Questions tagged [proof-reference]
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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 ...
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1
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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 ...
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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 $\{...
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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): $(x\succ z) \vee (z\succ y)$.
...
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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. ...
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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 ...
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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 ...
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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 $\...
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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 ...