Q: If u(x,y)=x2y3, I=50, Px=4, and Py=6, what is the optimal bundle?
A: The optimal bundle will be on the BC so 50=4x+6y. Also it will satisfy the optimal condition which for C-D preferences is MRS=Px/Py. The MRS=(2xy3)/(3x2y2)=(2y)/(3x). Px/Py=4/6 so the optimal condition works out to be (2y)/(3x)=4/6 or x=y. Plugging this into the BC gives 50=4x+6x or 50=10x or x=5. Hence y=5 and the optimal bundle is (5,5).