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According to wikipedia, "At equilibrium consumption levels (assuming no externalities), marginal rates of substitution are identical". Why is it so?

What does "equilibrium consumption levels" here mean? I thought that equilibrium means that demand equal to supply. How is it applicable for marginal rates of substitution?

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One explanation I could think of: MRS (which is equal to $MU_x/MU_y$) is equal to the price ratio $P_x/P_y$. In equilibrium, all consumers will consume where MRS = price ratio, and hence MRS will be "identical" across consumers.

I agree that this might not be a terribly good way of putting it.

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    $\begingroup$ Yes, "optimal consumption levels" would be better. $\endgroup$ – Bertrand Nov 7 '19 at 11:29
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Building on @Art's answer, you can also think of it in terms of a dynamic process. Given some initial endowment of goods X and Y, everyone in the economy will want to trade goods X and Y back and forth until they are indifferent to further trading - which is to say, until their private MRS is equal to the price ratio. That's why "marginal rates of substitution are identical" -- all actors in the economy are working to shift their MRS towards the same target.

At that point, since there is no further flow of goods, that's your connection to equilibrium - a state of balance in which the variables endogenous to the system (in this case, consumption of X and Y) do not change.

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