PsyQUESTION: Use the sheet 1( picture below) utility function and parameter values to find the optimal solution via analytical methods (calculus/lagrangean/algebra). Show your work. Note that x1<a/b, so we will use the first utility function given in the yellow box in the sheet. This sheet uses a U function that yields a Giffen x1 (over a certain price range)Goalmax Utility0 Endogenous Variables1 x12 x22535.51415 Exogenous Variables16 p117 p218 m19 a20 b21 c22 d23242526 Constraint27284411Reset1 price of x11 price of x255 income100 coefficient for x12 coefficient for x11 coefficient for x21 coefficient for x2Oincome left over88928206050403010020-p1/p2-1,000(X₁X₂)=x140ÂMRS at x1, x2-1.0001-a²26max (x,x)Kas.t. m2 px, + P₂x₂b+0%₂++ a₂ +72U=2535560dfor 0≤x, 5%for x, 2%Zoom In

Given u(x1,x2)=ax1-b2x12+cx2+d2x22 for 0≤x1≤ab ......... (1) Given x1<a/b Price…

Answered: QUESTION: Use the sheet 1( picture…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION: Use the sheet 1( picture below) utility function and parameter values to find the optimal solution via analytical methods (calculus/lagrangean/algebra). Show your work. Note that x1<a/b, so we will use the first utility function given in the yellow box in the sheet.

This sheet uses a U function that yields a Giffen x1 (over a certain price range)
Goal
max Utility
0 Endogenous Variables
1 x1
2 x2
2535.5
14
15 Exogenous Variables
16 p1
17 p2
18 m
19 a
20 b
21 c
22 d
23
24
25
26 Constraint
27
28
44
11
Reset
1 price of x1
1 price of x2
55 income
100 coefficient for x1
2 coefficient for x1
1 coefficient for x2
1 coefficient for x2
Oincome left over
8892820
60
50
40
30
10
0
20
-p1/p2
-1,000
(X₁X₂)=
x1
40
Â
MRS at x1, x2
-1.000
1-
a²
26
max (x,x)
Ka
s.t. m2 px, + P₂x₂
b
+0%₂
+
+ a₂ +
72
U=25355
60
d
for 0≤x, 5%
for x, 2%
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