Question #315315

Martha s preference over two goods x and y is represented by the utility function U = 5xy. Her budget constraint is given by 5x + y = 30

a) Find the MRS

b)Find MRT

c)Given her budget how much of each goods should she consume in order to maximise her utility? show your work.


1
Expert's answer
2022-03-22T11:06:09-0400

A).

U=5xy

budget line;

5x+y=30

MRSxy=MUxMUy\frac{MUx}{MUy} =pxPy\frac{px}{Py} ,from the budget line px=$5,Py=$1

=51\frac{5}{1}

MRSxy=5


B).

U=5xy

budget line;

5x+y=30

MRTxy=MCxMCy\frac{MCx}{MCy} =pxPy\frac{px}{Py} ,from the budget line px=$5,Py=$1

=51\frac{5}{1}

MRTxy=5


C).

At optimal utlity :

MUxMUy\frac{MUx}{MUy} =PxPy\frac{Px}{Py} ,from budget line Px=$5,Py=$1


MUX=dudx\frac{du}{dx} 5xy


MUX=5Y


MUY=dudy\frac{du}{dy} 5XY

MUY=5X

Therefore,

5Y5X=51\frac{5Y}{5X}=\frac{5}{1}


YX=5\frac{Y}{X}=5


Y=5X (Substitute in the budget line)


5x+y=30

5x+(5x)=30

10x=30

x=3


5(3)+y=30

15+y=30

y=30-15

y=15

at maximum utility X=3,Y=15



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS