Given the total utility function for a consumer, consuming two goods is U = x+2y + xy +2 the prices of x and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130 TL; a) Write the constraint ( budget) function. b) Write the lagrangian function. c) What are the first-order conditions for utility maximization? d) Find the critical values of x, y and \lambda (x*,y* and \lambda *) according to the first order conditions. e) is the second order suficent condition for maximum utility satisfied 2 4 10 - [ ¦ ¦] | - And d = 1 1 3 8 Write the appropriate commands to create A and d matrixes in R software. How can you formulate the equation X = A-1 . d in R language? Given A =
Given the total utility function for a consumer, consuming two goods is U = x+2y + xy +2 the prices of x and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130 TL; a) Write the constraint ( budget) function. b) Write the lagrangian function. c) What are the first-order conditions for utility maximization? d) Find the critical values of x, y and \lambda (x*,y* and \lambda *) according to the first order conditions. e) is the second order suficent condition for maximum utility satisfied 2 4 10 - [ ¦ ¦] | - And d = 1 1 3 8 Write the appropriate commands to create A and d matrixes in R software. How can you formulate the equation X = A-1 . d in R language? Given A =
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![Given the total utility function for a consumer, consuming two goods is U
=
x+2y + xy+2 the prices of x
and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130
TL;
a) Write the constraint ( budget) function.
b) Write the lagrangian function.
c) What are the first-order conditions for utility maximization?
d) Find the critical values of x, y and \lambda (x*,y*and \lambda *) according to the first order conditions.
e) is the second order suficent condition for maximum utility satisfied
2 4
10
[
[:]
8
Write the appropriate commands to create A and d matrixes in R software.
A-1. din R language?
Given A =
1 3
And d
=
How can you formulate the equation X
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0636fbd6-2ddf-4c2f-bab0-1de3627649dc%2Fc77d63d6-0dbd-44db-a56b-19f5253d7c94%2Fpxf9zf_processed.png&w=3840&q=75)
Transcribed Image Text:Given the total utility function for a consumer, consuming two goods is U
=
x+2y + xy+2 the prices of x
and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130
TL;
a) Write the constraint ( budget) function.
b) Write the lagrangian function.
c) What are the first-order conditions for utility maximization?
d) Find the critical values of x, y and \lambda (x*,y*and \lambda *) according to the first order conditions.
e) is the second order suficent condition for maximum utility satisfied
2 4
10
[
[:]
8
Write the appropriate commands to create A and d matrixes in R software.
A-1. din R language?
Given A =
1 3
And d
=
How can you formulate the equation X
=
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