. Consider the following utility function over goods 1 and 2, u (x1,x2)=√√√In A + alnæı + (1 − a) Inx2 where A 0 and a € (0, 1). (a) [15 points] Derive the Marshallian demand functions and the indirect utility function. (b) [15 points] Show two different ways to derive the Hicksian demand function for good 2. (c) [10 points] Using the functions you have derived in the above, show that the Hicksian demand function for goods 2 is homogeneous of degree zero in prices.
. Consider the following utility function over goods 1 and 2, u (x1,x2)=√√√In A + alnæı + (1 − a) Inx2 where A 0 and a € (0, 1). (a) [15 points] Derive the Marshallian demand functions and the indirect utility function. (b) [15 points] Show two different ways to derive the Hicksian demand function for good 2. (c) [10 points] Using the functions you have derived in the above, show that the Hicksian demand function for goods 2 is homogeneous of degree zero in prices.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.8P
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![. Consider the following utility function over goods 1 and 2,
u (x1,x2)=√√√In A + alnæı + (1 − a) Inx2
where A 0 and a € (0, 1).
(a) [15 points] Derive the Marshallian demand functions and the indirect utility
function.
(b) [15 points] Show two different ways to derive the Hicksian demand function for
good 2.
(c) [10 points] Using the functions you have derived in the above, show that the
Hicksian demand function for goods 2 is homogeneous of degree zero in prices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf58e778-209d-4051-b758-0c57e3f8187c%2Fd036e6f2-95df-4858-a10a-5045a8bb042d%2F86ldj4r_processed.png&w=3840&q=75)
Transcribed Image Text:. Consider the following utility function over goods 1 and 2,
u (x1,x2)=√√√In A + alnæı + (1 − a) Inx2
where A 0 and a € (0, 1).
(a) [15 points] Derive the Marshallian demand functions and the indirect utility
function.
(b) [15 points] Show two different ways to derive the Hicksian demand function for
good 2.
(c) [10 points] Using the functions you have derived in the above, show that the
Hicksian demand function for goods 2 is homogeneous of degree zero in prices.
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