Problem 2: Satiation point(s) There two goods, candy and soda, available in arbitrary non-negative quan- tities (so the consumption set is R²). A consumer has preferences over con- sumption bundles that are represented by the following utility function: u(x, y) = −|4 — x| − |4 − y| where x is the quantity of candy (in grams), y the quantity of soda (in liters), and |.| denotes the absolute value: for any real number r ≤R, |r| = r -r if r > 0 if r <0 The consumer has wealth of w> 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4,4), (4, 5), (5, 4), (4,3), (3, 4), and a(4, 5) + (1 − a)(3, 4) for a € [0, 1]. (b) In an appropriate diagram, illustrate the consumer's map of indiffer- ence curves. (c) Are the consumer's preferences monotone? Provide an explanation for your answer.
Problem 2: Satiation point(s) There two goods, candy and soda, available in arbitrary non-negative quan- tities (so the consumption set is R²). A consumer has preferences over con- sumption bundles that are represented by the following utility function: u(x, y) = −|4 — x| − |4 − y| where x is the quantity of candy (in grams), y the quantity of soda (in liters), and |.| denotes the absolute value: for any real number r ≤R, |r| = r -r if r > 0 if r <0 The consumer has wealth of w> 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4,4), (4, 5), (5, 4), (4,3), (3, 4), and a(4, 5) + (1 − a)(3, 4) for a € [0, 1]. (b) In an appropriate diagram, illustrate the consumer's map of indiffer- ence curves. (c) Are the consumer's preferences monotone? Provide an explanation for your answer.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.7P
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Transcribed Image Text:For each part (a), (b) and (c), illustrate the demand for candy as a
function of wealth in an appropriate diagram.
Now consider a different consumer who has preferences represented by the
following utility function.
-12 – x| – |8 – yl if x <y
u(x, y)
-18 – x| – |2 – y| if x > y
where x is the quantity of candy (in grams) and y is the quantity of soda
(in liters).
(e) In an appropriate diagram, illustrate the consumer's map of indiffer-
ence curves.
(f) Are the consumer's preferences monotone? Are the preferences convex?
Provide an explanation for each answer.
![Problem 2: Satiation point(s)
There two goods, candy and soda, available in arbitrary non-negative quan-
tities (so the consumption set is R). A consumer has preferences over con-
sumption bundles that are represented by the following utility function:
u(x, y) = -|4 – x| – |4 – y|
where x is the quantity of candy (in grams), y is the quantity of soda (in
liters), and |.| denotes the absolute value: for any real number r E R,
if r >0
|r| =
if r < 0
-r
The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0
Dirhams/gram, and the price of soda is q > 0 Dirhams/liter.
(a) Calculate the utility of the following consumption bundles: (4, 4),
(4,5), (5,4), (4, 3), (3,4), and a(4, 5) + (1 — а) (3,4) for a € [0, 1].
(b) In an appropriate diagram, illustrate the consumer's map of indiffer-
ence curves.
(c) Are the consumer's preferences monotone? Provide an explanation for
your answer.
(d) Find the demand for candy and soda as a function of wealth w > 0
for the following specific prices, explaining how you arrived at your
answers:
(i) when p = 1 and q = 2,
(ii) when p
2 and q = 1,
(iii) when p = q = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9d136fb-9681-408e-9d8b-7312c5869be3%2F80b34914-41e5-4617-9311-4b6610abe7da%2F2e4jri9_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2: Satiation point(s)
There two goods, candy and soda, available in arbitrary non-negative quan-
tities (so the consumption set is R). A consumer has preferences over con-
sumption bundles that are represented by the following utility function:
u(x, y) = -|4 – x| – |4 – y|
where x is the quantity of candy (in grams), y is the quantity of soda (in
liters), and |.| denotes the absolute value: for any real number r E R,
if r >0
|r| =
if r < 0
-r
The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0
Dirhams/gram, and the price of soda is q > 0 Dirhams/liter.
(a) Calculate the utility of the following consumption bundles: (4, 4),
(4,5), (5,4), (4, 3), (3,4), and a(4, 5) + (1 — а) (3,4) for a € [0, 1].
(b) In an appropriate diagram, illustrate the consumer's map of indiffer-
ence curves.
(c) Are the consumer's preferences monotone? Provide an explanation for
your answer.
(d) Find the demand for candy and soda as a function of wealth w > 0
for the following specific prices, explaining how you arrived at your
answers:
(i) when p = 1 and q = 2,
(ii) when p
2 and q = 1,
(iii) when p = q = 1.
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