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chirag
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Oct 06, 2016; 3:57pm
Doubt
21 posts
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
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Oct 07, 2016; 8:22am
Re: Doubt
162 posts
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
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Oct 09, 2016; 3:46am
Re: Doubt
97 posts
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by chirag
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
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Oct 09, 2016; 6:37am
Re: Doubt
133 posts
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by chirag
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)
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