Problem 3. Assume that 1 piece of cake and 1 can of coke cost $1 each and a consumer has $10 en total. Let us denote the cake and coke by x and Y, respectively. Hence, the consumer can buy 10 items in total, x + y < 10. It could be either 10 pieces of cake and no coke or 10 bottles of coke and no cake, or (5,5), or (2,8), or (2,2) or (0,0) or any other amount for which the total number of items is less than 10. Assume that the consumer's happiness (utility) function is one of the following and find its maximum: a). u (x, y) = x² + y? b). u (x, y) = 2x² + y? c). u (x, y) = x² – y?
Problem 3. Assume that 1 piece of cake and 1 can of coke cost $1 each and a consumer has $10 en total. Let us denote the cake and coke by x and Y, respectively. Hence, the consumer can buy 10 items in total, x + y < 10. It could be either 10 pieces of cake and no coke or 10 bottles of coke and no cake, or (5,5), or (2,8), or (2,2) or (0,0) or any other amount for which the total number of items is less than 10. Assume that the consumer's happiness (utility) function is one of the following and find its maximum: a). u (x, y) = x² + y? b). u (x, y) = 2x² + y? c). u (x, y) = x² – y?
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.12P
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Intermediate
![Problem 3. Assume that 1 piece of cake and 1 can of coke cost $1 each
and a consumer has $10 en total. Let us denote the cake and coke by x and
y, respectively. Hence, the consumer can buy 10 items in total, x + y < 10.
It could be either 10 pieces of cake and no coke or 10 bottles of coke and no
cake, or (5,5), or (2,8), or (2,2) or (0,0) or any other amount for which the
total number of items is less than 10. Assume that the consumer's happiness
(utility) function is one of the following and find its maximum:
a). u (x, y) = x² + y²
b). и (х, у) — 22 + у?
c). u (x, y) = x² – y?
d). u (x, y)
e). u (x, y) = –x² – y?
f). u (x, y) = xY
-x2 + 2y?
1
Comment on how much the consumer likes the two commodities under
each of the above utility functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ae25fae-0750-4427-81d8-44a1e496dd43%2F756730f9-d155-4867-8e30-2171f15e7714%2Fwtu6vmo_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3. Assume that 1 piece of cake and 1 can of coke cost $1 each
and a consumer has $10 en total. Let us denote the cake and coke by x and
y, respectively. Hence, the consumer can buy 10 items in total, x + y < 10.
It could be either 10 pieces of cake and no coke or 10 bottles of coke and no
cake, or (5,5), or (2,8), or (2,2) or (0,0) or any other amount for which the
total number of items is less than 10. Assume that the consumer's happiness
(utility) function is one of the following and find its maximum:
a). u (x, y) = x² + y²
b). и (х, у) — 22 + у?
c). u (x, y) = x² – y?
d). u (x, y)
e). u (x, y) = –x² – y?
f). u (x, y) = xY
-x2 + 2y?
1
Comment on how much the consumer likes the two commodities under
each of the above utility functions.
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