# Corner solution-consumer theory [closed]

$$U(q_1,q_2)=4{q_1}^{0.5}+q_2$$ $$P_1=1$$ and $$P_2=2$$ Initially $$Income=40$$ Then the question asks :how do I know what income I can get a corner solution?

Anyone can help me with this?

Thank you

• I'm voting to close this question as off-topic because it is a homework question with no effort shown. Apr 30 '15 at 17:19
• @denesp this is not a homework question and I have put in my effort to think but just cannot figure it out. The question is only asking about for what income I can get a corner solution. I ONLY NEED THE IDEA! Apr 30 '15 at 17:26
• The procedure to answer this question is outlined in the question below. Look at my answer on that question as a guide on how to answer it. economics.stackexchange.com/questions/4997/… May 1 '15 at 6:38
• @Jamzy I know how to find interior solution for income=40, However the question asks further about for what income it will get a corner solution? May 1 '15 at 7:50
• Set for it to be a corner solution, one of the quantities are no longer a choice variable. Change it to zero, then optimise. May 1 '15 at 7:53

The corner solutions are where $q_1=0$ or $q_2=0$. So just take the first-order conditions, plug in zero for the value, and solve for income. For incomes less than that amount, the quantity demanded is zero.
• but how do I know which 1 is zero in this case $$q_1$$ or $$q_2$$?N How you determine? Apr 30 '15 at 17:32