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5

The Pigovian taxes are non-distortionary. For example imagine situation where government optimal spending is 100e and before Pigovian tax all 100e was raised through income tax which creates distortions on Labour market. Let’s say that after imposing Pigovian tax government gets additional 30e. Now since government needs only 100e for its optimal spending it ...

3

A situation can be Pareto efficient without also being a Pareto improvement over every other situation. So, here for example, equilibrium is Pareto efficient, but -- as you have noted -- is not a Pareto improvement over every other situation. Example. Say I have 100 apples to divide between A and B. The allocation (60, 40) is Pareto efficient, but it is ...

2

[...] One way to interpret this result is to see our two-stage game as a mechanism to generate Cournot-like outcomes that dispenses with the mythical auctioneer. A justification is given in Kreps-Scheinkmann (1983). They argue that this is the outcome if price competition follows production. For details see the linked article.

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I might be wrong so feel free to point out any mistakes. Both of them have the same utility function $u(x,y)=max(x,y)$ This means when $Px > Py$ , they'll choose to consume $Y$ instead of $X$ since they get higher satisfaction by selling all units of x and purchasing y. Take the case of First seller, If he sells all X and purchases Y, His total demand ...

1

A pretty trivial assumption would do it: If the consumers preferences are strongly increasing, i.e. $$x \succ_i y, \mbox{ if x \geq y but x \neq y },$$ and unbounded for all $i$, then no $x$ can be an optimal bundle if $p \notin \mathbb{R}^C_{++}$ (assuming there are $C$ commodities). So zero price cannot arise in an Arrow-Debreu equilibrium.

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