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

1. ## 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.

2. Originally Posted by Alex_Of_Darkness
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?

3. Originally Posted by JeffM
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...

4. Originally Posted by JeffM
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!

5. 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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