1. Given the following information: U= (1/3)X^Y*; Px = 6; Py= 6; I = 2,430, a. calculate the effect on X*, Y*, and U* if the price of X is cut by half. b. graphically illustrate the price consumption curve and the demand curve for good X.
1. Given the following information: U= (1/3)X^Y*; Px = 6; Py= 6; I = 2,430, a. calculate the effect on X*, Y*, and U* if the price of X is cut by half. b. graphically illustrate the price consumption curve and the demand curve for good X.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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(2e)
Hello! I just want to ask for help whether the answers in the given pictures are correct. If it's not, please help me recheck and resolve it. Please refer to the given pictures below for the answers and questions.
After verifying the given answers shown in the subsequent picture, PLEASE ANSWER LETTER — b. graphically illustrate the
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Transcribed Image Text:1. Given the following information: U = (1/3)X²Y*; Px= 6; Py= 6; I = 2,430,
a. calculate the effect on X*, Y*, and U* if the price of X is cut by half.
b. graphically illustrate the price consumption curve and the demand curve for good X.
Transcribed Image Text:Step 1
Given Utility function
U=x0.5y0.5
Px=0.5
Ру-1
|=10
Step 2
U - X0.5ү0.5
dU
MUX =
dU
MUY
DY
MUX
MRS
%3D
MUY
Part 1)
Solving for the MRS
U = X0.5 y0.5
- (1)
-(2)
MUx =
dU = – -
= 0. 5X-0.5 y 0,5 = 0 -
MUy =
= 0. 5X0.5 Y -0.5 = 0 – –
%D
dY
Ву еquation 1 and 2
0.5X-05y0.5
0.5x05y-0.5
--0.:
MRS =
Y
MRS =
X
Marginal utility of X shows the additional utility received by 1 additional unit
of X consumption.
second order is negative, therefor it represents law of diminishing marginal
utility.
Marginal utility of Y shows the additional utility received by 1 additional unit
of Y consumption.
second order is negative, therefor it represents law of diminishing marginal
utility.
MRS represent sacrifice of Y inoredr to get 1 extra unit of X
Here to get 1 extra X he is ready to forgone 1 Y.
Part b)
Budget constraint
10 = 0. 5X + Y
By lagrange function
Max U = X05y05 + 2(10 – – Y )
М
0.5X -
ОМaxU
0. 5X-0.5 y0.5 – 0. 51
Xe
= 0. 5X0.5 Y-0.5 – 1 = 0 – –(2
(1) -
ƏMaxU
dY
Ву еquation 1 and 2
* = 4
Y
0.5
X
1
Y = 0. 5X
By substituting into budget constraint
10 = 0. 5X + Y
10 = 0. 5X + Y0. 5X
10 = X
By plugging X into Y
Y = 0. 5X
Y = 0. 5 * 10
Y = 5
X* = 10, Y * 5
U =
100.550.5
U =
7. 0708
%D
U* 3D 7 аррrox.
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