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$$U(q_1,q_2)=4{q_1}^{0.5}+q_2$$ $$P_1=1$$ 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

UnusualSkill
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    I'm voting to close this question as off-topic because it is a homework question with no effort shown. – Giskard 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! – UnusualSkill 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.

    http://economics.stackexchange.com/questions/4997/marshallian-demand-for-cobb-douglas?noredirect=1#comment5314_4997

     – Jamzy May 01 '15 at 06:38
  • @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? – UnusualSkill May 01 '15 at 07:50
  • Set for it to be a corner solution, one of the quantities are no longer a choice variable. Change it to zero, then optimise. – Jamzy May 01 '15 at 07:53
  • @Jamzy But How do I Know which quantity is no longer a choice variable?erm, can you show me some steps please, because I have several similar questions ,but Im stuck. To show that I have put in efforts, with Income=40, I found (16,12) as optimal bundle. But don know how to find income level for which corner sol exists. – UnusualSkill May 01 '15 at 09:02
  • @Jamzy R u able to find it?@@ – UnusualSkill May 01 '15 at 12:48

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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.

Matthew
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