Paige has the utility function U(x, y) = ln(x) + 4y. Do not worry about corner solutions when answering the following questions, you can use the Lagrangian multiplier method. Paige's budget constraint is 1. What are Paige's Marshallian Demand Functions? (a) gx (Px, Py, I) (b) gx (Px, Py, I) (c) 9x (Px, Py, I) (d) 9xPx, Py, I = = = = I Py (e) gx (Px, Py, I) = = Py 4px I Py 2 Py 2px " Px 4px · 2; ; Pxx+Pyy = I. gy (Pa, Pys I) - 4; gy (Pa, Pys I) = = gy(Px, Py, I) gy (Pa, Pys I) gy (Px, Py, I) = = I Py I Py = Py 2px I Px 4 2 Py 4px 4

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Question
Paige has the utility function
U(x, y) = ln(x) + 4y.
Do not worry about corner solutions when answering the following questions, you can use
the Lagrangian multiplier method. Paige's budget constraint is
1. What are Paige's
(a) gx (Px, Py, I)
(b) gx (Px, Py, I)
(d) GxPx, Py, I =
(e) 9x (Px, Py, I)
Marshallian Demand Functions?
=
=
Py.
4px
I
Py
=
;gy (Pa, Py, I)
Py
2px
Pxx+Pyy = I.
- 2;
I
Py
(c) 9x (Pa, Py, 1) = -4; 9y (Pa, Py, I) = Pv
I)
4px
Py
Px.
4px 9
gy (Px, Py, I)
=
=
gy (Px, Py, I)
gy (Px, Py, I)
I
Py
I
Py
=
=
Py
2px
1
4
2
I
Px
4
Transcribed Image Text:Paige has the utility function U(x, y) = ln(x) + 4y. Do not worry about corner solutions when answering the following questions, you can use the Lagrangian multiplier method. Paige's budget constraint is 1. What are Paige's (a) gx (Px, Py, I) (b) gx (Px, Py, I) (d) GxPx, Py, I = (e) 9x (Px, Py, I) Marshallian Demand Functions? = = Py. 4px I Py = ;gy (Pa, Py, I) Py 2px Pxx+Pyy = I. - 2; I Py (c) 9x (Pa, Py, 1) = -4; 9y (Pa, Py, I) = Pv I) 4px Py Px. 4px 9 gy (Px, Py, I) = = gy (Px, Py, I) gy (Px, Py, I) I Py I Py = = Py 2px 1 4 2 I Px 4
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