1. A consumer in a two-good economy (x1 and x2) with prices pi and p2 and utility equal to u faces the Cobb-Douglas expenditure function: (1-a) е(p, и) — ирір2 where a E (0, 1). 1.1 Derive the indirect utility function v(p, y) for this consumer. 1.2 Derive the Hicksian demand functions for the consumer r: (p, u). 1.3 Suppose you know that expenditure share for the ith good, wi, is defined as: P;a# (p, u) е(p, и) Wi = Using the Hicksian demand functions derived in part 1.2 above, along with the expenditure function provided at the beginning of the question, find an expression for wi + wz and interpret this expression within the context of the Cobb-Douglas framework.
1. A consumer in a two-good economy (x1 and x2) with prices pi and p2 and utility equal to u faces the Cobb-Douglas expenditure function: (1-a) е(p, и) — ирір2 where a E (0, 1). 1.1 Derive the indirect utility function v(p, y) for this consumer. 1.2 Derive the Hicksian demand functions for the consumer r: (p, u). 1.3 Suppose you know that expenditure share for the ith good, wi, is defined as: P;a# (p, u) е(p, и) Wi = Using the Hicksian demand functions derived in part 1.2 above, along with the expenditure function provided at the beginning of the question, find an expression for wi + wz and interpret this expression within the context of the Cobb-Douglas framework.
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.4P
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Transcribed Image Text:1. A consumer in a two-good economy (x1 and x2) with prices pi and p2 and utility equal to
u faces the Cobb-Douglas expenditure function:
(1-a)
e (p, и) — ир*р.
where a E (0, 1).
1.1 Derive the indirect utility function v(p, y) for this consumer.
1.2 Derive the Hicksian demand functions for the consumer x" (p, u).
1.3 Suppose you know that expenditure share for the ith good, w;, is defined as:
P;r# (p, u)
е (p, и)
Wi =
Using the Hicksian demand functions derived in part 1.2 above, along with the expenditure
function provided at the beginning of the question, find an expression for w1 + w2 and
interpret this expression within the context of the Cobb-Douglas framework.
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