Quiz 2

Q: A person has utility u(x,y)=x^{0.8}y^{0.2} and
income of I=100. The market prices are Px=10 and Py=20. Find the MRS
and the optimal bundle for this person to purchase.

A: The MRS = MUx/MUy=0.8 x ^{-0.2}y^{0.2} /0.2x^{0.8}y^{-0.8}
=4y/x.

To find the optimal bundle for a person with Cobb-Douglas preference we know
that

1) MRS=Px/Py which in this problem is 4y/x=10/20 or 8y=x.

and

2) I=x*Px+y*Py which in this problem is 100= 10x+20y.

Using these two equations we can solve for x and y. Since 8y=x we have
100=10(8y)+20y or 100=100y or y=1. Since y=1 and 8y=x, we have that
x=8. Therefore the optimal bundle is (8,1).