Quiz 3

Q:  1) If I=30, Px=1 and Py=1, what bundle would a person with preferences given by u(x,y)=min(2x,4y) buy?
2) If I=30, Px=1 and Py=1, what bundle would a person with preferences given by u(x,y)=2x+4y buy? 

A:  1)  With this type of preferences the optimal condition is 2x=4y or x=2y.  The budget constraint is 30=1x+1y.  Plugging the optimal condition into the budget constraint gives 30=2y+y or y=10.  Since x=2y, x=20.  The optimal bundle is (20,10).  
2)  With this type of preferences the person will buy either all x or all y.  So one can compare u(I/Px,0) and u(0,I/Py).  In this problem that is u(30,0) and u(0,30).  Since u(30,0)=60 and u(0,30)=120 the person would prefer (0,30), so this is the optimal bundle.