Find consumption that maximizes agent utility U(x1,x2)=alnx1+(1-a)lnx2 (with a∈]0,1[)

Alex_Of_Darkness

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Find consumption that maximizes agent utility U(x1,x2)=alnx1+(1-a)lnx2 (with a∈]0,1[)

Hi, it's my first post here and I'm kind of desperate right now because I have absolutely no clue how to resolve this problem.

The utility function of an economic agent is given by U(x1,x2)=alnx1+(1-a)lnx2 (with a]0,1[). If he consumes the quantity x1 of the good, he has only x2= (R-P1x1)/P2 left for the possibility of consumption of the second good. R is the agent's income, P1 and P2 are the prices of the two goods. R>1, P1>0 & P2>0 and they are fixed and known. Find the x1 and x2 consumptions that maximize the utility of the agent.

If anyone is able to help me, I would be the most grateful person in the entire universe.
 
Hi, it's my first post here and I'm kind of desperate right now because I have absolutely no clue how to resolve this problem.

The utility function of an economic agent is given by U(x1,x2)=alnx1+(1-a)lnx2 (with a]0,1[). If he consumes the quantity x1 of the good, he has only x2= (R-P1x1)/P2 left for the possibility of consumption of the second good. R is the agent's income, P1 and P2 are the prices of the two goods. R>1, P1>0 & P2>0 and they are fixed and known. Find the x1 and x2 consumptions that maximize the utility of the agent.

If anyone is able to help me, I would be the most grateful person in the entire universe.
This is a problem in finding the optimum of a function subject to constraint. Do you know multi-variate differential calculus? Are you familiar with LaGrangian multipliers? If so, can you express the relevant constraints as an inequality? Can you set up the LaGrangian function?
 
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This is a problem in finding the optimum of a function subject to constraint. Do you know multi-variate differential calculus? Are you familiar with LaGrangian multipliers? If so, can you express the relevant constraints as an inequality? Can you set up the LaGrangian function?

I never heard the "LaGrangian" name before... And no I don't know multi-variate differential calculus neither :/ We have to do this in our calculus class and I am beyond loss...
 
This is a problem in finding the optimum of a function subject to constraint. Do you know multi-variate differential calculus? Are you familiar with LaGrangian multipliers? If so, can you express the relevant constraints as an inequality? Can you set up the LaGrangian function?


Unfortunatly I never saw any of that! It’s only an average calculus class but just to have a small idea. How would you resolved it? Could link that with things I know!
 
I never saw any of that to be honest! But how would you resolve that? Would still give me a small idea of how it would work!
 
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