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Questions tagged [proof-reference]

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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. ...
2
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1answer
1k 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 ...
2
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1answer
47 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 $\...
6
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2answers
6k 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 ...
4
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2answers
211 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 ...