Quiz 3

Q:  A person has utility given by u(x,y)=min(2x,3y) and Income of 120.  If Px=8 and Py=6, what is the optimal bundle.  Determine if the goods are compliments or substitutes by finding the optimal bundle when Py=3.  

A:  Given the utility function 2x=3y.  The BC is 120=8x+6y so we have 120=8x+4x=12x or x=10.  Therefore y=20/3 and the optimal bundle is (10,20/3).  If Py falls to Py=3 then we have a BC of 120=8x+3y.  Substituting in 2x=3y gives us that 120=8x+2x=10x so x=12.  Therefore y=8 and the optimal bundle is (12,8).  Since Py fell and x increased, these goods are compliments.