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.