# Tag Info

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### Proof that if the MRS is increasing in one good, then the other is normal

Note that $(a_1,a_2)$ is the utility maximizing bundle at relative price $MRS(a) = (= p_1/p_2)$ and budget $w = MRS(a).a_1 + a_2$. First as $b$ is utility maximising, $MRS(b) = \frac{p_1^0}{p_2^0}$. ...
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### Proving that Every preference relation can be represented by utility function

Let $X=\{x_1,\dots, x_n\}$, we will use induction on size of $X$ to prove that utility representation exists. Base step $(|X|=1)$: In the base step $X=\{x_1\}$ and so utility representation exists ...
• 625
Accepted

### Proof that independence implies monotonicity in Osborne and Rubinstein

You're right. The proof is provided for the proposition $\alpha > \beta \implies \alpha \cdot a \ \oplus (1-\alpha) \cdot b \succ \beta \cdot a \ \oplus (1-\beta) \cdot b$ But note that proving the ...
• 9,086
1 vote

### Proving that Every preference relation can be represented by utility function

The following is a nice proof from Osborne and Rubinstein's Models in Microeconomic Theory. We want to prove that Every preference relation on a finite set can be represented by a utility function. ...

### How was the CES production function derived?

As a follow up to Ben's answer. Here's the derivation to get to the solution of the SODE. For notational convenience, let $y = f(k)$ and $y' = f'(k)$. We have: $$\frac{y'(ky' - y)}{k y y''} = s.$$ ...
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Accepted

### Challenging question on mathematical economics

What I say below in my answer is what I can say without having read Acemoglu and Autor's article (unfortunately I havenâ€™t it), an answer based on what you report in your question, of course. I ...
• 4,047