Doubt

[chirag]

sir please tell how to solve this question?
 A consumer has a utility function u(x,y,z) = min(x,y) + z. Find the optimal consumption bundle.

[Abhitesh]

x and y are compliments. Let x = y = k
Therefore we have to maximize U= min(x,y)+z = k+z; subject to budget constraint px*k+py*k+pz*z=m.
Now min(x,y) and z are perfect substitutes. So the solution will depend upon exact prices.

[RichaS]

x=m/(px+py) , y=m/(px+py) and z=0      if pz>(px+py)

x=0, y=0, z=m/pz                             if pz<(px+py)

[Nikkita]

Case 1: x=m/(px+py) , y=m/(px+py) and z=0      if pz>(px+py)

Case 2: x=0, y=0, z=m/pz                             if pz<(px+py)

Case 3: Any amount of x,y,z s.t. x=y and z= (m- Px.X-Py.Y)/Pz       if pz=(px+py)