference curve is the consumer’s equilibrium position.
Explain why any point where the budget line intersects an indifference curve will not be equilibrium.
Explain the following statement: “The consumer is in equilibrium where MRS = PB/PA.”
Column 1
Column 2
Column 3
Column 4
Column 5
Units of
Good A
MU
Units of
Good B
MU
Units of
Good C
MU
Units of
Good D
MU
Number of Dollars Saved
MU
1
72
1
24
1
15
1
36
1
5.00
2
54
2
15
2
12
2
30
2
4.00
3
45
3
12
3
8
3
24
3
3.00
4
36
4
9
4
7
4
18
4
2.00
5
27
5
7
5
5
5
13
5
1.00
6
18
6
5
6
4
6
7
6
0.50
7
15
7
2
7
3.5
7
4
7
0.25
8
12
8
1
8
3
8
2
8
0.13
Explanation / Answer
a. What quantities of A, B, C, and D will Sean purchase in maximizing his utility?
A = 4 units
B = 3 units
C = 3 units
D = 3 units
Note that this bundle has MU/$ same and is equal to 2 for each product as well as the MU/$ from saving is also 2. The budget is 18*4 + 6*3 + 4*3 + 12*3 = $138 and savings are $142 - $138
b. How many dollars will Sean choose to save? $4
c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.
This is done in the table and see that MU/$ for the above combination is true
Explain why the point of tangency of the budget line with an indifference curve is the consumer’s equilibrium position.
This is because at this level the slope of the budget line is same as the slope of the indifference curve. This also means that MU/$ for each of the product in the bundle is same across all bundles. In addition, the budget is exhausting.
Explain why any point where the budget line intersects an indifference curve will not be equilibrium.
Because that indifference curve will not maximize the utility. There will be some indifference curve that will lie above this indifference curve and will be tangent to the budget line. Slope of IC is not equal to slope of budget line which is a necessary condition for utility maximization
Explain the following statement: “The consumer is in equilibrium where MRS = PB/PA.”
This statement indicates that the point of tangency of the budget line with an indifference curve is the consumer’s equilibrium as at this level the slope of the budget line is same as the slope of the indifference curve. The slope of the budget line is PB/PA and the slope is slope of the indifference curve is MRS. At tangency, MRS = PB/PA
Units of MU MU/$ Units of MU MU/$ Units of MU MU/$ Units of MU MU/$ Number of Dollars Saved MU Good A Good B Good C Good D 1 72 4.0 1 24 4.0 1 15 3.8 1 36 3.0 1 5 2 54 3.0 2 15 2.5 2 12 3.0 2 30 2.5 2 4 3 45 2.5 3 12 2.0 3 8 2.0 3 24 2.0 3 3 4 36 2.0 4 9 1.5 4 7 1.8 4 18 1.5 4 2 5 27 1.5 5 7 1.2 5 5 1.3 5 13 1.1 5 1 6 18 1.0 6 5 0.8 6 4 1.0 6 7 0.6 6 0.5 7 15 0.8 7 2 0.3 7 3.5 0.9 7 4 0.3 7 0.25 8 12 0.7 8 1 0.2 8 3 0.8 8 2 0.2 8 0.13