# Growth Model Choices

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?

• 1. Does anything after (2), e.g. the law of motion have anything to do with your question? – Giskard Jun 10 at 7:09
• 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. – Giskard Jun 10 at 7:11
• @Giskard I like your example. Thanks! – Frank Swanton Jun 11 at 5:34
• @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 $\{c_t,k_{t+1}\}_{t=0}^\infty$. – Frank Swanton Jun 11 at 5:47
• And what does this have to do with the interpretation of trade offs in the utility function? – Giskard Jun 11 at 5:54