Quiz 2

Q:  A person has utility u(x,y)=x0.8y0.2 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 -0.2y0.2 /0.2x0.8y-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.
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).