Question 4 Solving Consumer's Choice Problem under CD Utility, Numerical The consumer with income Y has a preference represented by CD utility function 0.4 0.6 U(91,92) = 914926 Given prices for the two goods, denoted by P₁, P2, solve the consumer's optimal choice problem following the steps below. (a) Write down the consumer's maximization problem, i.e be clear about (1) the choice variables, (2) the objective function and (3) the constraint. (b) Write down the Lagrangian for this optimization problem. (c) Derive the three first-order conditions.
Question 4 Solving Consumer's Choice Problem under CD Utility, Numerical The consumer with income Y has a preference represented by CD utility function 0.4 0.6 U(91,92) = 914926 Given prices for the two goods, denoted by P₁, P2, solve the consumer's optimal choice problem following the steps below. (a) Write down the consumer's maximization problem, i.e be clear about (1) the choice variables, (2) the objective function and (3) the constraint. (b) Write down the Lagrangian for this optimization problem. (c) Derive the three first-order conditions.
Chapter21: Demand: Consumer Choic
Section: Chapter Questions
Problem 1E
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![UP this part).
Question 4
Solving Consumer's Choice Problem under CD Utility, Numerical
The consumer with income Y has a preference represented by CD utility function
U(91,92) = 90.492.6.
Given prices for the two goods, denoted by P₁, P2, solve the consumer's optimal choice
problem following the steps below.
(a) Write down the consumer's maximization problem, i.e be clear about (1) the choice
variables, (2) the objective function and (3) the constraint. mand
(b) Write down the Lagrangian for this optimization problem.
(c) Derive the three first-order conditions.
IM gaitaluste
(d) Solve for the optimal consumption bundles q1,92.
(e) Plugging optimal consumption bundles q,q into U(91,92) to get the expression
for indirect utility function, i.e. utility as a function of Y, P₁, P2.
(f) Now we analyze the properties of demand. How does q respond to changes in
P₁, P2 and Y? Specifically, does q increase or decrease if
1. p₁ increases?
2. p2 increases?
3. Y increases?
For simplicity, we only analyze qf, results for q2 are similar. (Hint: comparative
statics, calculate
aqt
др1'
etc.)
s 101 2AM gaidelis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e6f77a4-2bfc-4d58-b6c2-577005b77990%2F10347404-937b-4e09-8b47-c87662f3996d%2F9quhxmj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:UP this part).
Question 4
Solving Consumer's Choice Problem under CD Utility, Numerical
The consumer with income Y has a preference represented by CD utility function
U(91,92) = 90.492.6.
Given prices for the two goods, denoted by P₁, P2, solve the consumer's optimal choice
problem following the steps below.
(a) Write down the consumer's maximization problem, i.e be clear about (1) the choice
variables, (2) the objective function and (3) the constraint. mand
(b) Write down the Lagrangian for this optimization problem.
(c) Derive the three first-order conditions.
IM gaitaluste
(d) Solve for the optimal consumption bundles q1,92.
(e) Plugging optimal consumption bundles q,q into U(91,92) to get the expression
for indirect utility function, i.e. utility as a function of Y, P₁, P2.
(f) Now we analyze the properties of demand. How does q respond to changes in
P₁, P2 and Y? Specifically, does q increase or decrease if
1. p₁ increases?
2. p2 increases?
3. Y increases?
For simplicity, we only analyze qf, results for q2 are similar. (Hint: comparative
statics, calculate
aqt
др1'
etc.)
s 101 2AM gaidelis
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