Supose that a consumer has utility function U with U(₁,₂)= 14126, where ₁ and 2 are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility
Supose that a consumer has utility function U with U(₁,₂)= 14126, where ₁ and 2 are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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![2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are
demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5,
respectively. This consumer has money m = 12 to spend and wants to maximize utility with
constraint the money.
(a) Write the Lagrangian function.
(b) Find the critical point using first order condition.
(c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser.
(d) Find the maximum utility.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fc8cdf1-1696-4e19-9eab-8b0e4cff661f%2F8221596a-a52d-47f8-b9ae-6381abea3121%2F6kft802_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are
demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5,
respectively. This consumer has money m = 12 to spend and wants to maximize utility with
constraint the money.
(a) Write the Lagrangian function.
(b) Find the critical point using first order condition.
(c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser.
(d) Find the maximum utility.
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