Here the utility function is U = max (ax, ay) + min (x,y)
In order to take this further and find some direction, let's compare the values of x and y, because only that's going to affect utility functions which have max and min in general, let alone simple perfect complements and max functions which are simple in their own respect.
3 cases here.
i) x>y, U=ax+y
ii) x<y, U=ay+x
iii) x=y, U=(a+1)x or (a+1)y
p1/p2>a, for case (i) y=m/p2, x=0
p1/p2<a, for case (i) y=x=m/(p1+p2)
p1/p2=a, for case (i) x= 0 to m/(p1+p2) and y = m/p2 to m/(p1+p2)
Solve it for the other cases by the same logic.
Going to the second question, the square root is of no significance here, as it is a simple positive monotonic transformation of the function x+2y+3z. It pretty much looks like a perfect substitutes question. Consider the several possible slopes for the budget lines and take the question further. Needs too much of explanation if I start writing which is going to make this look a lot messier.
Locked
