Skip to main content

New answers tagged

1 vote
Accepted

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, $MRS(b) = \frac{p_1^0}{p_2^0}$. ...
tdm's user avatar
  • 12.4k
0 votes

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 ...
mynameparv's user avatar
5 votes
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 ...
Amit's user avatar
  • 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. ...
Riccardo Iorio's user avatar
4 votes

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: $$ \frac{y'(ky' - y)}{k y y''} = s. $$ ...
tdm's user avatar
  • 12.4k
5 votes
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 haven’t it), an answer based on what you report in your question, of course. I ...
BakerStreet's user avatar
  • 4,047
2 votes
Accepted

Properties of Multivariate Frechet Distributions

1 $\begin{aligned} \operatorname{Pr}\left(A_j Z_j \leq z\right)=\operatorname{Pr}\left(Z_j \leq \frac{z}{A_j}\right)=F\left(\frac{z}{A_j}\right) =\exp \left(-\left(\frac{z}{A_j}\right)^{-\theta}\right)...
Alalalalaki's user avatar
  • 2,474
0 votes
Accepted

Can global real GDP be calculated using nominal GDP and inflation rate? If so what is the error?

Inflation is not meant to be used that way. If you want to calculate real GDP you want either deflator or CPI or some measure of price level inflation measures the change in price level. What you want ...
1muflon1's user avatar
  • 57.1k
1 vote

Confusion on the Profit Maximization Equation

$\pi _{i}=p_{i}. q_{i}-c_{i}. q_{i}$ Do you talk about this equation ? This is a very traditional equation for profit. It just means that the profit of a firm $i$ is given by the difference between ...
krauuuus's user avatar
  • 115
1 vote
Accepted

Independence Axiom and Expected Utility Theorem Proof

Let us first show that the function $u$ is linear in the sense that for all lotteries $L$ and $L'$ and all $\alpha \in [0,1]$: $u(\alpha L + (1-\alpha) L') = \alpha u(L) + (1-\alpha) u(L')$. Let $L \...
tdm's user avatar
  • 12.4k

Top 50 recent answers are included