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.

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