Questions tagged [proof-reference]

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5 votes
2 answers
103 views

Why is exponential discounting considered rational?

I have repeatedly heard a claim that only an exponential discounting is the rational one, however I've never seen the proof. Why is it so? Intuitively, we would expect exponential discount since the ...
1 vote
1 answer
118 views

Intuition of two Measure theory statements

I'm struggling in getting the intuition of two statements about measure theory: Given a measure space $(X,F,\mu)$, $f \in M^+ $, where $M^+ = M^+(F) $ is the set of non negative F-measurable functions ...
3 votes
1 answer
130 views

Is this proof correct (measure theory)?

I'm trying to prove the following statement: I did the following proof but i donno if it makes sense: Proof of $(\Rightarrow)$ direction: Assume $\mathcal{F}$ is a $\sigma$-algebra. Assume also $\{...
1 vote
1 answer
689 views

Weak preferences and negative transitivity

Let $ \succ $ be a binary relationship on the set $X$ such that, given any $ x, y, z\in X $, if $x\succ y$: (Asymmetry): $\neg(y\succ x)$, (Negative transitivity): $(x\succ z) \vee (z\succ y)$. ...
1 vote
1 answer
200 views

Independence and Reduction Axioms

I have read that the Independence of Irrelevant Alternatives axiom in expected utility theory implies the fact that compound lotteries are equally preferred to their reduced form simple lotteries. ...
3 votes
1 answer
5k views

Prove all cost functions are concave in input prices and demand for inputs is downward

I've seen proofs that cost functions are concave of the form $C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$ although this neither feels convincing nor does it seem like a ...
9 votes
2 answers
10k views

Concave production function implies convex cost function

Let's assume we have an increasing production function $f:\mathbb{R^+} \to \mathbb{R^+}$ Now, assume this production function is concave and that the price of input z is fixed (this is a single-input ...
2 votes
1 answer
53 views

How to prove that GDP grows at the same rate as consumption on Lab Equipment Model?

I'm studying the Lab Equipment Model (Barro-Sala-i-Martin, Chapter 6). I'm having trouble when trying to prove that every variables grows at the same rate as consumption. I was able to prove that $\...
4 votes
2 answers
243 views

Proof of nestedness of subgame perfect equilibria

Below is a lemma which I believe to be true and which I would like to use to derive other results Take any two games in extensive form (complete information) $\Gamma$ and $\Gamma'$ differing only ...