For example, say the MRS has simplified to the form $MRS(x,y) = -y$, given a utility function \begin{equation*} U(x, y) = e^{(x + ln(y))^{1/3}} \end{equation*}

With a budget line of, say, $2x + y = 10$ which would yield a budget line slope of -2, equating the MRS to the BLS would simply yield $y = 2$, but there is no x to solve for in the equating of the two slopes.

Is the last step, in cases like this, to plug back into the budget constraint? In which case, one would get $x = 4$, yielding an optimal consumption bundle of $(4, 2)$?

  • Once you have $y=2$ and $2x+y=10$, don't you think you can infer $x=4$? – Oliv Feb 1 '16 at 7:03
  • 2
    Indeed. The more interesting question (which leads you to better understand the limits of MRS) is what to do when the consumer's total income is 1. – denesp Feb 1 '16 at 15:05

I wanted to add this as a reply to denesp's comment, but I do not have enough reps.

MRS and a binding BC gives a system of two equations from which we can solve the optimum bundle. In case of income = 10, these two equations have positive solutions, in case of income = 1, these two equations do not have positive solutions. See this:

enter image description here

Income = 1 just makes the choice set small enough that there is no MRS = price ratio, hence the corner solution.

I completely agree that income =1 is really the more fun question.

  • 1
    This is a nice response, but I believe you have a typo because you say "in case of income = 10" twice. – BKay Aug 10 at 10:08
  • That was a typo. Fixed it. Thanks for pointing out BKay. – erik Aug 10 at 10:32

Your Answer


By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

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