2. The consumer has Leontief preferences for two goods and y: u(x, y) = min{2r, 5y}. pz > 0, Py> 0 and m> 0 is given. a) Set up the Expenditure Minimization Problem. b) Write down the optimality condition for r and y. c) Solve for the compensated demand functions for good z and y. xº (Pz, Py, u)= y (Pz, Py, ū)=
2. The consumer has Leontief preferences for two goods and y: u(x, y) = min{2r, 5y}. pz > 0, Py> 0 and m> 0 is given. a) Set up the Expenditure Minimization Problem. b) Write down the optimality condition for r and y. c) Solve for the compensated demand functions for good z and y. xº (Pz, Py, u)= y (Pz, Py, ū)=
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![2. The consumer has Leontief preferences for two goods r and y: u(x, y) = min{2x, 5y}. Pz > 0,
Py> 0 and m> 0 is given.
a) Set up the Expenditure Minimization Problem.
b) Write down the optimality condition for x and y.
c) Solve for the compensated demand functions for good z and y.
• T² (Pr, Py, u) =
•y (Pz, Py, u) =
d) Graph the compensated demand function for rº(Pr. Py, u) when u = 50, Py = 1, and m = 100.
(place z on the z-axis and pr on the y-axis).
50
25
0
0
25
50
e) What is the reason for the extreme difference in the ordinary (Marshallian) demand function
and the compensated (Hicksian) demand function for the case of Leontief preferences?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06032bc2-aa37-4dfb-bd0e-ae77d4688028%2F5b822b62-5dd5-4fb3-99b3-aafe81c09c7e%2Fectage6e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. The consumer has Leontief preferences for two goods r and y: u(x, y) = min{2x, 5y}. Pz > 0,
Py> 0 and m> 0 is given.
a) Set up the Expenditure Minimization Problem.
b) Write down the optimality condition for x and y.
c) Solve for the compensated demand functions for good z and y.
• T² (Pr, Py, u) =
•y (Pz, Py, u) =
d) Graph the compensated demand function for rº(Pr. Py, u) when u = 50, Py = 1, and m = 100.
(place z on the z-axis and pr on the y-axis).
50
25
0
0
25
50
e) What is the reason for the extreme difference in the ordinary (Marshallian) demand function
and the compensated (Hicksian) demand function for the case of Leontief preferences?
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