I love the Austrian candy Mozartkugeln. They are a small part of my budget, and
ID: 1169595 • Letter: I
Question
I love the Austrian candy Mozartkugeln. They are a small part of my budget, and the only factor determining my willingness to pay for additional Mozartkugeln is how many I already have.
A. Suppose you know that I am willing to give up $1 of "other consumption" to get one more mozartkugeln when I consume bundle A: 100 mozartkugeln and $500 in other goods per month.
a) What is MRS when mozartkugeln consumption remains unchanged from bundle A but I only consume $200 per month in other goods?
b) Are my tastes quasilinear? Could they be homothetic?
c) You notice that this month I am consuming bundle B: $600 in other goods and only 25 mozartkugeln. When questioning me about my change in behavior (from bundle A), I tell you that I am just as happy as I was before. The following month, you observe that I consume bundle C: 400 mozartkugeln and $300 in other goods, and I once again tell you my happiness remains unchanged. Does the new information about B and C change your answer in (b)?
d) Is consumption (other than mozartkugeln) essential for me?
B. Suppose my tastes could be modeled with the utility function u(x1, x2) = 20x1^0.5 + x2, where x1 refers to mozartkugeln and x2 refers to other consumption.
a. calculate the MRS for these tastes and use your answer to prove that my tastes are quasilinear in x1.
b. consider the bundles A,B, and C as defined in part A. Verify that they lie on the indifference curve when tastes are described by the previously defined utility fuction.
c. verify that the MRS at bundle A is as described in part A and derive the MRS at bundle B and C
d. verify that the MRS at the bundle (100,200) corresponds to your answer A(a)
e. how much "other goods" consumption occurs on the indifference curve that contains (100,200) when my mozartkugeln consumption falls to 25 per month? what about when it rises to 400 per month?
f. are mozartkugeln essential for me?
Explanation / Answer
I love the Austrian candy Mozartkugeln. They are a small part of my budget, and the only factor determining my willingness to pay for additional Mozartkugeln is how many I already have.
A. Suppose you know that I am willing to give up $1 of "other consumption" to get one more mozartkugeln when I consume bundle A: 100 mozartkugeln and $500 in other goods per month.
a) What is MRS when mozartkugeln consumption remains unchanged from bundle A but I only consume $200 per month in other goods?
Bundles Mozartkugeln other goods
A 100 500
B 100 200
Marginal utility of Mozartkugeln = 100-100 = 0
Marginal utility of other goods = 500-200 = 300
MRS = 300:0
b) Are my tastes quasilinear? Could they be homothetic?
The tastes are quasilinear here.
c) You notice that this month I am consuming bundle B: $600 in other goods and only 25 mozartkugeln. When questioning me about my change in behavior (from bundle A), I tell you that I am just as happy as I was before. The following month, you observe that I consume bundle C: 400 mozartkugeln and $300 in other goods, and I once again tell you my happiness remains unchanged. Does the new information about B and C change your answer in (b)?
Bundles Mozartkugeln other goods MRS
A 100 500 -
B 25 600 100:75
C 400 300 300:375
Yes on the bases of above MRS, we can see that the MRS is changing due to change in both the units. This lead to change the preference from quasilinear to homothetic.
d) Is consumption (other than mozartkugeln) essential for me?
Yes, the consumption of other goods is necessary as the amount of utility received from other goods is more than the utility received from mozartkugeln.
B. Suppose my tastes could be modeled with the utility function u(x1, x2) = 20x1^0.5 + x2, where x1 refers to mozartkugeln and x2 refers to other consumption.
a. calculate the MRS for these tastes and use your answer to prove that my tastes are quasilinear in x1.
Bundles Mozartkugeln other goods MRS
A 100 500 -
B 25 600 100:75
C 400 300 300:375
Now, marginal Utilities from all the bundles depend on the consumption of Mozartkugeln, so it is a quasilinear consumption.
b. consider the bundles A,B, and C as defined in part A. Verify that they lie on the indifference curve when tastes are described by the previously defined utility fuction.
Utility From Bundle A
u(x1, x2) = 20x1^0.5 + x2
= 20 X 100^0.5 + 500
= 20 X 10 + 500
= 200 + 500 = 700
Utility From Bundle B
u(x1, x2) = 20x1^0.5 + x2
= 20 X 25^0.5 + 600
= 20 X 5 + 600
= 100 + 600 = 700
Utility From Bundle C
u(x1, x2) = 20x1^0.5 + x2
= 20 X 400^0.5 + 300
= 20 X 20 + 300
= 400 + 300 = 700
c. verify that the MRS at bundle A is as described in part A and derive the MRS at bundle B and C
MRS = -10 / x1^0.5
= -10 / 100^0.5
= -10 /10 = -1
MRS = -10 / x1^0.5
= -10 / 25^0.5
= -10 /5= -2
MRS = -10 / x1^0.5
= -10 / 400^0.5
= -10 /20 = -0.5
d. verify that the MRS at the bundle (100,200) corresponds to your answer A(a)
Utility From Bundle A
u(x1, x2) = 20x1^0.5 + x2
= 20 X 100^0.5 + 200
= 20 X 10 + 200
= 200 + 200 = 400
e. how much "other goods" consumption occurs on the indifference curve that contains (100,200) when my mozartkugeln consumption falls to 25 per month? what about when it rises to 400 per month?
u(x1, x2) = 20x1^0.5 + x2
400 = 20 X 25^0.5 +x2
400 = 20 X 5 + x2
400 = 100 + x2
X2 = 300
According to the calculations to stay on the same indifference curve we need to consume 300 units good other goods.
u(x1, x2) = 20x1^0.5 + x2
400 = 20 X 400^0.5 +x2
400 = 20 X 20 + x2
400 = 400 + x2
X2 = 0
According to the calculations to stay on the same indifference curve we need to consume 0 units good other goods.
f. are mozartkugeln essential for me?
No, mozartkugeln are not essential. Its essentiality is depend on the consumption of other goods.
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