$U(x,y) = x + 4y$, I tried to find demand function for good x, so I did utility maximization.

max $U(x,y) = x + 4y $ subjects to $P_x.x + P_y . y = I$

and I found the $Px /Py = 1/4$, so $4Px = Py$.

Plug it in budget constraint I found $P_x.x+4P_x.y = I$

My Question is when I write demand function for good x, should it be $x = I/P_x$ because I said $y = 0$

So, Can I say that there is corner solution?


1 Answer 1


In your case there could be multiple solutions to the problem not just $y=0$. Any combination of $x$ and $y$ that would satisfy the budget with equality would be optimal in this case.

Hence I think it would probably be best just express demand for $x$ as:

$x=\frac{I}{P_x} - 4 y$

In fact this also gives you all potential optimum solutions to the problem since you can verify that for some parameters for example $I=100$ and $P_x=1$, when you consume 0 units of $y$ (implying that $x=100$) you get exactly the same utility as when you consume $x=96$ and $y=1$, or $x=92$ and $y=2$ and so on. So the $x= \frac{I}{P_x}-4y$ gives the combination of all possible optimum solutions. I personally don't see an reason to just assume that $y$ should be zero in such situation (unless this is for a classroom setting and that was recommended by instructor in these situations).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.