Hicksian demand

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter6: Demand Relationships Among Goods
Section: Chapter Questions
Problem 6.10P
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< Please help with questions D...
Please help with questions DE & F.
Thank you!
3. Explain in what sense the expenditure minimization problem (the Hick-
sian demand problem) is a "dual" representation of the consumer choice problem
to the utility maximization problem (the Marshallian demand problem).
(a) write now both problems for the case of utility function that represents
strictly convex preferences (for example, when u(21, 22) is strictly concave)
(b) Define the value function in each problem, and interpret it (with words).
(c) Then, using the value function definition in the two problems, show how:
(i) a Hicksian demand can be computed as a Marshallian demand.
(ii) a Marshallian demand can be computed as a Hicksian demand
(d) Now, state the Slutsky relationship between the two demands (Hicksian
and Marshallian).
(e) In the Slutsky equation, using the mathematical formulation the income
effect vs the substitution effect, decompose the effects of an "own price change"
for good 1 in a consumer choice problem with 2 goods.
(f) Can you develop a notion of a income and substitution effect for good
2 when the price of good 1 changes? If so, provide a detailed explanation. If
not, explain why you cannot identify with the income or substitution effect of
a "cross price" change.
Transcribed Image Text:< Please help with questions D... Please help with questions DE & F. Thank you! 3. Explain in what sense the expenditure minimization problem (the Hick- sian demand problem) is a "dual" representation of the consumer choice problem to the utility maximization problem (the Marshallian demand problem). (a) write now both problems for the case of utility function that represents strictly convex preferences (for example, when u(21, 22) is strictly concave) (b) Define the value function in each problem, and interpret it (with words). (c) Then, using the value function definition in the two problems, show how: (i) a Hicksian demand can be computed as a Marshallian demand. (ii) a Marshallian demand can be computed as a Hicksian demand (d) Now, state the Slutsky relationship between the two demands (Hicksian and Marshallian). (e) In the Slutsky equation, using the mathematical formulation the income effect vs the substitution effect, decompose the effects of an "own price change" for good 1 in a consumer choice problem with 2 goods. (f) Can you develop a notion of a income and substitution effect for good 2 when the price of good 1 changes? If so, provide a detailed explanation. If not, explain why you cannot identify with the income or substitution effect of a "cross price" change.
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