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The Euler equation is an a solution concept in most macroeconomic models which determine the optimal path to be taken in a consumption sequence. In a case where we have multiple consumption goods (say the simplest case where we have two $c_{1t}$ and $c_{2t}$) we have an intertemporal optimality condition (roughly the ratio in which $c_{1t}$ and $c_{1t+1}$/ $c_{2t}$ and $c_{2t+1}$ are consumed for all time) and intratemporal optimality condition ( the ratio in which $c_{1t}$ and $c_{2t}$ ought to be consumed in a specific period $t$).

My current impression is that time adds another dimension to our problem which is not the same as adding another good. As such I'm wondering if (like a problem with multiple constraints) we can have one set of optimality conditions which "bind" another with this consideration for time.

Is it possible for one of these conditions to impact another?

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    $\begingroup$ Can you please elaborate on what exactly you mean by "bind" here? $\endgroup$
    – Giskard
    Sep 7, 2022 at 17:58

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In the general case, it is not always possible to disentangle intratemporal and intertemporal optimisation. Take, for example, consumption habits or preferences that change over time. Both conditions can interact and impose restrictions on each other.

I would consider the situation where it's possible to solve the intratemporal and intertemporal problem independently a special case. I suspect a strong motivation for using that particular setup in many models is that the problem becomes much more tractable than in setups where both conditions interact while not necessarily leading to significantly deeper insights.

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