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2

There are several reason for that. First, issue here is that you are talking about high inflation. Most economists are in favor of small inflation (around 2% per year for reasons you can read about in this and this old Economics.SE answers). Second, inflation does not generally have the beneficial properties you ascribe to it. Inflation can stimulate output ...


1

Let $\delta_i=N_i\beta_i$. I think what you want is for generation $i$'s utility to be something like: \begin{equation} U_i=u(x_i)+\delta_{i+1}U_{i+1}+\cdots+\delta_{i+n}U_{i+n}, \end{equation} where $i$ derives utility from his own consumption $u(x_i)$ as well as from his descendants' utilities, $U_{i+t}$ for $t=1,\dots,n$, over their own consumption and ...


2

Here are two nice papers on recursive utility functions, a generalization of additive utility functions and compatible with "utility of the dynastic head to be partly a function of the utility of his children and grandchildren's utility, but where his children's utility is again partly a function of his grandchildren's and great-grandchildren's utility, ...


3

Local non-satiation means that you always want a little bit more. There are no sweet spots where you are content and wouldn't accept any more of $x_i$. What this means in practice is that if you are optimising your allocation of goods $x_i$, you will exhaust all of your resources ($w$). If you don't have (2), it's possible that your optimal bundle will ...


4

The most common version of Pareto dominance says that an allocation is Pareto-dominated if there is another feasible allocation in which at least one agent is better off and everyone else is at least as well off. In particular, the latter allocation can include consumers that are just as well off as before. It follows from the very definition of a ...


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No. And yes. For any set $X$ we have (by definition) $$X^k=\underbrace{X\times\cdots\times X}_{k\text{-times}}=\{(x_1,x_2,\ldots,x_k)\mid x_i\in X\text{ for }i=1,\ldots,k\}.$$ Now let, for example, $m=2$ and $n=3$. Then $$(\mathbb{R}^m\big)^n=(\mathbb{R}^m\big)^n$$ $$=\big(\mathbb{R}^2\big)^3=\Big\{\big((x_1,x_2),(x_3,x_4),(x_5,x_6)\big)\mid (x_1,x_2)\in\...


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