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consumer theory doubt

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consumer theory doubt

Noel
a consumer of three goods has utility function
u(x,y,z)=((min{x,y})^a).z^a, with 0<a<1.
determine the demand functions for x,y and z.
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Re: consumer theory doubt

Dreyfus
Noel are u sure both terms hv power a...?
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Re: consumer theory doubt

Noel
yes
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Re: consumer theory doubt

Dreyfus
This post was updated on Jul 30, 2014; 1:36am.
I m getting following dd functions,
x=y=(m/2(P1+P2))
z=m/2P3
Where P1, P2 & P3 are prices of x, y & z respectively and m is income
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Re: consumer theory doubt

Noel
thank you dreyfus..can you please show the workings
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Re: consumer theory doubt

Dreyfus
This post was updated on Jul 30, 2014; 1:37am.
I proceeded this way, there are three goods x, y and z so that the budget constraint is P1x+P2y+P3z=m
With x and y being perfect complements the agent will always choose equal amounts of both no matter what the prices are.
So the utility function and budget constraint can be written as either U(x,z) = (x^a)*z^a, (P1+P2)x+P3z=m or U(y,z) = (y^a)*z^a, (P1+P2)y+P3z=m. Now you can solve either of these set of equations.
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Re: consumer theory doubt

Harshita...
In reply to this post by Noel
May be the ans.  Is M/3Px for X*  , M/3Py for Y* , M /3Pz for Z*