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Inferring Tastes for "Mozartkugeln": I love the Austrian candy "Mozartkugeln".

Inferring Tastes for “Mozartkugeln”: 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 Mozartkugel
when I consume bundle A — 100 Mozartkugeln and $500 in other goods per month.
(a) What is my MRS when my 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 gain tell you my happiness remains unchanged. Does the new information
about B and C change your answer in (b)?
(d) Is consumption (other than of Mozartkugeln) essential for me?
B: Suppose my tastes could be modeled with the utility function u(x1, x2) = 20(x1^0.5) + 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 the my tastes are quasilinear in
x1.
(b) Consider the bundles A, B and C as defined in part A. Verify that they lie on one indifference curve when
tastes are described by the utility function defined above.
(c) Verify that the MRS at bundle A is as described in part A and derive the MRS at bundles B and C.
(d) Verify that the MRS at the bundle (100,200) corresponds to your answer to 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?

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