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.