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In a typical macro growth model, a set-up usually concerns with the following trade-offs or choices to be made in each $t$:

(1) $c_t$ v. $c_{t+1}$, consumption today versus tomorrow.

(2) $c_t$ v. $1-h_t$, consumption today versus leisure today.

When we have a typical law of motion of capital:

$k_{t+1}=i_t+(1-\delta)k$

Then, we can rewrite (1) as:

(1)' $c_t$ v. $k_{t+1}$, consupmtion today versus how much to invest thus to leave out for tomorrow's capital stock

$\textbf{My question:}$

How would you clearly explain (1) and (2) are distinct choices a representative agent or social planner has to make? Why are they two distinct trade-offs?

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    $\begingroup$ 1. Does anything after (2), e.g. the law of motion have anything to do with your question? $\endgroup$ – Giskard Jun 10 at 7:09
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    $\begingroup$ 2. Aren't your explanations, "consumption today versus tomorrow" and "consumption today versus leisure today" clear enough? E.g.: (1) If I eat this chocolate bar I will not have it anymore and cannot eat it later. (2) I do not have a chocolate bar, but by working in the grocery store for half an hour I can earn enough money to buy it. Sadly this takes time away from skateboarding. $\endgroup$ – Giskard Jun 10 at 7:11
  • $\begingroup$ @Giskard I like your example. Thanks! $\endgroup$ – Frank Swanton Jun 11 at 5:34
  • $\begingroup$ @Giskard To your first question, yest it does. For a typical control-state formulation of the classical sequence problem, we solve for an optimal sequence $\{c_t,k_{t+1}\}_{t=0}^\infty$. $\endgroup$ – Frank Swanton Jun 11 at 5:47
  • $\begingroup$ And what does this have to do with the interpretation of trade offs in the utility function? $\endgroup$ – Giskard Jun 11 at 5:54

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