# why is the MRS same for everyone?

If the consumers are optimizing and at interior solutions and facing the same prices, then the MRS=p1/p2 will be the same for everyone no matter the preferences and income. but why? I don't understand it intuively.

• Do you understand why a single optimizing consumer selects her $x_1,x_2$ consumption values in such a way that $|MRS(x_1,x_2)| = p_1/p_2$ will hold (with some usual caveats)? Oct 31 at 14:48
• @Giskard I'm not too sure about that either but I think the equilibrium / optimum will be struck only when what the consumer is willing to sacrifice is equal to what he has to sacrifice. Because at that point he doesn't have an incentive to further trade Oct 31 at 17:48
• So, I edited a Desmos slide from one of my old lectures for you. It has two consumers, A and B. Try to maximize both of their utilities by sliding the red dots on the $x$ axis. The price ratio is $p_1/p_2 = 3/2$. See, if when they are maximized, they are 1) equal to the price ratio 2) perhaps equal to each other? (approximately) Oct 31 at 20:49
• @Giskard Thank you so much for your help and efforts, i really appreciate it. When they are maximized they are equal to the price ratio and equal to eachother, that did help me see that. but i still don't really understand how if for example i dislike milk and have a low income and someone else loves milk and has a high income, we end up having the same MRS at the optimum. we're willing to substitute one good for the other at the same rate, it just doesn't satisfy my brain from what i know so far. but i think i'll just stick to the mathematical explanation. thank you again for your answer Nov 1 at 0:44
• @tessa Because if you think you would be more satisfied by buying a bit less milk and more of something else for the same amount of money, then your consumption is not actually optimal and you would rather buy less milk. Of course, if you really dislike milk, you might not be buying any milk (the solution is not interior), then the marginal rate of substitution does not need to equal the price ratio. Nov 1 at 12:21