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.
A).
U=5xy
budget line;
5x+y=30
MRSxy= = ,from the budget line px=$5,Py=$1
=
MRSxy=5
B).
U=5xy
budget line;
5x+y=30
MRTxy= = ,from the budget line px=$5,Py=$1
=
MRTxy=5
C).
At optimal utlity :
= ,from budget line Px=$5,Py=$1
MUX= 5xy
MUX=5Y
MUY= 5XY
MUY=5X
Therefore,
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
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